04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri...

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Stefano Olivares Quantum Technology Lab Dipartimento di Fisica “Aldo Pontremoli” Università degli Studi di Milano, Italy “Aldo Pontremoli” La teoria cinetica Termodinamica - Corso B [email protected] http://users.unimi.it/aqm https://solivarest.ariel.ctu.unimi.it Termodinamica — a.a. 2019-2020

Transcript of 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri...

Page 1: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Stefano Olivares Quantum Technology Lab Dipartimento di Fisica “Aldo Pontremoli” Università degli Studi di Milano, Italy

“Aldo Pontremoli”

La teoria cinetica Termodinamica - Corso B

[email protected]://users.unimi.it/aqm

https://solivarest.ariel.ctu.unimi.it

Termodinamica — a.a. 2019-2020

Page 2: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Dal macroscopico al microscopico

Per questa trattazione si assume, in generale: •gas con molte molecole non interagenti; •velocità elevate (~103 m/s); •moto rettilineo nello spazio vuoto (~ 102 rm).

La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche.

La Termodinamica si occupa della descrizione di un sistema utilizzando parametri macroscopici (p, V, T,…).

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Il gas perfetto

Un gas perfetto è caratterizzato da: •urti elastici tra le molecole; •particelle non interagenti e moto rettilineo (casuale); •distribuzione uniforme (assenza di forze esterne in media); •distribuzione isotropa (assenza di direzioni o posizioni privilegiate); •contenitore con pareti rigide (urti elastici senza attriti).

Pressione — Legge di Joule-Clausius —

Energia interna

Temperatura — Definizione cinetica —

Equipartizione dell’energia

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mvx,i<latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit>

Pressione

Cubo di lato a N particelle di massa m

x

y

z

a

a

a

~vi = (vx,i, vy,i, vz,i)<latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">AAACDXicdVDLSsNAFJ34rPUVdelmsBQqlJCkRduFUHDjsoK1hbaEyXTSDp08mJkEa+gXuPFX3LhQcevenX/jpK2goheGczjnXu7c40aMCmmaH9rS8srq2npuI7+5tb2zq+/tX4sw5pi0cMhC3nGRIIwGpCWpZKQTcYJ8l5G2Oz7P/HZCuKBhcCUnEen7aBhQj2IkleToxV5CcJpMHQrPYClx0psynZYVThZ4q/DY0QumYdetulmDGTmxKlVFKmbVrtnQMsxZFcCimo7+3huEOPZJIDFDQnQtM5L9FHFJMSPTfC8WJEJ4jIakq2iAfCL66eycKSwqZQC9kKsXSDhTv0+kyBdi4ruq00dyJH57mfiX142lV+unNIhiSQI8X+TFDMoQZtnAAeUESzZRBGFO1V8hHiGOsFQJ5lUIX5fC/0nLNuqGeVktNBqLNHLgEByBErDAKWiAC9AELYDBHXgAT+BZu9cetRftdd66pC1mDsCP0t4+ASFLm74=</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit>

x

parete

~qi = m~vi<latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit>

Variazione della quantità di moto lungo l’asse x dopo l’urto sulla parete:

�qx = 2mvx,i<latexit sha1_base64="LJKmln8gaOm1EcDdDco3OMoxAbo=">AAACAHicdVDLSsNAFJ34rPUVdSO4GSyCCylJW1O7UAq6cFnB2EIbwmQ6bYdOHs5MSkuoG3/FjQsVt36GO//GSVtBRQ9cOJxzL/fe40WMCmkYH9rc/MLi0nJmJbu6tr6xqW9t34gw5pjYOGQhb3hIEEYDYksqGWlEnCDfY6Tu9c9Tvz4gXNAwuJajiDg+6ga0QzGSSnL13dYFYRLBW3cIT2EB+nDgJsMjOnb1nJEvWkXDNGFKypZVSUnZMkvH0MwbE+TADDVXf2+1Qxz7JJCYISGaphFJJ0FcUszIONuKBYkQ7qMuaSoaIJ8IJ5l8MIYHSmnDTshVBRJO1O8TCfKFGPme6vSR7InfXir+5TVj2TlxEhpEsSQBni7qxAzKEKZxwDblBEs2UgRhTtWtEPcQR1iq0LIqhK9P4f/ELuQreeOqlKuezdLIgD2wDw6BCcqgCi5BDdgAgzvwAJ7As3avPWov2uu0dU6bzeyAH9DePgEfkpWb</latexit><latexit sha1_base64="LJKmln8gaOm1EcDdDco3OMoxAbo=">AAACAHicdVDLSsNAFJ34rPUVdSO4GSyCCylJW1O7UAq6cFnB2EIbwmQ6bYdOHs5MSkuoG3/FjQsVt36GO//GSVtBRQ9cOJxzL/fe40WMCmkYH9rc/MLi0nJmJbu6tr6xqW9t34gw5pjYOGQhb3hIEEYDYksqGWlEnCDfY6Tu9c9Tvz4gXNAwuJajiDg+6ga0QzGSSnL13dYFYRLBW3cIT2EB+nDgJsMjOnb1nJEvWkXDNGFKypZVSUnZMkvH0MwbE+TADDVXf2+1Qxz7JJCYISGaphFJJ0FcUszIONuKBYkQ7qMuaSoaIJ8IJ5l8MIYHSmnDTshVBRJO1O8TCfKFGPme6vSR7InfXir+5TVj2TlxEhpEsSQBni7qxAzKEKZxwDblBEs2UgRhTtWtEPcQR1iq0LIqhK9P4f/ELuQreeOqlKuezdLIgD2wDw6BCcqgCi5BDdgAgzvwAJ7As3avPWov2uu0dU6bzeyAH9DePgEfkpWb</latexit><latexit sha1_base64="LJKmln8gaOm1EcDdDco3OMoxAbo=">AAACAHicdVDLSsNAFJ34rPUVdSO4GSyCCylJW1O7UAq6cFnB2EIbwmQ6bYdOHs5MSkuoG3/FjQsVt36GO//GSVtBRQ9cOJxzL/fe40WMCmkYH9rc/MLi0nJmJbu6tr6xqW9t34gw5pjYOGQhb3hIEEYDYksqGWlEnCDfY6Tu9c9Tvz4gXNAwuJajiDg+6ga0QzGSSnL13dYFYRLBW3cIT2EB+nDgJsMjOnb1nJEvWkXDNGFKypZVSUnZMkvH0MwbE+TADDVXf2+1Qxz7JJCYISGaphFJJ0FcUszIONuKBYkQ7qMuaSoaIJ8IJ5l8MIYHSmnDTshVBRJO1O8TCfKFGPme6vSR7InfXir+5TVj2TlxEhpEsSQBni7qxAzKEKZxwDblBEs2UgRhTtWtEPcQR1iq0LIqhK9P4f/ELuQreeOqlKuezdLIgD2wDw6BCcqgCi5BDdgAgzvwAJ7As3avPWov2uu0dU6bzeyAH9DePgEfkpWb</latexit>

Per avere un secondo urto occorre attendere un intervallo tempo:

