Helium gas of $
u$ moles is expanded adiabatically $n$ times and then compressed isobarically down

Question

Helium gas of $
u$ moles is expanded adiabatically $n$ times and then compressed isobarically down to the initial volume. The magnitude of entropy increment of the gas in this process is given by $\frac{k}{2} 
u R \ln n$. Find the value of $k$.

Professor PC Thomas Classes · Answer

Adiabatic expansion: $\Delta S_1 = 0$. Isobaric compression to initial volume $V_0$: $\Delta S_2 = 
u C_p \ln(V_f/V_i) = 
u (\frac{5R}{2}) \ln(1/n) = -\frac{5}{2}
u R \ln n$. Magnitude is $\frac{5}{2}
u R \ln n \Rightarrow k=5$.