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## Homework Statement

A 26-L sample of an ideal gas with (gamma)= 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.

## Homework Equations

I've called the three states a,b, and c, so the subscripts are W_(from-to)

W_ab= (P_a*V_a - P_b*V_b)/(gamma-1)

P_b=(50 kPa)(3)=150 kPa

P_a(V_a)^gamma=P_b(V_b)^gamma

W_bc= 0

W_ca= nRT*ln(V_a/V_c)

pV=nRT

V_c=V_b

## The Attempt at a Solution

The first process is adiabatic, so I used the first equation to find the work. I first needed to find the V_b, so I used the second equation: (50 kPa)(26 L)^1.67=(150 kPa)(V_b)^1.67

I found that V_b= 13 L (based on another part of the question that I solved correctly I know that they rounded it to 13).

Then W_ab= [(50)(26 )-(150)(13)]/(1.67-1) = -970 J

The second process was isochoric, so W= 0.

The third process is isothermal, so I used:

W_ca= p_a(V_a)ln(V_a/V_c) = (50)(26) * ln (26/13) = 901 J

So then the total work done is: W= 901-970 = -69 J

can someone please tell me where my mistake is? Thanks!

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