06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica...

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Stefano Olivares Quantum Technology Lab Dipartimento di Fisica “Aldo Pontremoli” Università degli Studi di Milano, Italy “Aldo Pontremoli” Il primo principio della Termodinamica — 1 Termodinamica - Corso B [email protected] http://users.unimi.it/aqm https://solivarest.ariel.ctu.unimi.it Termodinamica — a.a. 2019-2020

Transcript of 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica...

Page 1: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

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

“Aldo Pontremoli”

Il primo principio della Termodinamica — 1 Termodinamica - Corso B

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

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

Termodinamica — a.a. 2019-2020

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Equilibrio e trasformazioni

Equilibrio termodinamico

le variabili termodinamiche macroscopiche non variano nel tempo.

In caso di equilibrio possiamo assegnare una funzione di stato:

f(p, V, T ) = 0<latexit sha1_base64="3VdZbmxXt3O3Avy11zzk1Kc9eXs=">AAAB8nicdVBdSwJBFJ21L7Mvq8dehiQwkGVWLfWhEHrp0cBVQReZHWd1cPaDmdlAFv9GLz1U9Nqv6a1/06waVNSBC4dz7uXee9yIM6kQ+jAya+sbm1vZ7dzO7t7+Qf7wqCPDWBBqk5CHoudiSTkLqK2Y4rQXCYp9l9OuO71J/e49FZKFQVvNIur4eBwwjxGstDTwilGpU2qfwyuIhvkCMquVRtm6hJpUK1allpIL1KgjaJlogQJYoTXMvw9GIYl9GijCsZR9C0XKSbBQjHA6zw1iSSNMpnhM+5oG2KfSSRY3z+GZVkbQC4WuQMGF+n0iwb6UM9/VnT5WE/nbS8W/vH6svLqTsCCKFQ3IcpEXc6hCmAYAR0xQovhME0wE07dCMsECE6VjyukQvj6F/xO7bDZMdFctNK9XaWTBCTgFRWCBGmiCW9ACNiAgAg/gCTwbsfFovBivy9aMsZo5Bj9gvH0C+OWP4A==</latexit><latexit sha1_base64="3VdZbmxXt3O3Avy11zzk1Kc9eXs=">AAAB8nicdVBdSwJBFJ21L7Mvq8dehiQwkGVWLfWhEHrp0cBVQReZHWd1cPaDmdlAFv9GLz1U9Nqv6a1/06waVNSBC4dz7uXee9yIM6kQ+jAya+sbm1vZ7dzO7t7+Qf7wqCPDWBBqk5CHoudiSTkLqK2Y4rQXCYp9l9OuO71J/e49FZKFQVvNIur4eBwwjxGstDTwilGpU2qfwyuIhvkCMquVRtm6hJpUK1allpIL1KgjaJlogQJYoTXMvw9GIYl9GijCsZR9C0XKSbBQjHA6zw1iSSNMpnhM+5oG2KfSSRY3z+GZVkbQC4WuQMGF+n0iwb6UM9/VnT5WE/nbS8W/vH6svLqTsCCKFQ3IcpEXc6hCmAYAR0xQovhME0wE07dCMsECE6VjyukQvj6F/xO7bDZMdFctNK9XaWTBCTgFRWCBGmiCW9ACNiAgAg/gCTwbsfFovBivy9aMsZo5Bj9gvH0C+OWP4A==</latexit><latexit sha1_base64="3VdZbmxXt3O3Avy11zzk1Kc9eXs=">AAAB8nicdVBdSwJBFJ21L7Mvq8dehiQwkGVWLfWhEHrp0cBVQReZHWd1cPaDmdlAFv9GLz1U9Nqv6a1/06waVNSBC4dz7uXee9yIM6kQ+jAya+sbm1vZ7dzO7t7+Qf7wqCPDWBBqk5CHoudiSTkLqK2Y4rQXCYp9l9OuO71J/e49FZKFQVvNIur4eBwwjxGstDTwilGpU2qfwyuIhvkCMquVRtm6hJpUK1allpIL1KgjaJlogQJYoTXMvw9GIYl9GijCsZR9C0XKSbBQjHA6zw1iSSNMpnhM+5oG2KfSSRY3z+GZVkbQC4WuQMGF+n0iwb6UM9/VnT5WE/nbS8W/vH6svLqTsCCKFQ3IcpEXc6hCmAYAR0xQovhME0wE07dCMsECE6VjyukQvj6F/xO7bDZMdFctNK9XaWTBCTgFRWCBGmiCW9ACNiAgAg/gCTwbsfFovBivy9aMsZo5Bj9gvH0C+OWP4A==</latexit>

Meccanico (le forze si equilibrano)

Termico (temperatura uniforme)

Chimico (composizione costante)

I sistemi che incontreremo possono essere descritti da poche variabili termodinamiche: p, V e T.