�⌧ =2a

vx,i<latexit sha1_base64="4iV0oQu7VwGHpiRe0/2op2RJTSM=">AAACCHicdVA9SwNBEN3z2/gVtbRZDIKFhLskJlooghaWCkaFXAhzmz2zZO+D3TkxHNfa+FdsLFRs/Ql2/hv3YgQVfTDweG+GmXleLIVG2363xsYnJqemZ2YLc/MLi0vF5ZVzHSWK8SaLZKQuPdBcipA3UaDkl7HiEHiSX3j9w9y/uOZKiyg8w0HM2wFchcIXDNBInSJ1j7hEoC5CQveo6ytgaQWy9LqT3myJLOsUS3a5Wq/ajkNz0qjXd3PSqDu1beqU7SFKZISTTvHN7UYsCXiITILWLceOsZ2CQsEkzwpuonkMrA9XvGVoCAHX7XT4SUY3jNKlfqRMhUiH6veJFAKtB4FnOgPAnv7t5eJfXitBf6edijBOkIfsc5GfSIoRzWOhXaE4QzkwBJgS5lbKemDCQBNewYTw9Sn9nzQr5d2yfVorHeyP0pgha2SdbBKHNMgBOSYnpEkYuSX35JE8WXfWg/VsvXy2jlmjmVXyA9brB6H0meU=</latexit><latexit sha1_base64="4iV0oQu7VwGHpiRe0/2op2RJTSM=">AAACCHicdVA9SwNBEN3z2/gVtbRZDIKFhLskJlooghaWCkaFXAhzmz2zZO+D3TkxHNfa+FdsLFRs/Ql2/hv3YgQVfTDweG+GmXleLIVG2363xsYnJqemZ2YLc/MLi0vF5ZVzHSWK8SaLZKQuPdBcipA3UaDkl7HiEHiSX3j9w9y/uOZKiyg8w0HM2wFchcIXDNBInSJ1j7hEoC5CQveo6ytgaQWy9LqT3myJLOsUS3a5Wq/ajkNz0qjXd3PSqDu1beqU7SFKZISTTvHN7UYsCXiITILWLceOsZ2CQsEkzwpuonkMrA9XvGVoCAHX7XT4SUY3jNKlfqRMhUiH6veJFAKtB4FnOgPAnv7t5eJfXitBf6edijBOkIfsc5GfSIoRzWOhXaE4QzkwBJgS5lbKemDCQBNewYTw9Sn9nzQr5d2yfVorHeyP0pgha2SdbBKHNMgBOSYnpEkYuSX35JE8WXfWg/VsvXy2jlmjmVXyA9brB6H0meU=</latexit><latexit sha1_base64="4iV0oQu7VwGHpiRe0/2op2RJTSM=">AAACCHicdVA9SwNBEN3z2/gVtbRZDIKFhLskJlooghaWCkaFXAhzmz2zZO+D3TkxHNfa+FdsLFRs/Ql2/hv3YgQVfTDweG+GmXleLIVG2363xsYnJqemZ2YLc/MLi0vF5ZVzHSWK8SaLZKQuPdBcipA3UaDkl7HiEHiSX3j9w9y/uOZKiyg8w0HM2wFchcIXDNBInSJ1j7hEoC5CQveo6ytgaQWy9LqT3myJLOsUS3a5Wq/ajkNz0qjXd3PSqDu1beqU7SFKZISTTvHN7UYsCXiITILWLceOsZ2CQsEkzwpuonkMrA9XvGVoCAHX7XT4SUY3jNKlfqRMhUiH6veJFAKtB4FnOgPAnv7t5eJfXitBf6edijBOkIfsc5GfSIoRzWOhXaE4QzkwBJgS5lbKemDCQBNewYTw9Sn9nzQr5d2yfVorHeyP0pgha2SdbBKHNMgBOSYnpEkYuSX35JE8WXfWg/VsvXy2jlmjmVXyA9brB6H0meU=</latexit>

Calcoliamo la pressione sulla “parete x”.

Variazione di quantità di moto della parete nell’unità di tempo:

Fx,i =�qx,i�⌧

=mv2x,ia

<latexit sha1_base64="K7w/sYfmZnhVJ1Ar2F23AF7Days=">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</latexit><latexit sha1_base64="K7w/sYfmZnhVJ1Ar2F23AF7Days=">AAACLHicdVDLSgMxFM34tr6qLt0Ei+BCyoyPVheKoIhLBatCp5Y7aaYGMw+TO2IZ5ofc+CsiuFBx63eYaSs+0AOBk3POJbnHi6XQaNvP1sDg0PDI6Nh4YWJyanqmODt3qqNEMV5jkYzUuQeaSxHyGgqU/DxWHAJP8jPvai/3z2640iIKT7AT80YA7VD4ggEaqVncP2imtysio9vU9RWw1N3nEoFe9+Ts8+4iJF+hgN70/IvVLIWsWSzZ5bXKmu04NCfVSmUrJ9WKs75BnbLdRYn0cdQsPrqtiCUBD5FJ0Lru2DE2UlAomORZwU00j4FdQZvXDQ0h4LqRdrfN6JJRWtSPlDkh0q76fSKFQOtO4JlkAHipf3u5+JdXT9DfbKQijBPkIes95CeSYkTz6mhLKM5QdgwBpoT5K2WXYPpAU3DBlPC5Kf2f1FbLW2X7eL20u9NvY4wskEWyTBxSJbvkkByRGmHkjjyQZ/Ji3VtP1qv11osOWP2ZefID1vsHZa6ogg==</latexit><latexit sha1_base64="K7w/sYfmZnhVJ1Ar2F23AF7Days=">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</latexit>

Page 5: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

mvx,i<latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit>

Pressione

Cubo di lato a N particelle di massa m

x

y

z

a

a

a

~vi = (vx,i, vy,i, vz,i)<latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit>

x

parete

~qi = m~vi<latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit>

La pressione sulla faccia x dovuta alla i-esima molecola è:

px,i =Fx,i

a2=

mv2x,ia3

<latexit sha1_base64="ydqfsj2G32ImsZMhG9L1+3oNUPc=">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</latexit><latexit sha1_base64="ydqfsj2G32ImsZMhG9L1+3oNUPc=">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</latexit><latexit sha1_base64="ydqfsj2G32ImsZMhG9L1+3oNUPc=">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</latexit>

e, sommando su tutte le molecole:

px =m

a3

X

i

v2x,i =Nm

a3

Pi v

2x,i

N<latexit sha1_base64="4T65qWJXGtlAy+zYdbodyPZj2G0=">AAACPnicdVA9SwNBFNzz2/gVtbR5GAQLCXdGEy0UwcYqRDBRSOKxt9kzi7t3x+6eGI77Zzb+BTtbGwsVW0v3kviJDiwMM/N4+8aLOFPatu+tkdGx8YnJqenczOzc/EJ+camhwlgSWichD+WZhxXlLKB1zTSnZ5GkWHicnnqXh5l/ekWlYmFwonsRbQt8ETCfEayN5OYbkZtcp7AHLV9ikog0weelFKClYuEyuDLuBkvPNz8TVfjK9IXfyTSppuDmC3axVC7ZjgMZqZTLuxmplJ2tbXCKdh8FNETNzd+1OiGJBQ004VippmNHup1gqRnhNM21YkUjTC7xBW0aGmBBVTvp35/CmlE64IfSvEBDX/0+kWChVE94Jimw7qrfXib+5TVj7e+0ExZEsaYBGSzyYw46hKxM6DBJieY9QzCRzPwVSBebVrSpPGdK+LgU/if1zeJu0T7eKhzsD9uYQitoFa0jB1XQATpCNVRHBN2gB/SEnq1b69F6sV4H0RFrOLOMfsB6ewcIrK80</latexit><latexit sha1_base64="4T65qWJXGtlAy+zYdbodyPZj2G0=">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</latexit><latexit sha1_base64="4T65qWJXGtlAy+zYdbodyPZj2G0=">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</latexit>

