One mole of a diatomic gas is heated under a "kibolinsky process" in which gas pressure is temperature controlled according to law `P=(4)/(5)CT^(3//2)`. Where `C` is kibolinsky constant. In this process, gas is heated by `300K` temperature. Answer the following questions.
Under above a process the molar specific heat of gas is:

Options

A. `(R)/(2)`
B. `R`
C. `2R`
D. None of these

Explanation

For `P =(4)/(5)CT^(3//2)`
We have `PV^(3)` =Constant
Thus molar specific heat of gas is
`C=C_(V)+(R)/(1-3)=C_(V)-(R)/(2)=2R ["as" C_(V)=(5R)/(2)]`
Heat supplied to gas in temperature increment by `DeltaT=300K` in the process is
`Q =nCDeltaT=n(2R)(300)=600R`
Charge in internal energy of gas in this process is
`DeltaU =nC_(V)DeltaT=(5R)/(2)xx300=750R`.
Thus work done by the gas is `DeltaW =Q-DeltaU-150R`.