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Equilibrio e trasformazioni

Trasformazioni termodinamiche tra stati di equilibrio: A ! B<latexit sha1_base64="oiK1YFdJ2wCXa2XxZQ97rWu3u58=">AAAB7XicdVBNSwMxFHzrZ61fVY9egkXwVHbbatuLVL14rODaQruUbJptQ7PZJckKZemP8OJBxav/x5v/xmxbQUUHAsPMe+TN+DFnStv2h7W0vLK6tp7byG9ube/sFvb271SUSEJdEvFIdnysKGeCupppTjuxpDj0OW3746vMb99TqVgkbvUkpl6Ih4IFjGBtpPYF6ukIXfYLRbtUrTTKzhkypFpxKrWMnNqNuo2ckj1DERZo9QvvvUFEkpAKTThWquvYsfZSLDUjnE7zvUTRGJMxHtKuoQKHVHnp7NwpOjbKAAWRNE9oNFO/b6Q4VGoS+mYyxHqkfnuZ+JfXTXRQ91Im4kRTQeYfBQlHJmKWHQ2YpETziSGYSGZuRWSEJSbaNJQ3JXwlRf8Tt1xqlOybarF5vmgjB4dwBCfgQA2acA0tcIHAGB7gCZ6t2Hq0XqzX+eiStdg5gB+w3j4B85aO2g==</latexit><latexit sha1_base64="oiK1YFdJ2wCXa2XxZQ97rWu3u58=">AAAB7XicdVBNSwMxFHzrZ61fVY9egkXwVHbbatuLVL14rODaQruUbJptQ7PZJckKZemP8OJBxav/x5v/xmxbQUUHAsPMe+TN+DFnStv2h7W0vLK6tp7byG9ube/sFvb271SUSEJdEvFIdnysKGeCupppTjuxpDj0OW3746vMb99TqVgkbvUkpl6Ih4IFjGBtpPYF6ukIXfYLRbtUrTTKzhkypFpxKrWMnNqNuo2ckj1DERZo9QvvvUFEkpAKTThWquvYsfZSLDUjnE7zvUTRGJMxHtKuoQKHVHnp7NwpOjbKAAWRNE9oNFO/b6Q4VGoS+mYyxHqkfnuZ+JfXTXRQ91Im4kRTQeYfBQlHJmKWHQ2YpETziSGYSGZuRWSEJSbaNJQ3JXwlRf8Tt1xqlOybarF5vmgjB4dwBCfgQA2acA0tcIHAGB7gCZ6t2Hq0XqzX+eiStdg5gB+w3j4B85aO2g==</latexit><latexit sha1_base64="oiK1YFdJ2wCXa2XxZQ97rWu3u58=">AAAB7XicdVBNSwMxFHzrZ61fVY9egkXwVHbbatuLVL14rODaQruUbJptQ7PZJckKZemP8OJBxav/x5v/xmxbQUUHAsPMe+TN+DFnStv2h7W0vLK6tp7byG9ube/sFvb271SUSEJdEvFIdnysKGeCupppTjuxpDj0OW3746vMb99TqVgkbvUkpl6Ih4IFjGBtpPYF6ukIXfYLRbtUrTTKzhkypFpxKrWMnNqNuo2ckj1DERZo9QvvvUFEkpAKTThWquvYsfZSLDUjnE7zvUTRGJMxHtKuoQKHVHnp7NwpOjbKAAWRNE9oNFO/b6Q4VGoS+mYyxHqkfnuZ+JfXTXRQ91Im4kRTQeYfBQlHJmKWHQ2YpETziSGYSGZuRWSEJSbaNJQ3JXwlRf8Tt1xqlOybarF5vmgjB4dwBCfgQA2acA0tcIHAGB7gCZ6t2Hq0XqzX+eiStdg5gB+w3j4B85aO2g==</latexit>

Trasf. REVERSIBILE: trasformazione da A a B e da B ad A passando solo tra stati di equilibrio. Dopo la trasformazione inversa, l’ambiente deve trovarsi anch’esso nello stato iniziale, senza alcuna modificazione.

Trasf. IRREVERSIBILE: durante la trasformazione non si hanno stati di equilibrio e/o si hanno effetti dissipativi.

Trasf. SPONTANEA: avviene in un sistema isolato, senza che venga compiuto lavoro dall’esterno.

Trasf. QUASI-STATICA: il sistema si trasforma da A a B passando solo tra stati di equilibrio.

Trasf. lontane dall’equilibrio.

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tr. reversibiletr. reversibile