= % v2x,i<latexit sha1_base64="s6yFgEZe/vm7AHnYvbLacIaG/qk=">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</latexit><latexit sha1_base64="s6yFgEZe/vm7AHnYvbLacIaG/qk=">AAACCHicdVBPT8IwHO38i/hv6tFLIzHxQMgGCHLQkHjxiIkICZtLVwo0dOvSdkSycPXiV/HiQY1XP4I3v40dYKJGX9Lk5b33a/t7fsSoVJb1YSwsLi2vrGbWsusbm1vb5s7uteSxwKSJOeOi7SNJGA1JU1HFSDsSBAU+Iy1/eJ76rRERkvLwSo0j4gaoH9IexUhpyTPhKXRGSIgBd/LQ4Tqa3pSMvOQ2Tyc3xYln5qxCqVKybBumpFqp1FJSrdjlY2gXrClyYI6GZ747XY7jgIQKMyRlx7Yi5SZIKIoZmWSdWJII4SHqk46mIQqIdJPpJhN4qJUu7HGhT6jgVP0+kaBAynHg62SA1ED+9lLxL68Tq96Jm9AwihUJ8eyhXsyg4jCtBXapIFixsSYIC6r/CvEACYSVLi+rS/jaFP5PmsVCrWBdlnP1s3kbGbAPDsARsEEV1MEFaIAmwOAOPIAn8GzcG4/Gi/E6iy4Y85k98APG2yf6m5oc</latexit><latexit sha1_base64="s6yFgEZe/vm7AHnYvbLacIaG/qk=">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</latexit>

densità del gas

Page 6: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

mvx,i<latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit><latexit sha1_base64="pCiCX515LzF8FOQsUPgLZq1rdy4=">AAAB73icdVBNS8NAEN34WetX1aOXxSJ4kJDYmtpbwYvHCsZW2lA22027dHcTdjfFEvorvHhQ8erf8ea/cdNWUNEHA4/3ZpiZFyaMKu04H9bS8srq2npho7i5tb2zW9rbv1VxKjHxccxi2Q6RIowK4muqGWknkiAeMtIKR5e53xoTqWgsbvQkIQFHA0EjipE20h2H4152f0qnvVLZsStexXFdmJOa59VzUvPc6jl0bWeGMlig2Su9d/sxTjkRGjOkVMd1Eh1kSGqKGZkWu6kiCcIjNCAdQwXiRAXZ7OApPDZKH0axNCU0nKnfJzLElZrw0HRypIfqt5eLf3mdVEcXQUZFkmoi8HxRlDKoY5h/D/tUEqzZxBCEJTW3QjxEEmFtMiqaEL4+hf8T/8yu2851tdyoL9IogENwBE6AC2qgAa5AE/gAAw4ewBN4tqT1aL1Yr/PWJWsxcwB+wHr7BGREkFI=</latexit>

Pressione

Cubo di lato a N particelle di massa m

x

y

z

a

a

a

~vi = (vx,i, vy,i, vz,i)<latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit>

x

parete

~qi = m~vi<latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit><latexit sha1_base64="hdwkzYjYKxyyooPC8cBeqkY0080=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbdF2IRTduKxgbKENYTKdtEMnD2cmhRKy8VfcuFBx62+482+cpBVU9MDAuefcy517vJhRIU3zQystLa+srpXXKxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5DL3u1PCBY3CGzmLiROgUUh9ipFUkqsfDKYEp3eZS+E5DGBRTVXl6lXTqLWsltmEOTm16g1F6maj1qxByzALVMECHVd/HwwjnAQklJghIfqWGUsnRVxSzEhWGSSCxAhP0Ij0FQ1RQISTFgdk8FgpQ+hHXL1QwkL9PpGiQIhZ4KnOAMmx+O3l4l9eP5F+00lpGCeShHi+yE8YlBHM04BDygmWbKYIwpyqv0I8RhxhqTKrqBC+LoX/E7tmtAzzulFtXyzSKINDcAROgAXOQBtcgQ6wAQYZeABP4Fm71x61F+113lrSFjP74Ae0t08fRpZS</latexit>

Quindi, la pressione sulla faccia x: px = % v2x,i<latexit sha1_base64="ri2vezcVECQEtPlwCgII3rEOrVE=">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</latexit><latexit sha1_base64="ri2vezcVECQEtPlwCgII3rEOrVE=">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</latexit><latexit sha1_base64="ri2vezcVECQEtPlwCgII3rEOrVE=">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</latexit>

Isotropia del gas: v2x,i = v2y,i = v2z,i =1

3v2

<latexit sha1_base64="O1Td0eUbU9i+abEjgcyaF2Tm46w=">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</latexit><latexit sha1_base64="O1Td0eUbU9i+abEjgcyaF2Tm46w=">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</latexit><latexit sha1_base64="O1Td0eUbU9i+abEjgcyaF2Tm46w=">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</latexit>

(v2 = v2x,i + v2y,i + v2z,i)<latexit sha1_base64="grTpzLtOFrjv1Pw5Kdg6GHlKPtE=">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</latexit><latexit sha1_base64="grTpzLtOFrjv1Pw5Kdg6GHlKPtE=">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</latexit><latexit sha1_base64="grTpzLtOFrjv1Pw5Kdg6GHlKPtE=">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</latexit>

Sempre per isotropia, sulle altre facce avremo la stessa pressione, ovvero:

px = py = pz ⌘ p<latexit sha1_base64="EfulP9Z+hpW5ok4hv+mqkf8aNxE=">AAACAHicdZBPS8MwGMbT+W/Of1UvgpfgEDyV1s3OHZSBF48TnBtspaRZtoWlbUzS4Rzz4lfx4kHFqx/Dm9/GdJugoi8k/Hie9yV5n4AzKpVtfxiZufmFxaXscm5ldW19w9zcupJxIjCp4ZjFohEgSRiNSE1RxUiDC4LCgJF60D9L/fqACEnj6FINOfFC1I1oh2KktOSbO9y/gSeQ+8PJfQtb5DqhA41m3rYKbsF2HJhCyXXLKZRcp3gEHcueVB7Mquqb7612jJOQRAozJGXTsbnyRkgoihkZ51qJJBzhPuqSpsYIhUR6o8kGY7ivlTbsxEKfSMGJ+n1ihEIph2GgO0OkevK3l4p/ec1EdY69EY14okiEpw91EgZVDNM4YJsKghUbakBYUP1XiHtIIKx0aDkdwtem8H+oHVply74o5iunszSyYBfsgQPggBKogHNQBTWAwR14AE/g2bg3Ho0X43XamjFmM9vgRxlvn1Wplb8=</latexit><latexit sha1_base64="EfulP9Z+hpW5ok4hv+mqkf8aNxE=">AAACAHicdZBPS8MwGMbT+W/Of1UvgpfgEDyV1s3OHZSBF48TnBtspaRZtoWlbUzS4Rzz4lfx4kHFqx/Dm9/GdJugoi8k/Hie9yV5n4AzKpVtfxiZufmFxaXscm5ldW19w9zcupJxIjCp4ZjFohEgSRiNSE1RxUiDC4LCgJF60D9L/fqACEnj6FINOfFC1I1oh2KktOSbO9y/gSeQ+8PJfQtb5DqhA41m3rYKbsF2HJhCyXXLKZRcp3gEHcueVB7Mquqb7612jJOQRAozJGXTsbnyRkgoihkZ51qJJBzhPuqSpsYIhUR6o8kGY7ivlTbsxEKfSMGJ+n1ihEIph2GgO0OkevK3l4p/ec1EdY69EY14okiEpw91EgZVDNM4YJsKghUbakBYUP1XiHtIIKx0aDkdwtem8H+oHVply74o5iunszSyYBfsgQPggBKogHNQBTWAwR14AE/g2bg3Ho0X43XamjFmM9vgRxlvn1Wplb8=</latexit><latexit sha1_base64="EfulP9Z+hpW5ok4hv+mqkf8aNxE=">AAACAHicdZBPS8MwGMbT+W/Of1UvgpfgEDyV1s3OHZSBF48TnBtspaRZtoWlbUzS4Rzz4lfx4kHFqx/Dm9/GdJugoi8k/Hie9yV5n4AzKpVtfxiZufmFxaXscm5ldW19w9zcupJxIjCp4ZjFohEgSRiNSE1RxUiDC4LCgJF60D9L/fqACEnj6FINOfFC1I1oh2KktOSbO9y/gSeQ+8PJfQtb5DqhA41m3rYKbsF2HJhCyXXLKZRcp3gEHcueVB7Mquqb7612jJOQRAozJGXTsbnyRkgoihkZ51qJJBzhPuqSpsYIhUR6o8kGY7ivlTbsxEKfSMGJ+n1ihEIph2GgO0OkevK3l4p/ec1EdY69EY14okiEpw91EgZVDNM4YJsKghUbakBYUP1XiHtIIKx0aDkdwtem8H+oHVply74o5iunszSyYBfsgQPggBKogHNQBTWAwR14AE/g2bg3Ho0X43XamjFmM9vgRxlvn1Wplb8=</latexit>

