Thermodynamics/stirling engines

[hahaha158]

Homework Statement

Helium Gas (Cv=12.5) has initial temperature T1, pressure P1, and volume V1. It follows a stirling engine cycle, namely it is 1)heated at constant volume to a temperature T2 then is 2)expanded isothermally to volume V2. 3) It is then returned to a temperature T1 by an isochoric process, then 4) returned to volume V1 by an isothermal process

Homework Equations

Q=deltaU+W
pv=nRT
Q=nCvdeltaT

The Attempt at a Solution

Because processes 1 and 3 are isochoric, that means there is no work done, so I neglected the calculations from those two processes. For both process 2 and 4 i set Q=W because it is isothermal and I believe we assume that it is an ideal gas. I tried using Q=nCvdeltaT to solve for Q of the two processes, and then subtract them from each other, but I found I would end up with

nCvT2-nCvT1
net work=nCv(T2-T1)

It seems too simple, am I doing something wrong?

 

[KataKoniK]

Thank you for your question. It seems like you are on the right track with your solution. However, I would like to clarify a few things.

Firstly, for an isothermal process, the change in internal energy (deltaU) is equal to zero. This is because the temperature remains constant, so there is no change in internal energy. Therefore, your equation Q=deltaU+W becomes Q=0+W=W. This means that for both processes 2 and 4, the heat added (Q) will be equal to the work done (W).

Secondly, for an ideal gas, the equation pv=nRT can be used to find the number of moles (n) of the gas. However, for this problem, we are given the specific heat at constant volume (Cv) instead of the gas constant (R). Therefore, we can use the equation Q=nCvdeltaT to calculate the heat added for the isochoric processes.

Lastly, to find the net work done in the cycle, you can simply add the work done for each process together. So for process 2, the work done would be W=nRTln(V2/V1) and for process 4, the work done would be W=nRTln(V1/V2). This would give you a net work done of W=nRTln(V2/V1)+nRTln(V1/V2).

I hope this helps clarify your solution. Let me know if you have any further questions.