A monoatomic ideal gas undergoes a process in which the ratio of `P` to `V` at any istant is constant and equal to unity. The molar heat capacity of the gas is

Options

A. `(5R)/(2)`
B. `(3R)/(2)`
C. `(4R)/(2)`
D. Zero

Explanation

Let `P_(1)` and `V_(1)` be the pressure and volume and monoatomic gas at temperature `T`, respectively.
`P_(1)V_(1)=RT`
`P_(2)(V_(1)+dV)=R(T+1)`
` :. P_(2)^(2)=RT+R ( :' (P_(2))/(V_(1)+dV)=1)`
or `2((delP)/(delT))_(V)=R`
`((delP)/(delT))_(V)=(R)/(2)`
Thus, `C=C_(V)=((delP)/(delT))_(V)` for a process
`=(3)/(2)R+(R)/(2)=((4R)/(2))`