Page 7: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Pressione

Cubo di lato a N particelle di massa m

x

y

z

a

a

a

~vi = (vx,i, vy,i, vz,i)<latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit><latexit sha1_base64="gVCltaDZWd4rOZPd6sT2ZucLtdQ=">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</latexit>

vqm =p

v2<latexit sha1_base64="kshZyO3niGwNOody/IIEUHHadB8=">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</latexit><latexit sha1_base64="kshZyO3niGwNOody/IIEUHHadB8=">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</latexit><latexit sha1_base64="kshZyO3niGwNOody/IIEUHHadB8=">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</latexit>

velocità quadratica media

• Validità generale per quanto riguarda il contenitore. • Urti tra molecole trascurati, ma… conservazione della quantità di moto.

Abbiamo quindi trovato il legame tra la pressione p del gas (macroscopica) e la velocità delle sue molecole (microscopica):

p =1

3% v2qm

<latexit sha1_base64="sM32J4/ZuYD3XbKB0sCp5osZhHY=">AAACCnicdVBNS8NAEN34WetX1aOXpUXwICVpa2sPSsGLxwrGFppYNttNu3Q3ibubQgm9e/GvePGg4tVf4M1/46atoKIPBh7vzTAzz4sYlco0P4yFxaXlldXMWnZ9Y3NrO7ezey3DWGBi45CFou0hSRgNiK2oYqQdCYK4x0jLG56nfmtEhKRhcKXGEXE56gfUpxgpLXVz+QieQscXCFtl6IyQEIPQOYKjbuIIDm/55KbUzRXMYrlaNi0LpqRWrdZTUqtalWNoFc0pCmCOZjf37vRCHHMSKMyQlB3LjJSbIKEoZmSSdWJJIoSHqE86mgaIE+km018m8EArPeiHQleg4FT9PpEgLuWYe7qTIzWQv71U/MvrxMo/cRMaRLEiAZ4t8mMGVQjTYGCPCoIVG2uCsKD6VogHSAejdHxZHcLXp/B/YpeK9aJ5WSk0zuZpZMA+yINDYIEaaIAL0AQ2wOAOPIAn8GzcG4/Gi/E6a10w5jN74AeMt0+F45mw</latexit><latexit sha1_base64="sM32J4/ZuYD3XbKB0sCp5osZhHY=">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</latexit><latexit sha1_base64="sM32J4/ZuYD3XbKB0sCp5osZhHY=">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</latexit>

Legge di Joule—Clausius

Page 8: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Energia interna

Nell’ipotesi del gas perfetto, non ci sono forze di coesione agenti tra le molecole, quindi si considera solo la loro energia cinetica assumendo urti elastici.

L’energia interna U del gas perfetto è quindi data dalla somma delle energie cinetiche della sue N molecole:

U =m

2

X

i

v2i =Nm

2

Pi v

2i

N=

1

2Mtot v

2qm

<latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit><latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit><latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit>

Mtot = Nm<latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit><latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit><latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit>

Assumiamo che il gas sia monoatomico (solo energia traslazionale) si trovi a pressione p in un volume V e a temperatura T.

Page 9: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Energia interna

L’energia interna U del gas perfetto è quindi data dalla somma delle energie cinetiche della sue N molecole:

U =m

2

X

i

v2i =Nm

2

Pi v

2i

N=

1

2Mtot v

2qm

<latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit><latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit><latexit sha1_base64="PUUuqx6VHvDlnyB0Y637l5soPr0=">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</latexit>

Mtot = Nm<latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit><latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit><latexit sha1_base64="P91SyWqIwmdhfhRcC1y5kDhssOo=">AAAB+nicdVBNS8NAEN3Ur1q/Yj16WSyCp5DYmtqDUPDiRalgbKEtZbPdtEt3k7C7EUvIX/HiQcWrv8Sb/8ZNW0FFHww83pthZp4fMyqVbX8YhaXlldW14nppY3Nre8fcLd/KKBGYeDhikej4SBJGQ+IpqhjpxIIg7jPS9ifnud++I0LSKLxR05j0ORqFNKAYKS0NzDK8HKQ9waGKVAbP4BXkA7NiW1W3ajsOzEnddRs5qbtO7QQ6lj1DBSzQGpjvvWGEE05ChRmSsuvYseqnSCiKGclKvUSSGOEJGpGupiHiRPbT2e0ZPNTKEAaR0BUqOFO/T6SISznlvu7kSI3lby8X//K6iQpO+ykN40SREM8XBQnTj8I8CDikgmDFppogLKi+FeIxEggrHVdJh/D1KfyfeMdWw7Kva5VmY5FGEeyDA3AEHFAHTXABWsADGNyDB/AEno3MeDRejNd5a8FYzOyBHzDePgHxkpNE</latexit>

Ma abbiamo anche con , quindi: v2qm =3p

%<latexit sha1_base64="kU6QtfpVDt7qC9ZjKYsc1G+DKCg=">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</latexit><latexit sha1_base64="kU6QtfpVDt7qC9ZjKYsc1G+DKCg=">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</latexit><latexit sha1_base64="kU6QtfpVDt7qC9ZjKYsc1G+DKCg=">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</latexit>

% =Mtot

V<latexit sha1_base64="EMDnF2wpwQcwLjVtwDtPYKX7Gr8=">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</latexit><latexit sha1_base64="EMDnF2wpwQcwLjVtwDtPYKX7Gr8=">AAACB3icdVDLSsNAFJ34rPUVdenCwSK4KomtqV0oBTduhAr2AU0pk+mkHTqThJlJoYQs3fgrblyouPUX3Pk3TtoKKnpg4HDOvdw5x4sYlcqyPoyFxaXlldXcWn59Y3Nr29zZbcowFpg0cMhC0faQJIwGpKGoYqQdCYK4x0jLG11mfmtMhKRhcKsmEelyNAioTzFSWuqZB+4YCTEM4Tl0fYFwct1LXMGhClWaJs20ZxasYskpWbYNM1JxnGpGKo5dPoV20ZqiAOao98x3tx/imJNAYYak7NhWpLoJEopiRtK8G0sSITxCA9LRNECcyG4yDZLCI630oR8K/QIFp+r3jQRxKSfc05McqaH87WXiX14nVv5ZN6FBFCsS4NkhP2Y6JsxagX0qCFZsognCguq/QjxEug+lu8vrEr6Swv9J46RYLVo35ULtYt5GDuyDQ3AMbFABNXAF6qABMLgDD+AJPBv3xqPxYrzORheM+c4e+AHj7ROs15n8</latexit><latexit 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U =3

2pV

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U =3

2nRT

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Utilizzando l’equazione di Clapeyron otteniamo:

che mostra il legame tra l’energia interna del gas perfetto e la sua temperatura assoluta (verificata sperimentalmente da Joule).