Il piano di Clapeyron

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V<latexit sha1_base64="JV/NyZ7o6X5Y35UA168+QueTZng=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUC9S8OKxBdMW2lA220m7drMJuxuhlP4CLx5UvPqXvPlv3LY5aOuDgcd7M8zMC1PBtXHdb6ewtr6xuVXcLu3s7u0flA+PmjrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApHdzO/9YRK80Q+mHGKQUwHkkecUWOlRrNXrrhVdw6ySrycVCBHvVf+6vYTlsUoDRNU647npiaYUGU4EzgtdTONKWUjOsCOpZLGqIPJ/NApObNKn0SJsiUNmau/JyY01noch7Yzpmaol72Z+J/XyUx0HUy4TDODki0WRZkgJiGzr0mfK2RGjC2hTHF7K2FDqigzNpuSDcFbfnmV+BfVm6rbuKzUbvM0inACp3AOHlxBDe6hDj4wQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBH7OMqQ==</latexit><latexit sha1_base64="JV/NyZ7o6X5Y35UA168+QueTZng=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUC9S8OKxBdMW2lA220m7drMJuxuhlP4CLx5UvPqXvPlv3LY5aOuDgcd7M8zMC1PBtXHdb6ewtr6xuVXcLu3s7u0flA+PmjrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApHdzO/9YRK80Q+mHGKQUwHkkecUWOlRrNXrrhVdw6ySrycVCBHvVf+6vYTlsUoDRNU647npiaYUGU4EzgtdTONKWUjOsCOpZLGqIPJ/NApObNKn0SJsiUNmau/JyY01noch7Yzpmaol72Z+J/XyUx0HUy4TDODki0WRZkgJiGzr0mfK2RGjC2hTHF7K2FDqigzNpuSDcFbfnmV+BfVm6rbuKzUbvM0inACp3AOHlxBDe6hDj4wQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBH7OMqQ==</latexit><latexit sha1_base64="JV/NyZ7o6X5Y35UA168+QueTZng=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUC9S8OKxBdMW2lA220m7drMJuxuhlP4CLx5UvPqXvPlv3LY5aOuDgcd7M8zMC1PBtXHdb6ewtr6xuVXcLu3s7u0flA+PmjrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApHdzO/9YRK80Q+mHGKQUwHkkecUWOlRrNXrrhVdw6ySrycVCBHvVf+6vYTlsUoDRNU647npiaYUGU4EzgtdTONKWUjOsCOpZLGqIPJ/NApObNKn0SJsiUNmau/JyY01noch7Yzpmaol72Z+J/XyUx0HUy4TDODki0WRZkgJiGzr0mfK2RGjC2hTHF7K2FDqigzNpuSDcFbfnmV+BfVm6rbuKzUbvM0inACp3AOHlxBDe6hDj4wQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBH7OMqQ==</latexit>

Condizioni di reversibilità:

• variazione infinitesima di temperatura tra sistema e sorgenti;

• variazione infinitesima di pressione tra sistema e ambiente;

• no dissipazione (assenza di attriti meccanici e interni).

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A

B

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Il piano di Clapeyron

In genere i processi naturali sono non reversibili — trasformazioni spontanee.

Processo quasi-statico Processo reversibile

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tr. reversibile

tr. irreversibile

A

B C

D

C’

D’

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Page 6: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il piano di Clapeyron

Diffusione di due gas differenti:

gas A

gas B

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tr. reversibile

tr. irreversibile

A

B C

D

C’

D’

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Page 7: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il piano di Clapeyron

Diffusione di due gas differenti:

gas A

gas B

TA = TB , pA = pB<latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit><latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit><latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit>

Può avvenire in modo quasi-statico, ma è irreversibile.

Per ripristinare le condizioni iniziali occorre intervenire dall’esterno (compiere lavoro).

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tr. reversibile

tr. irreversibile

A

B C

D

C’

D’

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Page 8: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il piano di Clapeyron

gas A

gas B

TA = TB , pA = pB<latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit><latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit><latexit sha1_base64="r4aCQLRz1c33+ZPNkaq2uszO5k4=">AAACAnicdVDLSsNAFJ3UV62vqDvdDBbBhZSkrbZdCLVuXFZobKEtYTKdtEMnD2cmQgkFN/6KGxcqbv0Kd/6Nk7SCih64cDjnXu69xwkZFdIwPrTMwuLS8kp2Nbe2vrG5pW/vXIsg4phYOGAB7zhIEEZ9YkkqGemEnCDPYaTtjC8Sv31LuKCB35KTkPQ9NPSpSzGSSrL1vZZ9Ds9gy24cw95NhAYwTIXQbth63iiUS7WieQoVKZfMUiUhJ0atakCzYKTIgzmatv7eGwQ48ogvMUNCdE0jlP0YcUkxI9NcLxIkRHiMhqSrqI88Ivpx+sMUHiplAN2Aq/IlTNXvEzHyhJh4jur0kByJ314i/uV1I+lW+zH1w0gSH88WuRGDMoBJIHBAOcGSTRRBmFN1K8QjxBGWKracCuHrU/g/sYqFWsG4KufrtXkaWbAPDsARMEEF1MElaAILYHAHHsATeNbutUftRXudtWa0+cwu+AHt7RPAHJU5</latexit>

Interpretazione probabilistica dei processi termodinamici.

Diffusione di due gas differenti:

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tr. reversibile

tr. irreversibile

A

B C

D

C’

D’

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Entropia

I processi più probabili sono quelli irreversibili!

Page 9: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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pressione atmosferica

gas

Page 10: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

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area pistone

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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pressione atmosferica

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non è un differenziale esatto: dipende dalla trasformazione!

gas

Page 11: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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pressione atmosferica

dh<latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit> �L = F dh, F = pA

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area pistone

�L = pAdh = p dV<latexit sha1_base64="5yqNPbzyYbX9gvXGwkkdNADIDpo=">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</latexit><latexit sha1_base64="5yqNPbzyYbX9gvXGwkkdNADIDpo=">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</latexit><latexit sha1_base64="5yqNPbzyYbX9gvXGwkkdNADIDpo=">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</latexit>

gas

Page 12: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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Trasformazione quasi-statica, in ogni stato di equilibrio per cui passa: p = p0

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�L = pAdh = p0 dV<latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">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</latexit><latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">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</latexit><latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">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</latexit>

gas

Page 13: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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Trasformazione non quasi-statica: la trasformazione non è reversibile e p non è definito ad ogni istante…

Tuttavia, il lavoro compiuto dal sistema sarà uguale e contrario a quello fatto dall’ambiente a p0 costante.gas

Page 14: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Espansione di un gas (lavoro elementare)

