One mole of an ideal gas undergoes a process whose molar heat capacity is 4R and in which work done by gas for small change in temperature is given by the relation dW=2RdT, then the ratio `(C_(P))/(C_(V))` is

Options

A. `7//5`
B. `5//3`
C. `3//2`
D. `2`

Answer

C

Explanation

For small change `dQ = dU+ dW`
`nCdT = nC_(V)dT + 2nRdT therefore C = C_(V) + 2R, 4R = C_(V) + 2R " " therefore C_(V) = 2R`
Also `C_(V) = (R)/(gamma-1) therefore (R)/(gamma-1) = 2R implies 2gamma -2 implies gamma = (3)/(2)`