The discussion revolves around the work done during the compression of a gas in a thermally isolated piston-cylinder system. The original poster presents an equation for adiabatic work and questions the use of specific variables, including the heat capacity ratio (γ) and the number of moles of gas. Participants explore the nature of the process, debating whether it is adiabatic or isothermal, and the implications of thermal equilibrium between the gas and the piston.
The conversation is ongoing, with various interpretations of the problem being explored. Some participants suggest that the process is adiabatic, while others argue for a more nuanced understanding of the thermal interactions involved. There is no explicit consensus, but several lines of reasoning are being developed regarding the nature of the work done on the gas.
Participants note that the problem statement does not clearly define whether the process is isothermal or adiabatic, leading to confusion. The lack of mention of the number of moles in the list of symbols is also highlighted as a potential oversight. Additionally, the thermal equilibrium condition between the gas and the piston is a point of contention in determining the nature of the compression process.
@Delta2 is referring to the approach I proposed in post #13.TSny said:I don't understand the question. But, I need to get some shut-eye. It's well past midnight here.
So, I'll leave it for now. Enjoy.
OK I understand that's what we should do if we want to find an explicit formula for the work, however what about my earlier post where I give the work as integral of T,V and dV, this satisfies all the requirements of the statement of the problem but I agree that it is funny and fishy.haruspex said:@Delta2 is referring to the approach I proposed in post #13.
I don't know about thermodynamic processes in general, but it certainly seems reasonable here since it mirrors reality. If we move the piston in small steps, pausing after each, that should approximate a slow steady movement.
It is unclear whether an integral involving an undefined function would constitute an acceptable answer. If we can find a more definitive expression then I would think not.Delta2 said:OK I understand that's what we should do if we want to find an explicit formula for the work, however what about my earlier post where I give the work as integral of T,V and dV, this satisfies all the requirements of the statement of the problem but I agree that it is funny and fishy.
yes well, though I don't like this very much, I think you might be right.haruspex said:It is unclear whether an integral involving an undefined function would constitute an acceptable answer. If we can find a more definitive expression then I would think not.
Ehm, is it ok to say that the ##dU## of piston is just ##CdT##?Chestermiller said:This problem is really straightforward if one chooses as the "system" the combination of gas plus piston. Then, from the first law of thermodynamics, we have: $$dU=(nC_v+C)dT=-PdV=-\frac{nRT}{V}dV$$where n is the number of moles of gas, Cv is the molar heat capacity of the gas, and C is the heat capacity of the piston.
Sure. It is considered an incompressible solid.Delta2 said:Ehm, is it ok to say that the ##dU## of piston is just ##CdT##?
Yes. This leads to a very simple result for the work done on the gas during the process in terms of the overall temperature change ##\Delta T## for the process. Maybe this is what they want. So, perhaps ##dT## in the statement of the problem is meant to be ##\Delta T##. I don't know.Chestermiller said:we have: $$dU=(nC_v+C)dT=-PdV=-\frac{nRT}{V}dV$$