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I am confused with adiabatic expansions. I have a homework problem wherein 2.75 moles of an ideal gas at 375 K expands adiabatically with an initial pressure of 4.75 bar and a final pressure of 1.00 bar with a C(p,m)=5R/2. I need to calculate the work done by the expansion.

Where do I start (I don't want just the answer, as I could have just copied that from the back of the book)?

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Adiabatic means that there was no heat exchange with the environment $\Delta Q=0$. Thus, by the 1st law of thermodynamics, the work done by the gas is equal to the change in internal energy: $A=\Delta U$. Since this is an ideal gan, it's internal energy is function of temperature only. You just need to use the right formula for the internal energy...

EDIT (inspired by comments): This solution uses only the energy conservation condition and does not require the process to be reversible. In a reversible process, there is no internal entropy production and, if there is also no heat exchange, the entropy of the gas remains constant. Thus an adiabatic reversible process is necessarily isoentropic. Sometimes the word "adiabatic" is understood as a synonym to conservation of entropy. However, reversible or not, the external work must be done at the expense of the internal energy if no heat is exchanged. Hence in your problem "adiabatic" must mean "no heat exchange", otherwise no unique solution is possible.

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Adiabatic in this context does not mean only that there is no heat exchange with the environment, it also means that the expansion was sufficiently slow that it is isentropic. If you expand the gas lightning fast, the no-heat-flow expansion is at constant temperature. –  Ron Maimon Sep 19 '11 at 4:31
    
Adiabatic+ reversible = isoentropic. As for "expand the gas lightning fast, the no-heat-flow expansion is at constant temperature." - I can not agree. The gas will inevitably cool. –  Slaviks Sep 19 '11 at 4:45
    
If you open a valve for a gas to expand into vacuum, it does not cool at all. If you expand the wall at the speed of sound, it does not cool at all. If you expand the wall near the speed of sound, it cools less. These are well known facts. –  Ron Maimon Sep 19 '11 at 4:58
    
My apologies, it was a rush to judgement on my side. –  Slaviks Sep 19 '11 at 5:23
    
""Sometimes the word "adiabatic" is understood as a synonym to conservation of entropy. "" No, that is maybe Rons impression, but adiabatic means thermally isolated, nothing else. Rons wiev may arise from the fact, that classical thermodynamics (should be called thermostatics!) does not deal with irreversible processes. Exemptions to that is the work of Onsager et. al. on some special irreversibles. –  Georg Sep 19 '11 at 11:16
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