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

Answer 1

For an adiabatic process,
\[PV^{\gamma} = const \Rightarrow P(\frac{T}{P}) ^{\gamma} = const \Rightarrow P = cT^{\gamma/(\gamma -1)}\]

comparing with given data, \[\gamma/(\gamma-1) = 3 \Rightarrow \gamma = 3/2\]

Answer 2

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

Answer 3

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

Answer 4

Thanks @FoolAroundMath !