Page 10: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

v2qm =3nRT

V %=

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V

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V

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Abbiamo:

Temperatura

Pressione

p =1

3% v2qm

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% =Mtot

V<latexit sha1_base64="EMDnF2wpwQcwLjVtwDtPYKX7Gr8=">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</latexit><latexit sha1_base64="EMDnF2wpwQcwLjVtwDtPYKX7Gr8=">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</latexit><latexit sha1_base64="EMDnF2wpwQcwLjVtwDtPYKX7Gr8=">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</latexit>

pV = nRT<latexit sha1_base64="5vUH2kTrfz7cNOzR+Xc8DqHWpDM=">AAAB7nicdVBNTwIxEO3iF+IX6tFLIzHxtOkCChw0JF48omGBBDakW7rQ0O2ubdeEEP6EFw9qvPp7vPlv7AImavQlk7y8N5OZeX7MmdIIfViZldW19Y3sZm5re2d3L79/0FJRIgl1ScQj2fGxopwJ6mqmOe3EkuLQ57Ttj69Sv31PpWKRaOpJTL0QDwULGMHaSJ24BS+guG328wVkl0u1onMODSmXnFIlJWeoVkXQsdEcBbBEo59/7w0ikoRUaMKxUl0HxdqbYqkZ4XSW6yWKxpiM8ZB2DRU4pMqbzu+dwROjDGAQSVNCw7n6fWKKQ6UmoW86Q6xH6reXin953UQHVW/KRJxoKshiUZBwqCOYPg8HTFKi+cQQTCQzt0IywhITbSLKmRC+PoX/E7do12x0Uy7UL5dpZMEROAanwAEVUAfXoAFcQAAHD+AJPFt31qP1Yr0uWjPWcuYQ/ID19gmbWY85</latexit><latexit sha1_base64="5vUH2kTrfz7cNOzR+Xc8DqHWpDM=">AAAB7nicdVBNTwIxEO3iF+IX6tFLIzHxtOkCChw0JF48omGBBDakW7rQ0O2ubdeEEP6EFw9qvPp7vPlv7AImavQlk7y8N5OZeX7MmdIIfViZldW19Y3sZm5re2d3L79/0FJRIgl1ScQj2fGxopwJ6mqmOe3EkuLQ57Ttj69Sv31PpWKRaOpJTL0QDwULGMHaSJ24BS+guG328wVkl0u1onMODSmXnFIlJWeoVkXQsdEcBbBEo59/7w0ikoRUaMKxUl0HxdqbYqkZ4XSW6yWKxpiM8ZB2DRU4pMqbzu+dwROjDGAQSVNCw7n6fWKKQ6UmoW86Q6xH6reXin953UQHVW/KRJxoKshiUZBwqCOYPg8HTFKi+cQQTCQzt0IywhITbSLKmRC+PoX/E7do12x0Uy7UL5dpZMEROAanwAEVUAfXoAFcQAAHD+AJPFt31qP1Yr0uWjPWcuYQ/ID19gmbWY85</latexit><latexit sha1_base64="5vUH2kTrfz7cNOzR+Xc8DqHWpDM=">AAAB7nicdVBNTwIxEO3iF+IX6tFLIzHxtOkCChw0JF48omGBBDakW7rQ0O2ubdeEEP6EFw9qvPp7vPlv7AImavQlk7y8N5OZeX7MmdIIfViZldW19Y3sZm5re2d3L79/0FJRIgl1ScQj2fGxopwJ6mqmOe3EkuLQ57Ttj69Sv31PpWKRaOpJTL0QDwULGMHaSJ24BS+guG328wVkl0u1onMODSmXnFIlJWeoVkXQsdEcBbBEo59/7w0ikoRUaMKxUl0HxdqbYqkZ4XSW6yWKxpiM8ZB2DRU4pMqbzu+dwROjDGAQSVNCw7n6fWKKQ6UmoW86Q6xH6reXin953UQHVW/KRJxoKshiUZBwqCOYPg8HTFKi+cQQTCQzt0IywhITbSLKmRC+PoX/E7do12x0Uy7UL5dpZMEROAanwAEVUAfXoAFcQAAHD+AJPFt31qP1Yr0uWjPWcuYQ/ID19gmbWY85</latexit>

Equazione gas perfetti

n =Mtot

M<latexit sha1_base64="Gwb5y/EKx3YdpDJaB98fq8drgrM=">AAACAXicdVDNSsNAGNzUv1r/op7Ey2IRPJXE1tQelIIXL4UKxhbaUjbbTbt0swm7G6GE4MVX8eJBxatv4c23cdNWUNGBhWHm+/h2xosYlcqyPozcwuLS8kp+tbC2vrG5ZW7v3MgwFpi4OGShaHtIEkY5cRVVjLQjQVDgMdLyxheZ37olQtKQX6tJRHoBGnLqU4yUlvrmHodnsOsLhJNGP+mKAKpQpWnSSPtm0SqVnbJl2zAjVcepZaTq2JUTaJesKYpgjmbffO8OQhwHhCvMkJQd24pUL0FCUcxIWujGkkQIj9GQdDTlKCCyl0wjpPBQKwPoh0I/ruBU/b6RoEDKSeDpyQCpkfztZeJfXidW/mkvoTyKFeF4dsiPmY4Jsz7ggAqCFZtogrCg+q8Qj5DuQ+nWCrqEr6Twf+Iel2ol66pSrJ/P28iDfXAAjoANqqAOLkETuACDO/AAnsCzcW88Gi/G62w0Z8x3dsEPGG+fs4KXNw==</latexit><latexit sha1_base64="Gwb5y/EKx3YdpDJaB98fq8drgrM=">AAACAXicdVDNSsNAGNzUv1r/op7Ey2IRPJXE1tQelIIXL4UKxhbaUjbbTbt0swm7G6GE4MVX8eJBxatv4c23cdNWUNGBhWHm+/h2xosYlcqyPozcwuLS8kp+tbC2vrG5ZW7v3MgwFpi4OGShaHtIEkY5cRVVjLQjQVDgMdLyxheZ37olQtKQX6tJRHoBGnLqU4yUlvrmHodnsOsLhJNGP+mKAKpQpWnSSPtm0SqVnbJl2zAjVcepZaTq2JUTaJesKYpgjmbffO8OQhwHhCvMkJQd24pUL0FCUcxIWujGkkQIj9GQdDTlKCCyl0wjpPBQKwPoh0I/ruBU/b6RoEDKSeDpyQCpkfztZeJfXidW/mkvoTyKFeF4dsiPmY4Jsz7ggAqCFZtogrCg+q8Qj5DuQ+nWCrqEr6Twf+Iel2ol66pSrJ/P28iDfXAAjoANqqAOLkETuACDO/AAnsCzcW88Gi/G62w0Z8x3dsEPGG+fs4KXNw==</latexit><latexit sha1_base64="Gwb5y/EKx3YdpDJaB98fq8drgrM=">AAACAXicdVDNSsNAGNzUv1r/op7Ey2IRPJXE1tQelIIXL4UKxhbaUjbbTbt0swm7G6GE4MVX8eJBxatv4c23cdNWUNGBhWHm+/h2xosYlcqyPozcwuLS8kp+tbC2vrG5ZW7v3MgwFpi4OGShaHtIEkY5cRVVjLQjQVDgMdLyxheZ37olQtKQX6tJRHoBGnLqU4yUlvrmHodnsOsLhJNGP+mKAKpQpWnSSPtm0SqVnbJl2zAjVcepZaTq2JUTaJesKYpgjmbffO8OQhwHhCvMkJQd24pUL0FCUcxIWujGkkQIj9GQdDTlKCCyl0wjpPBQKwPoh0I/ruBU/b6RoEDKSeDpyQCpkfztZeJfXidW/mkvoTyKFeF4dsiPmY4Jsz7ggAqCFZtogrCg+q8Qj5DuQ+nWCrqEr6Twf+Iel2ol66pSrJ/P28iDfXAAjoANqqAOLkETuACDO/AAnsCzcW88Gi/G62w0Z8x3dsEPGG+fs4KXNw==</latexit>

