During an adiabatic process, pressure of gas is found to be directly proportional to cube of its absolute temperature. The ratio of $C_P/C_V$ is
a)2
b)5/3
c)3/2
d)4/3

Question

During an adiabatic process, pressure of gas is found to be directly proportional to cube of its absolute temperature. The ratio of $C_P/C_V$ is 
a)2
b)5/3
c)3/2
d)4/3

foolaroundmath · Answer

For an adiabatic process,
$$PV^{\gamma} = const \Rightarrow P(\frac{T}{P}) ^{\gamma} = const \Rightarrow P = cT^{\gamma/(\gamma -1)}$$ 

comparing with given data, $$\gamma/(\gamma-1) = 3 \Rightarrow \gamma = 3/2$$

ujjwal · Answer

@FoolAroundMath , Can we replace V by (T/P)? I didn't get that part..

foolaroundmath · Answer

PV = nRT.
V =(T/P)*(nR) .... replace nR = const, it will just get factored in the "const"

ujjwal · Answer

Thanks @FoolAroundMath !