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dh<latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit>

Trasformazione non quasi-statica: la trasformazione non è reversibile e p non è definito ad ogni istante…

�L = pAdh = p0 dV<latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">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</latexit><latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">AAACK3icdVDPaxNBFJ6NVmNsdatHL4NB6KGE2Sba5qBEcvHQQwvdJJANYXb2pRk6+4OZt8Ww7B/kpf9KQTwY8dr/o7PbFFTqBw8+vu+9efO+MFPSIGNrp/Ho8daTp81nrefbOy9euruvRibNtQBfpCrVk5AbUDIBHyUqmGQaeBwqGIcXw8ofX4I2Mk3OcJXBLObniVxIwdFKc3cYRKCQ02P6kWbBPg0QvmL9bBGqHMric7AfLcvKnbOH/GhUzt026/S6/QPvA7Wk1/W6hxV5z/pHjHodVqNNNjiZu9+DKBV5DAkKxY2ZeizDWcE1SqGgbAW5gYyLC34OU0sTHoOZFfXWkr6zSkQXqbaVIK3VPycKHhuzikPbGXNcmn+9SnzIm+a4OJoVMslyhETcLVrkimJKq+RoJDUIVCtLuNDS/pWKJddcoM23ZUO4v5T+n/gHnX6Hnfbag0+bNJrkDXlL9ohHDsmAfCEnxCeCfCPX5CdZO1fOD+eX8/uuteFsZl6Tv+Dc3AI7o6fr</latexit><latexit sha1_base64="0dYQZtZfckLe3Djj6Q2AzGC+f3k=">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</latexit>

stesso risultato ma… significato diverso!

gas

Page 15: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Trasformazione reversibile — ogni stato è uno stato di equilibrio, quindi nel caso del lavoro elementare in una trasformazione quasi-statica si pone:

pint = pest<latexit sha1_base64="Mi9ggvNzxxFqMNa3uOxydZmPza8=">AAACAXicdVDLSgMxFM34rPU16krcBIvgqsy01bYLpeDGZQXHFtqhZNK0Dc1khuSOUIbixl9x40LFrX/hzr8xfQgqeuDCyTn3kntPEAuuwXE+rIXFpeWV1cxadn1jc2vb3tm90VGiKPNoJCLVDIhmgkvmAQfBmrFiJAwEawTDi4nfuGVK80hewyhmfkj6kvc4JWCkjr0fd9K2CjGXMMZneP5iGsYdO+fkS8VqwT3FhpSKbrE8ISdOteJgN+9MkUNz1Dv2e7sb0SRkEqggWrdcJwY/JQo4FWycbSeaxYQOSZ+1DJUkZNpPpyeM8ZFRurgXKVMS8FT9PpGSUOtRGJjOkMBA//Ym4l9eK4FexU+5jBNgks4+6iUCQ4QneeAuV4yCGBlCqOJmV0wHRBEKJrWsCeHrUvw/8Qr5at65KuVq5/M0MugAHaJj5KIyqqFLVEceougOPaAn9GzdW4/Wi/U6a12w5jN76Aest0+H+5cV</latexit><latexit sha1_base64="Mi9ggvNzxxFqMNa3uOxydZmPza8=">AAACAXicdVDLSgMxFM34rPU16krcBIvgqsy01bYLpeDGZQXHFtqhZNK0Dc1khuSOUIbixl9x40LFrX/hzr8xfQgqeuDCyTn3kntPEAuuwXE+rIXFpeWV1cxadn1jc2vb3tm90VGiKPNoJCLVDIhmgkvmAQfBmrFiJAwEawTDi4nfuGVK80hewyhmfkj6kvc4JWCkjr0fd9K2CjGXMMZneP5iGsYdO+fkS8VqwT3FhpSKbrE8ISdOteJgN+9MkUNz1Dv2e7sb0SRkEqggWrdcJwY/JQo4FWycbSeaxYQOSZ+1DJUkZNpPpyeM8ZFRurgXKVMS8FT9PpGSUOtRGJjOkMBA//Ym4l9eK4FexU+5jBNgks4+6iUCQ4QneeAuV4yCGBlCqOJmV0wHRBEKJrWsCeHrUvw/8Qr5at65KuVq5/M0MugAHaJj5KIyqqFLVEceougOPaAn9GzdW4/Wi/U6a12w5jN76Aest0+H+5cV</latexit><latexit sha1_base64="Mi9ggvNzxxFqMNa3uOxydZmPza8=">AAACAXicdVDLSgMxFM34rPU16krcBIvgqsy01bYLpeDGZQXHFtqhZNK0Dc1khuSOUIbixl9x40LFrX/hzr8xfQgqeuDCyTn3kntPEAuuwXE+rIXFpeWV1cxadn1jc2vb3tm90VGiKPNoJCLVDIhmgkvmAQfBmrFiJAwEawTDi4nfuGVK80hewyhmfkj6kvc4JWCkjr0fd9K2CjGXMMZneP5iGsYdO+fkS8VqwT3FhpSKbrE8ISdOteJgN+9MkUNz1Dv2e7sb0SRkEqggWrdcJwY/JQo4FWycbSeaxYQOSZ+1DJUkZNpPpyeM8ZFRurgXKVMS8FT9PpGSUOtRGJjOkMBA//Ym4l9eK4FexU+5jBNgks4+6iUCQ4QneeAuV4yCGBlCqOJmV0wHRBEKJrWsCeHrUvw/8Qr5at65KuVq5/M0MugAHaJj5KIyqqFLVEceougOPaAn9GzdW4/Wi/U6a12w5jN76Aest0+H+5cV</latexit>

Page 16: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

Trasformazione non quasi-statica — non è reversibile e il lavoro elementare non può essere espresso in funzione delle coordinate termodinamiche macroscopiche del sistema.

