Work done in adiabatic compression

[haruspex]

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.

@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.

 

[Delta2]

@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.

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.

 

[Delta2]

Oh unless of course the gas isn't ideal so we can't use $PV=nRT$. But I think the problem can't be solved with your way too if we don't assume an ideal gas...

 

[haruspex]

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.

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]

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.

yes well, though I don't like this very much, I think you might be right.

 

[Chestermiller]

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.

 

[Delta2]

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.

Ehm, is it ok to say that the $dU$ of piston is just $CdT$?

That leads to a nice and neat separable ODE btw, we can find T(V) relatively easily...

 

[Chestermiller]

Ehm, is it ok to say that the $dU$ of piston is just $CdT$?

Sure. It is considered an incompressible solid.

 

[TSny]

we have: $$dU=(nC_v+C)dT=-PdV=-\frac{nRT}{V}dV$$

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.

You can also use Chestermiller's equations to derive the relation between $T$ and $V$ during the process. Then you can express the work done on the gas in terms of the initial temperature and the initial and final volumes of the gas. This is what I had in mind in post #17.

 

[so_gr_lo]

Yeah maybe it was that simple, I just wasn’t sure if they wanted me to use nm as it wasn’t in the variable list