Question

A 25-L sample of an ideal gas with ? = 1.67 is at 250 K and 50 kPa. The gas is compressed adiabatically until its pressure triples, then cooled at constant volume back to 250 K, and finally allowed to expand isothermally to its original state.

a. Sketch this cyclical process in a pV diagram (the sketch should be drawn to scale and labelled).

b. How much work is done on the gas?

c. For each step in the process determine the heat energy.

Answer 1

By using PV=nRT we can solve for n.

isothermal work is -nRT*ln(V2/V1)= -1375 joules.

now at state 2, the gas is heated to a point on the adiabatic line that passes through the original state. Since that is true, we can find the pressure after heating because P2*V2^gamma=P1*V1^gamma.

Solving for pressure after heating i get 313.15kPa. Now the gas expands adiabatically, so the equation
W=P2*V2^gamma *(V1^(1-gamma)-V2^(1-gamma))/(1-gamma) gives you work done by the system.

that value is 2029 joules, so subtracting 1,375 = 654 joules of net work.

The key here is using the adiabatic line to solve for the pressure after heating (P1V1^gamma=P2*V2^gamma). Once you have the pressure after heating you can solve for work.

Sorry i confused you at first, it's been a while since i have solved any thermo problems. But now i'm confident that this is correct. But, please resolve to check my maths and see for yourself that the solution makes sense.