Page 17: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

In generale: p<latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit>

S<latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit>

Page 18: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

p<latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit> dh

<latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit>

ds<latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit><latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit><latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit>

S<latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit>

In generale: �L = p

Z

Sds dh = pS dh

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Page 19: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

�L = p dV<latexit sha1_base64="Poqqv6pXWq341uGnM/x63Q2Drq8=">AAAB+XicdVDLSsNAFJ3UV62vVJduBovgQkLSVtsulIIbFy4qmLbQhDKZTNqhkwczE6XUfoobFypu/RN3/o2TtoKKHrhwOOde7r3HSxgV0jQ/tNzS8srqWn69sLG5tb2jF3fbIk45JjaOWcy7HhKE0YjYkkpGugknKPQY6Xiji8zv3BIuaBzdyHFC3BANIhpQjKSS+nrR8QmTCF7BM5g4x9Bv9/WSaVQrjbJ1ChWpVqxKLSMnZqNuQsswZyiBBVp9/d3xY5yGJJKYISF6lplId4K4pJiRacFJBUkQHqEB6SkaoZAIdzI7fQoPleLDIOaqIgln6veJCQqFGIee6gyRHIrfXib+5fVSGdTdCY2SVJIIzxcFKYMyhlkO0KecYMnGiiDMqboV4iHiCEuVVkGF8PUp/J/YZaNhmNfVUvN8kUYe7IMDcAQsUANNcAlawAYY3IEH8ASetXvtUXvRXuetOW0xswd+QHv7BLvIko4=</latexit><latexit sha1_base64="Poqqv6pXWq341uGnM/x63Q2Drq8=">AAAB+XicdVDLSsNAFJ3UV62vVJduBovgQkLSVtsulIIbFy4qmLbQhDKZTNqhkwczE6XUfoobFypu/RN3/o2TtoKKHrhwOOde7r3HSxgV0jQ/tNzS8srqWn69sLG5tb2jF3fbIk45JjaOWcy7HhKE0YjYkkpGugknKPQY6Xiji8zv3BIuaBzdyHFC3BANIhpQjKSS+nrR8QmTCF7BM5g4x9Bv9/WSaVQrjbJ1ChWpVqxKLSMnZqNuQsswZyiBBVp9/d3xY5yGJJKYISF6lplId4K4pJiRacFJBUkQHqEB6SkaoZAIdzI7fQoPleLDIOaqIgln6veJCQqFGIee6gyRHIrfXib+5fVSGdTdCY2SVJIIzxcFKYMyhlkO0KecYMnGiiDMqboV4iHiCEuVVkGF8PUp/J/YZaNhmNfVUvN8kUYe7IMDcAQsUANNcAlawAYY3IEH8ASetXvtUXvRXuetOW0xswd+QHv7BLvIko4=</latexit><latexit sha1_base64="Poqqv6pXWq341uGnM/x63Q2Drq8=">AAAB+XicdVDLSsNAFJ3UV62vVJduBovgQkLSVtsulIIbFy4qmLbQhDKZTNqhkwczE6XUfoobFypu/RN3/o2TtoKKHrhwOOde7r3HSxgV0jQ/tNzS8srqWn69sLG5tb2jF3fbIk45JjaOWcy7HhKE0YjYkkpGugknKPQY6Xiji8zv3BIuaBzdyHFC3BANIhpQjKSS+nrR8QmTCF7BM5g4x9Bv9/WSaVQrjbJ1ChWpVqxKLSMnZqNuQsswZyiBBVp9/d3xY5yGJJKYISF6lplId4K4pJiRacFJBUkQHqEB6SkaoZAIdzI7fQoPleLDIOaqIgln6veJCQqFGIee6gyRHIrfXib+5fVSGdTdCY2SVJIIzxcFKYMyhlkO0KecYMnGiiDMqboV4iHiCEuVVkGF8PUp/J/YZaNhmNfVUvN8kUYe7IMDcAQsUANNcAlawAYY3IEH8ASetXvtUXvRXuetOW0xswd+QHv7BLvIko4=</latexit>

�L = p

Z

Sds dh = pS dh

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In generale: p<latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit><latexit sha1_base64="p0uPXcX/NHHCN3sWurf458zmC0o=">AAAB53icdVDLSgNBEJz1GeMr6tHLYBA8LbNJNMlFAl48JuCaQLKE2UlvMmb2wcysEEK+wIsHFa/+kjf/xtkkgooWNBRV3XR3+YngShPyYa2srq1vbOa28ts7u3v7hYPDWxWnkoHLYhHLjk8VCB6Bq7kW0Ekk0NAX0PbHV5nfvgepeBzd6EkCXkiHEQ84o9pIraRfKBK7Uq6XnAtsSKXslKsZOSf1GsGOTeYooiWa/cJ7bxCzNIRIM0GV6jok0d6USs2ZgFm+lypIKBvTIXQNjWgIypvOD53hU6MMcBBLU5HGc/X7xJSGSk1C33SGVI/Uby8T//K6qQ5q3pRHSaohYotFQSqwjnH2NR5wCUyLiSGUSW5uxWxEJWXaZJM3IXx9iv8nbsmu26RVKTYul2nk0DE6QWfIQVXUQNeoiVzEEKAH9ISerTvr0XqxXhetK9Zy5gj9gPX2CbBTjQw=</latexit> dh

<latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit><latexit sha1_base64="ZurTy3xb6XfxUzcTa59MklMrjaM=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW6C8bBcQXa91qo659CQes2pNXJyhlpNBB0bzVEBS3SG5fdBEJM0okITjpXqOyjRXoalZoTTWWmQKppgMsEj2jdU4IgqL5tfOoMnRglgGEtTQsO5+n0iw5FS08g3nRHWY/Xby8W/vH6qw6aXMZGkmgqyWBSmHOoY5m/DgElKNJ8agolk5lZIxlhiok04JRPC16fwf+JW7ZaNruuV9sUyjSI4AsfgFDigAdrgCnSACwgIwQN4As/WxHq0XqzXRWvBWs4cgh+w3j4BYL2Ncg==</latexit>

ds<latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit><latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit><latexit sha1_base64="myhZb+PwwnY0Ig7cESu0oK5c74E=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXYQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/uFNxKgl1Scxj2fOxopwJ6mqmOe0lkuLI57TrTy5zv3tPpWKxuNXThHoRHgkWMoK1kW4CNSxXkF2vtarOOTSkXnNqjZycoVYTQcdGc1TAEp1h+X0QxCSNqNCEY6X6Dkq0l2GpGeF0VhqkiiaYTPCI9g0VOKLKy+aXzuCJUQIYxtKU0HCufp/IcKTUNPJNZ4T1WP32cvEvr5/qsOllTCSppoIsFoUphzqG+dswYJISzaeGYCKZuRWSMZaYaBNOyYTw9Sn8n7hVu2Wj63qlfbFMowiOwDE4BQ5ogDa4Ah3gAgJC8ACewLM1sR6tF+t10VqwljOH4Aest09xXo19</latexit>

S<latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit><latexit sha1_base64="pvMxrGBzvGbmXBtr7bDCR7cjR1U=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklbbXuRghePFY0ttKFsttt26WYTdzdCCf0TXjyoePX3ePPfuGkrqOiDgcd7M8zMC2LOlHacD2tpeWV1bT23kd/c2t7ZLezt36ookYR6JOKRbAdYUc4E9TTTnLZjSXEYcNoKxheZ37qnUrFI3OhJTP0QDwUbMIK1kdppl2COrqe9QtGxK+V6yT1DhlTKbrmakVOnXnOQazszFGGBZq/w3u1HJAmp0IRjpTquE2s/xVIzwuk0300UjTEZ4yHtGCpwSJWfzu6domOj9NEgkqaERjP1+0SKQ6UmYWA6Q6xH6reXiX95nUQPan7KRJxoKsh80SDhSEcoex71maRE84khmEhmbkVkhCUm2kSUNyF8fYr+J17JrtvOVaXYOF+kkYNDOIITcKEKDbiEJnhAgMMDPMGzdWc9Wi/W67x1yVrMHMAPWG+fj+GP2Q==</latexit>

dV<latexit sha1_base64="Vy5FcHTTZQgNR47zPEir7ce6+8U=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXUQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/6Ko4lYS6JOax7PlYUc4EdTXTnPYSSXHkc3rnTy5z/+6eSsVicaunCfUiPBIsZARrI90E3WG5gux6rVV1zqEh9ZpTa+TkDLWaCDo2mqMClugMy++DICZpRIUmHCvVd1CivQxLzQins9IgVTTBZIJHtG+owBFVXja/dAZPjBLAMJamhIZz9ftEhiOlppFvOiOsx+q3l4t/ef1Uh00vYyJJNRVksShMOdQxzN+GAZOUaD41BBPJzK2QjLHERJtwSiaEr0/h/8St2i0bXdcr7YtlGkVwBI7BKXBAA7TBFegAFxAQggfwBJ6tifVovVivi9aCtZw5BD9gvX0CRYeNYA==</latexit><latexit sha1_base64="Vy5FcHTTZQgNR47zPEir7ce6+8U=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXUQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/6Ko4lYS6JOax7PlYUc4EdTXTnPYSSXHkc3rnTy5z/+6eSsVicaunCfUiPBIsZARrI90E3WG5gux6rVV1zqEh9ZpTa+TkDLWaCDo2mqMClugMy++DICZpRIUmHCvVd1CivQxLzQins9IgVTTBZIJHtG+owBFVXja/dAZPjBLAMJamhIZz9ftEhiOlppFvOiOsx+q3l4t/ef1Uh00vYyJJNRVksShMOdQxzN+GAZOUaD41BBPJzK2QjLHERJtwSiaEr0/h/8St2i0bXdcr7YtlGkVwBI7BKXBAA7TBFegAFxAQggfwBJ6tifVovVivi9aCtZw5BD9gvX0CRYeNYA==</latexit><latexit sha1_base64="Vy5FcHTTZQgNR47zPEir7ce6+8U=">AAAB6HicdVBNS8NAEN3Ur1q/qh69LBbBU9i01bYXKXjxWMXUQhvKZrNpl242YXcjlNB/4MWDild/kjf/jZu2goo+GHi8N8PMPD/hTGmEPqzCyura+kZxs7S1vbO7V94/6Ko4lYS6JOax7PlYUc4EdTXTnPYSSXHkc3rnTy5z/+6eSsVicaunCfUiPBIsZARrI90E3WG5gux6rVV1zqEh9ZpTa+TkDLWaCDo2mqMClugMy++DICZpRIUmHCvVd1CivQxLzQins9IgVTTBZIJHtG+owBFVXja/dAZPjBLAMJamhIZz9ftEhiOlppFvOiOsx+q3l4t/ef1Uh00vYyJJNRVksShMOdQxzN+GAZOUaD41BBPJzK2QjLHERJtwSiaEr0/h/8St2i0bXdcr7YtlGkVwBI7BKXBAA7TBFegAFxAQggfwBJ6tifVovVivi9aCtZw5BD9gvX0CRYeNYA==</latexit>