La temperatura di un gas è indice del suo grado di agitazione termica:

definizione cineticaT =M v2qm3R

<latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit><latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit><latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit>

Page 11: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Temperatura

La temperatura è un indice dello stato termico di un corpo che descrive l’attitudine di esso a scambiare calore con altri corpi.

— J. C. Maxwell

La temperatura di un gas è indice del suo grado di agitazione termica:

definizione cineticaT =M v2qm3R

<latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit><latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit><latexit sha1_base64="ScUkavo9CD/x7I0qsISmtc6iqzk=">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</latexit>

Page 12: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (gas perfetto)

L’energia interna U di 1 mole di gas monoatomico è data da: U =3

2RT

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L’energia per singola particella è:U

NA=

3

2

R

NAT =

3

2kBT

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NA = 6.022⇥ 1023 mol�1<latexit sha1_base64="jYQYQPIOpavqxnDZdIIyk1Dqz8k=">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</latexit><latexit sha1_base64="jYQYQPIOpavqxnDZdIIyk1Dqz8k=">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</latexit><latexit sha1_base64="jYQYQPIOpavqxnDZdIIyk1Dqz8k=">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</latexit>

kB = 1.38⇥ 10�23 JK�1<latexit sha1_base64="fjIgVEUQBGg3eD94zzVnF8DzhLc=">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</latexit><latexit sha1_base64="fjIgVEUQBGg3eD94zzVnF8DzhLc=">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</latexit><latexit sha1_base64="fjIgVEUQBGg3eD94zzVnF8DzhLc=">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</latexit>

U =1

2kBT

| {z }x

+1

2kBT

| {z }y

+1

2kBT

| {z }z

=3

2kBT

<latexit sha1_base64="+UopeNiAomowVXiA4gKueZJM9MQ=">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</latexit><latexit sha1_base64="+UopeNiAomowVXiA4gKueZJM9MQ=">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</latexit><latexit sha1_base64="+UopeNiAomowVXiA4gKueZJM9MQ=">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</latexit>

Particella libera (3 gradi di libertà):

xy

z

Page 13: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (gas perfetto)Intuitivamente, il nostro ragionamento suggerisce:

EQUIPARTIZIONE DELL’ENERGIA: ad ogni grado di libertà di una molecola è associata un’energia cinetica media di

1

2kBT

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In realtà si tratta di un teorema enunciato da Boltzmann e Clausius applicando la statistica di Boltzmann alle molecole di un gas.

In generale, per una molecola con f gradi di libertà, si ha:

U =f

2kBT

<latexit sha1_base64="XTDBXDSJPAGaIJ4h9eXsKAVrjzE=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbbXtQim6cVmhsYU2hMl00g6dPJiZCCVk46+4caHi1t9w5984aSuo6IELh3Pu5d57vJhRIU3zQyssLa+srhXXSxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5Cr3u3eECxqFHTmNiROgUUh9ipFUkqsf2PAcDnyOcOpnaSWDEze9zGDH1cumUas2K9YZVKRWtar1nJyazYYJLcOcoQwWaLv6+2AY4SQgocQMCdG3zFg6KeKSYkay0iARJEZ4gkakr2iIAiKcdPZABo+VMoR+xFWFEs7U7xMpCoSYBp7qDJAci99eLv7l9RPpN5yUhnEiSYjni/yEQRnBPA04pJxgyaaKIMypuhXiMVJpSJVZSYXw9Sn8n9gVo2mYN7Vy62KRRhEcgiNwAixQBy1wDdrABhhk4AE8gWftXnvUXrTXeWtBW8zsgx/Q3j4B+PCVkw==</latexit><latexit sha1_base64="XTDBXDSJPAGaIJ4h9eXsKAVrjzE=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbbXtQim6cVmhsYU2hMl00g6dPJiZCCVk46+4caHi1t9w5984aSuo6IELh3Pu5d57vJhRIU3zQyssLa+srhXXSxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5Cr3u3eECxqFHTmNiROgUUh9ipFUkqsf2PAcDnyOcOpnaSWDEze9zGDH1cumUas2K9YZVKRWtar1nJyazYYJLcOcoQwWaLv6+2AY4SQgocQMCdG3zFg6KeKSYkay0iARJEZ4gkakr2iIAiKcdPZABo+VMoR+xFWFEs7U7xMpCoSYBp7qDJAci99eLv7l9RPpN5yUhnEiSYjni/yEQRnBPA04pJxgyaaKIMypuhXiMVJpSJVZSYXw9Sn8n9gVo2mYN7Vy62KRRhEcgiNwAixQBy1wDdrABhhk4AE8gWftXnvUXrTXeWtBW8zsgx/Q3j4B+PCVkw==</latexit><latexit sha1_base64="XTDBXDSJPAGaIJ4h9eXsKAVrjzE=">AAAB/3icdVDLSsNAFJ3UV62vqAsXbgaL4CokbbXtQim6cVmhsYU2hMl00g6dPJiZCCVk46+4caHi1t9w5984aSuo6IELh3Pu5d57vJhRIU3zQyssLa+srhXXSxubW9s7+u7erYgSjomNIxbxnocEYTQktqSSkV7MCQo8Rrre5Cr3u3eECxqFHTmNiROgUUh9ipFUkqsf2PAcDnyOcOpnaSWDEze9zGDH1cumUas2K9YZVKRWtar1nJyazYYJLcOcoQwWaLv6+2AY4SQgocQMCdG3zFg6KeKSYkay0iARJEZ4gkakr2iIAiKcdPZABo+VMoR+xFWFEs7U7xMpCoSYBp7qDJAci99eLv7l9RPpN5yUhnEiSYjni/yEQRnBPA04pJxgyaaKIMypuhXiMVJpSJVZSYXw9Sn8n9gVo2mYN7Vy62KRRhEcgiNwAixQBy1wDdrABhhk4AE8gWftXnvUXrTXeWtBW8zsgx/Q3j4B+PCVkw==</latexit>

Page 14: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (gas perfetto)Intuitivamente, il nostro ragionamento suggerisce:

EQUIPARTIZIONE DELL’ENERGIA: ad ogni grado di libertà di una molecola è associata un’energia cinetica media di

1

2kBT

<latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit><latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit><latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit>

In realtà si tratta di un teorema enunciato da Boltzmann e Clausius applicando la statistica di Boltzmann alle molecole di un gas.

yx

zGas biatomico

f = 5<latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit><latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit><latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit>

xy

z

Gas monoatomico

f = 3<latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit><latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit><latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit>

Gas poliatomico

f = 6<latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit><latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit><latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit>

Page 15: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (gas perfetto)Intuitivamente, il nostro ragionamento suggerisce:

