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.
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
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!