Page 20: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

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VA<latexit sha1_base64="WDhy25mcIy+lEyee/m5tyASPztE=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFU0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DjopTSahHYh7LboAV5UxQTzPNaTeRFEcBp3fB5DL37+6pVCwWt3qaUD/CI8FCRrA20k1ncDEoV5Bdr7lV5xwaUq85tUZOzpDbRNCx0RwVsER7UH7vD2OSRlRowrFSPQcl2s+w1IxwOiv1U0UTTCZ4RHuGChxR5WfzU2fwxChDGMbSlNBwrn6fyHCk1DQKTGeE9Vj99nLxL6+X6rDpZ0wkqaaCLBaFKYc6hvnfcMgkJZpPDcFEMnMrJGMsMdEmnZIJ4etT+D/xqrZro+t6peUu0yiCI3AMToEDGqAFrkAbeICAEXgAT+DZ4taj9WK9LloL1nLmEPyA9fYJxEaNoQ==</latexit><latexit sha1_base64="WDhy25mcIy+lEyee/m5tyASPztE=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFU0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DjopTSahHYh7LboAV5UxQTzPNaTeRFEcBp3fB5DL37+6pVCwWt3qaUD/CI8FCRrA20k1ncDEoV5Bdr7lV5xwaUq85tUZOzpDbRNCx0RwVsER7UH7vD2OSRlRowrFSPQcl2s+w1IxwOiv1U0UTTCZ4RHuGChxR5WfzU2fwxChDGMbSlNBwrn6fyHCk1DQKTGeE9Vj99nLxL6+X6rDpZ0wkqaaCLBaFKYc6hvnfcMgkJZpPDcFEMnMrJGMsMdEmnZIJ4etT+D/xqrZro+t6peUu0yiCI3AMToEDGqAFrkAbeICAEXgAT+DZ4taj9WK9LloL1nLmEPyA9fYJxEaNoQ==</latexit><latexit sha1_base64="WDhy25mcIy+lEyee/m5tyASPztE=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFU0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DjopTSahHYh7LboAV5UxQTzPNaTeRFEcBp3fB5DL37+6pVCwWt3qaUD/CI8FCRrA20k1ncDEoV5Bdr7lV5xwaUq85tUZOzpDbRNCx0RwVsER7UH7vD2OSRlRowrFSPQcl2s+w1IxwOiv1U0UTTCZ4RHuGChxR5WfzU2fwxChDGMbSlNBwrn6fyHCk1DQKTGeE9Vj99nLxL6+X6rDpZ0wkqaaCLBaFKYc6hvnfcMgkJZpPDcFEMnMrJGMsMdEmnZIJ4etT+D/xqrZro+t6peUu0yiCI3AMToEDGqAFrkAbeICAEXgAT+DZ4taj9WK9LloL1nLmEPyA9fYJxEaNoQ==</latexit>

Il lavoro

Il primo principio della termodinamica introduce il concetto di energia.

In Termodinamica si introduce il lavoro esterno: •L > 0 se compiuto dal sistema; •L < 0 se compiuto sul sistema.

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tr. reversibile

A

B

=

Z B

Ap dV

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specificando la trasformazione

LAB =

Z

lAB

p dV<latexit sha1_base64="NB8U3A50FAsMgpOvN40DqkOGun4=">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</latexit><latexit sha1_base64="NB8U3A50FAsMgpOvN40DqkOGun4=">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</latexit><latexit sha1_base64="NB8U3A50FAsMgpOvN40DqkOGun4=">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</latexit>

LBA =

Z A

Bp dV = �

Z B

Ap dV = �LAB

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Page 21: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Il lavoro: reversibile vs irreversibile

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espansione reversibile

A

B

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Per avere un’espansione reversibile occorre passare da stati di equilibrio: la pressione del gas deve variare in modo tale da richiedere più lavoro da parte del sistema…