EQUIPARTIZIONE DELL’ENERGIA: ad ogni grado di libertà di una molecola è associata un’energia cinetica media di

1

2kBT

<latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit><latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit><latexit sha1_base64="jDSI13rHXDHhjBmQFEHESMKPWlg=">AAAB93icdVBNS8NAEN34WetHox69LBbBU0jaatuLFL14rNDYQhvCZrtpl242YXcj1NBf4sWDilf/ijf/jZu2goo+GHi8N8PMvCBhVCrb/jBWVtfWNzYLW8Xtnd29krl/cCvjVGDi4pjFohcgSRjlxFVUMdJLBEFRwEg3mFzlfveOCElj3lHThHgRGnEaUoyUlnyzNAgFwk4FTvzscgY7vlm2rVq1WXHOoSa1qlOt5+TMbjZs6Fj2HGWwRNs33wfDGKcR4QozJGXfsRPlZUgoihmZFQepJAnCEzQifU05ioj0svnhM3iilSEMY6GLKzhXv09kKJJyGgW6M0JqLH97ufiX109V2PAyypNUEY4Xi8KUQRXDPAU4pIJgxaaaICyovhXiMdJJKJ1VUYfw9Sn8n7gVq2nZN7Vy62KZRgEcgWNwChxQBy1wDdrABRik4AE8gWfj3ng0XozXReuKsZw5BD9gvH0CI5GSTA==</latexit>

In realtà si tratta di un teorema enunciato da Boltzmann e Clausius applicando la statistica di Boltzmann alle molecole di un gas.

Gas biatomico

f = 5<latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit><latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit><latexit sha1_base64="1HxJry6kBtUA7BbOa0fKlHXy4Uo=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiR92HahFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmX3DBlSrbiV+ozUnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0STjdw=</latexit>

U =5

2kBT

<latexit sha1_base64="I94CfVUIlLoZkySJZghXUpriVPY=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiR92HahFN24rNBooQ1hMp20QycPZiZCCPVX3LhQceuPuPNvnLQVVPTAhcM593LvPV7MqJCm+aEVVlbX1jeKm6Wt7Z3dPX3/4EZECcfExhGLeN9DgjAaEltSyUg/5gQFHiO33vQy92/vCBc0CnsyjYkToHFIfYqRVJKrl214Boc+R7hRhVM3u5jBnqtXTKNea1etU6hIvWbVmjlpmO2WCS3DnKMClui6+vtwFOEkIKHEDAkxsMxYOhnikmJGZqVhIkiM8BSNyUDREAVEONn8+Bk8VsoI+hFXFUo4V79PZCgQIg081RkgORG/vVz8yxsk0m85GQ3jRJIQLxb5CYMygnkScEQ5wZKliiDMqboV4glSSUiVV0mF8PUp/J/YVaNtmNf1Sud8mUYRHIIjcAIs0AQdcAW6wAYYpOABPIFn7V571F6010VrQVvOlMEPaG+fCaOTSg==</latexit><latexit sha1_base64="I94CfVUIlLoZkySJZghXUpriVPY=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiR92HahFN24rNBooQ1hMp20QycPZiZCCPVX3LhQceuPuPNvnLQVVPTAhcM593LvPV7MqJCm+aEVVlbX1jeKm6Wt7Z3dPX3/4EZECcfExhGLeN9DgjAaEltSyUg/5gQFHiO33vQy92/vCBc0CnsyjYkToHFIfYqRVJKrl214Boc+R7hRhVM3u5jBnqtXTKNea1etU6hIvWbVmjlpmO2WCS3DnKMClui6+vtwFOEkIKHEDAkxsMxYOhnikmJGZqVhIkiM8BSNyUDREAVEONn8+Bk8VsoI+hFXFUo4V79PZCgQIg081RkgORG/vVz8yxsk0m85GQ3jRJIQLxb5CYMygnkScEQ5wZKliiDMqboV4glSSUiVV0mF8PUp/J/YVaNtmNf1Sud8mUYRHIIjcAIs0AQdcAW6wAYYpOABPIFn7V571F6010VrQVvOlMEPaG+fCaOTSg==</latexit><latexit sha1_base64="I94CfVUIlLoZkySJZghXUpriVPY=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiR92HahFN24rNBooQ1hMp20QycPZiZCCPVX3LhQceuPuPNvnLQVVPTAhcM593LvPV7MqJCm+aEVVlbX1jeKm6Wt7Z3dPX3/4EZECcfExhGLeN9DgjAaEltSyUg/5gQFHiO33vQy92/vCBc0CnsyjYkToHFIfYqRVJKrl214Boc+R7hRhVM3u5jBnqtXTKNea1etU6hIvWbVmjlpmO2WCS3DnKMClui6+vtwFOEkIKHEDAkxsMxYOhnikmJGZqVhIkiM8BSNyUDREAVEONn8+Bk8VsoI+hFXFUo4V79PZCgQIg081RkgORG/vVz8yxsk0m85GQ3jRJIQLxb5CYMygnkScEQ5wZKliiDMqboV4glSSUiVV0mF8PUp/J/YVaNtmNf1Sud8mUYRHIIjcAIs0AQdcAW6wAYYpOABPIFn7V571F6010VrQVvOlMEPaG+fCaOTSg==</latexit>

Gas monoatomico

f = 3<latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit><latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit><latexit sha1_base64="/Ao3vR0T6qWdYyVMLGbyI0xEM/o=">AAAB63icdVBNS8NAEN3Ur1q/qh69LBbBU9g01bYHpeDFYwVjC20om+2mXbrZhN2NUEJ/gxcPKl79Q978N27aCir6YODx3gwz84KEM6UR+rAKK6tr6xvFzdLW9s7uXnn/4E7FqSTUIzGPZTfAinImqKeZ5rSbSIqjgNNOMLnK/c49lYrF4lZPE+pHeCRYyAjWRvJCeAHdQbmC7JrbrDrn0JCa67j1nJyhZgNBx0ZzVMAS7UH5vT+MSRpRoQnHSvUclGg/w1Izwums1E8VTTCZ4BHtGSpwRJWfzY+dwROjDGEYS1NCw7n6fSLDkVLTKDCdEdZj9dvLxb+8XqrDhp8xkaSaCrJYFKYc6hjmn8Mhk5RoPjUEE8nMrZCMscREm3xKJoSvT+H/xKvaTRvd1Cqty2UaRXAEjsEpcEAdtMA1aAMPEMDAA3gCz5awHq0X63XRWrCWM4fgB6y3T0GNjdo=</latexit>

U =3

2kBT

<latexit sha1_base64="XDrNyrLPCjbezV0cw4zXPEs7kYU=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiRtte1CKbpxWaGxhTaEyXTSDp08mJkIIdRfceNCxa0/4s6/cdJWUNEDFw7n3Mu993gxo0Ka5odWWFldW98obpa2tnd29/T9g1sRJRwTG0cs4n0PCcJoSGxJJSP9mBMUeIz0vOlV7vfuCBc0CrsyjYkToHFIfYqRVJKrl214Doc+R7hWhVM3u5zBrqtXTKNea1WtM6hIvWbVGjk5NVtNE1qGOUcFLNFx9ffhKMJJQEKJGRJiYJmxdDLEJcWMzErDRJAY4Skak4GiIQqIcLL58TN4rJQR9COuKpRwrn6fyFAgRBp4qjNAciJ+e7n4lzdIpN90MhrGiSQhXizyEwZlBPMk4IhygiVLFUGYU3UrxBOkkpAqr5IK4etT+D+xq0bLMG/qlfbFMo0iOARH4ARYoAHa4Bp0gA0wSMEDeALP2r32qL1or4vWgracKYMf0N4+AQaLk0g=</latexit><latexit sha1_base64="XDrNyrLPCjbezV0cw4zXPEs7kYU=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiRtte1CKbpxWaGxhTaEyXTSDp08mJkIIdRfceNCxa0/4s6/cdJWUNEDFw7n3Mu993gxo0Ka5odWWFldW98obpa2tnd29/T9g1sRJRwTG0cs4n0PCcJoSGxJJSP9mBMUeIz0vOlV7vfuCBc0CrsyjYkToHFIfYqRVJKrl214Doc+R7hWhVM3u5zBrqtXTKNea1WtM6hIvWbVGjk5NVtNE1qGOUcFLNFx9ffhKMJJQEKJGRJiYJmxdDLEJcWMzErDRJAY4Skak4GiIQqIcLL58TN4rJQR9COuKpRwrn6fyFAgRBp4qjNAciJ+e7n4lzdIpN90MhrGiSQhXizyEwZlBPMk4IhygiVLFUGYU3UrxBOkkpAqr5IK4etT+D+xq0bLMG/qlfbFMo0iOARH4ARYoAHa4Bp0gA0wSMEDeALP2r32qL1or4vWgracKYMf0N4+AQaLk0g=</latexit><latexit sha1_base64="XDrNyrLPCjbezV0cw4zXPEs7kYU=">AAAB+3icdVDLSsNAFJ3UV62vaJduBovgKiRtte1CKbpxWaGxhTaEyXTSDp08mJkIIdRfceNCxa0/4s6/cdJWUNEDFw7n3Mu993gxo0Ka5odWWFldW98obpa2tnd29/T9g1sRJRwTG0cs4n0PCcJoSGxJJSP9mBMUeIz0vOlV7vfuCBc0CrsyjYkToHFIfYqRVJKrl214Doc+R7hWhVM3u5zBrqtXTKNea1WtM6hIvWbVGjk5NVtNE1qGOUcFLNFx9ffhKMJJQEKJGRJiYJmxdDLEJcWMzErDRJAY4Skak4GiIQqIcLL58TN4rJQR9COuKpRwrn6fyFAgRBp4qjNAciJ+e7n4lzdIpN90MhrGiSQhXizyEwZlBPMk4IhygiVLFUGYU3UrxBOkkpAqr5IK4etT+D+xq0bLMG/qlfbFMo0iOARH4ARYoAHa4Bp0gA0wSMEDeALP2r32qL1or4vWgracKYMf0N4+AQaLk0g=</latexit>

f = 6<latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit><latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit><latexit sha1_base64="QHRXPe47kyPcWKOC1Ker8x4gtAc=">AAAB63icdVDLSsNAFL2pr1pfVZduBovgKiRt7WOhFNy4rGC00IYymU7aoZNJmJkIJfQb3LhQcesPufNvnD4EFT1w4XDOvdx7T5BwprTjfFi5ldW19Y38ZmFre2d3r7h/cKviVBLqkZjHshNgRTkT1NNMc9pJJMVRwOldML6c+Xf3VCoWixs9Sagf4aFgISNYG8kL0Tmq9Yslx65WmmW3hgypVtxKfUbOnGbDQa7tzFGCJdr94ntvEJM0okITjpXquk6i/QxLzQin00IvVTTBZIyHtGuowBFVfjY/dopOjDJAYSxNCY3m6veJDEdKTaLAdEZYj9Rvbyb+5XVTHTb8jIkk1VSQxaIw5UjHaPY5GjBJieYTQzCRzNyKyAhLTLTJp2BC+PoU/U+8st20netqqXWxTCMPR3AMp+BCHVpwBW3wgACDB3iCZ0tYj9aL9bpozVnLmUP4AevtE0YWjd0=</latexit>

U = 3kBT<latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit>

Gas poliatomico

Page 16: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (solido cristallino)

Page 17: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (solido cristallino)

Ad ogni atomo di un solido cristallino (in particolare un metallo) possiamo associare 3 gradi di libertà per un’energia cinetica e altri 3 gradi di libertà per l’energia potenziale elastica:

1

2m(v2x + v2y + v2z) +

1

2k(x2 + y2 + z2)

<latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit><latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit><latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit>

Quindi si ottiene: U = 3kBT<latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit>

Vedremo che questo risultato porta ad ottenere per il calore specifico di un solido cV = 3 R (legge di Dulong—Petit).

3R<latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit><latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit><latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit>

Page 18: 04 Teoria cinetica · 2020. 5. 21. · La Teoria cinetica dei gas mette in relazione i parametri macroscopici con i valori medi di grandezze microscopiche. La Termodinamica si occupa

Equipartizione dell’energia (solido cristallino)

Ad ogni atomo di un solido cristallino (in particolare un metallo) possiamo associare 3 gradi di libertà per un’energia cinetica e altri 3 gradi di libertà per l’energia potenziale elastica:

1

2m(v2x + v2y + v2z) +

1

2k(x2 + y2 + z2)

<latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit><latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit><latexit sha1_base64="SWZ7533ZkyuSfk8xhBJQf4tp8cg=">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</latexit>

Quindi si ottiene: U = 3kBT<latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit><latexit sha1_base64="YCRjlf1pHA7fif9fUTAzwdP4n0c=">AAAB83icdVDLTgIxFO3gC/GFunTTSExcTToMCiw0RDcuMWGEBCakUzrQ0HnYdkjIhO9w40KNW3/GnX9jBzBRoye5yck59+bee7yYM6kQ+jByK6tr6xv5zcLW9s7uXnH/4E5GiSDUIRGPRMfDknIWUkcxxWknFhQHHqdtb3yd+e0JFZJFYUtNY+oGeBgynxGstOQ68ALacNxPr2aw1S+WkFmx62XrHGpSsS27mpEzVK8haJlojhJYotkvvvcGEUkCGirCsZRdC8XKTbFQjHA6K/QSSWNMxnhIu5qGOKDSTedHz+CJVgbQj4SuUMG5+n0ixYGU08DTnQFWI/nby8S/vG6i/JqbsjBOFA3JYpGfcKgimCUAB0xQovhUE0wE07dCMsICE6VzKugQvj6F/xOnbNZNdFspNS6XaeTBETgGp8ACVdAAN6AJHEDAPXgAT+DZmBiPxovxumjNGcuZQ/ADxtsnTGqQsQ==</latexit>

Vedremo che questo risultato porta ad ottenere per il calore specifico di un solido cV = 3 R (legge di Dulong—Petit).

3R<latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit><latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit><latexit sha1_base64="GN5m/0pEtbZSEVOU5QRujB1AJQ8=">AAAB6XicdVDLSsNAFJ3UV62vqks3g0VwFSZp6GMjBTcu66NaaEOZTCft0MkkzEyEEvoJblyouPWP3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/uFVxKgntkJjHshtgRTkTtKOZ5rSbSIqjgNO7YHKe+3f3VCoWixs9Tagf4ZFgISNYG+m6Cq8G5Qqym42a69UgshGqO66TE7fuVT3oGCVHBSzRHpTf+8OYpBEVmnCsVM9BifYzLDUjnM5K/VTRBJMJHtGeoQJHVPnZ/NQZPDHKEIaxNCU0nKvfJzIcKTWNAtMZYT1Wv71c/MvrpTps+BkTSaqpIItFYcqhjmH+NxwySYnmU0MwkczcCskYS0y0SadkQvj6FP5POq7dtNGlV2mdLdMogiNwDE6BA+qgBS5AG3QAASPwAJ7As8WtR+vFel20FqzlzCH4AevtE0FKjU4=</latexit>