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A

B

espansione irreversibile

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pB<latexit sha1_base64="xA99cV9T1dCLhf0tkQlCVakRGB0=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ohePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C7UuNvA==</latexit><latexit sha1_base64="xA99cV9T1dCLhf0tkQlCVakRGB0=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ohePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C7UuNvA==</latexit><latexit sha1_base64="xA99cV9T1dCLhf0tkQlCVakRGB0=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ohePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C7UuNvA==</latexit>

pA<latexit sha1_base64="1ZZx1/lxM8YAxQ1ybna2/cYKjIQ=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C68iNuw==</latexit><latexit sha1_base64="1ZZx1/lxM8YAxQ1ybna2/cYKjIQ=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C68iNuw==</latexit><latexit sha1_base64="1ZZx1/lxM8YAxQ1ybna2/cYKjIQ=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LBbBU9i01Ta3ihePFY0ttKFstpt26WYTdjdCCf0JXjyoePUfefPfuGkrqOiDgcd7M8zMCxLOlEbowyqsrK6tbxQ3S1vbO7t75f2DOxWnklCPxDyW3QArypmgnmaa024iKY4CTjvB5DL3O/dUKhaLWz1NqB/hkWAhI1gb6SYZXAzKFWTXa27VOYeG1GtOrZGTM+Q2EXRsNEcFLNEelN/7w5ikERWacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hAkdU+dn81Bk8McoQhrE0JTScq98nMhwpNY0C0xlhPVa/vVz8y+ulOmz6GRNJqqkgi0VhyqGOYf43HDJJieZTQzCRzNwKyRhLTLRJp2RC+PoU/k+8qu3a6LpeabnLNIrgCByDU+CABmiBK9AGHiBgBB7AE3i2uPVovVivi9aCtZw5BD9gvX0C68iNuw==</latexit>

Page 22: 06 Primo principio 1 - unimi.it · 2020. 5. 21. · Il primo principio della termodinamica introduce il concetto di energia. In Termodinamica si introduce il lavoro esterno: •L

Ciclo termico e ciclo frigorifero

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A

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L > 0<latexit sha1_base64="i2SYGWMubzwcest+tgVsT5fRmlo=">AAAB63icdVBNSwMxEJ2tX7V+VT16CRbB05Jtq20vpeDFg4cKrhbaUrJptg3NZpckK5TS3+DFg4pX/5A3/43ph6CiDwYe780wMy9IBNcG4w8ns7K6tr6R3cxtbe/s7uX3D251nCrKfBqLWLUCopngkvmGG8FaiWIkCgS7C0YXM//uninNY3ljxgnrRmQgecgpMVbyr1Ad4V6+gN1yqVb0zpEl5ZJXqszIGa5VMfJcPEcBlmj28u+dfkzTiElDBdG67eHEdCdEGU4Fm+Y6qWYJoSMyYG1LJYmY7k7mx07RiVX6KIyVLWnQXP0+MSGR1uMosJ0RMUP925uJf3nt1ITV7oTLJDVM0sWiMBXIxGj2OepzxagRY0sIVdzeiuiQKEKNzSdnQ/j6FP1P/KJbc/F1udCoL9PIwhEcwyl4UIEGXEITfKDA4QGe4NmRzqPz4rwuWjPOcuYQfsB5+wQW042+</latexit><latexit sha1_base64="i2SYGWMubzwcest+tgVsT5fRmlo=">AAAB63icdVBNSwMxEJ2tX7V+VT16CRbB05Jtq20vpeDFg4cKrhbaUrJptg3NZpckK5TS3+DFg4pX/5A3/43ph6CiDwYe780wMy9IBNcG4w8ns7K6tr6R3cxtbe/s7uX3D251nCrKfBqLWLUCopngkvmGG8FaiWIkCgS7C0YXM//uninNY3ljxgnrRmQgecgpMVbyr1Ad4V6+gN1yqVb0zpEl5ZJXqszIGa5VMfJcPEcBlmj28u+dfkzTiElDBdG67eHEdCdEGU4Fm+Y6qWYJoSMyYG1LJYmY7k7mx07RiVX6KIyVLWnQXP0+MSGR1uMosJ0RMUP925uJf3nt1ITV7oTLJDVM0sWiMBXIxGj2OepzxagRY0sIVdzeiuiQKEKNzSdnQ/j6FP1P/KJbc/F1udCoL9PIwhEcwyl4UIEGXEITfKDA4QGe4NmRzqPz4rwuWjPOcuYQfsB5+wQW042+</latexit><latexit sha1_base64="i2SYGWMubzwcest+tgVsT5fRmlo=">AAAB63icdVBNSwMxEJ2tX7V+VT16CRbB05Jtq20vpeDFg4cKrhbaUrJptg3NZpckK5TS3+DFg4pX/5A3/43ph6CiDwYe780wMy9IBNcG4w8ns7K6tr6R3cxtbe/s7uX3D251nCrKfBqLWLUCopngkvmGG8FaiWIkCgS7C0YXM//uninNY3ljxgnrRmQgecgpMVbyr1Ad4V6+gN1yqVb0zpEl5ZJXqszIGa5VMfJcPEcBlmj28u+dfkzTiElDBdG67eHEdCdEGU4Fm+Y6qWYJoSMyYG1LJYmY7k7mx07RiVX6KIyVLWnQXP0+MSGR1uMosJ0RMUP925uJf3nt1ITV7oTLJDVM0sWiMBXIxGj2OepzxagRY0sIVdzeiuiQKEKNzSdnQ/j6FP1P/KJbc/F1udCoL9PIwhEcwyl4UIEGXEITfKDA4QGe4NmRzqPz4rwuWjPOcuYQfsB5+wQW042+</latexit>

CICLO TERMICO

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A

B

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CICLO FRIGORIFERO