One mole of an ideal monoatomic gas under goes a process `V=aT^(2)`. The temperature of the gas increases by `100 K`. Which of the following is incorrect ?

Options

A. the work done by the gas in the process is `200 R` Joule
B. the molar heat capacity for the process is `(7R)/(2)`
C. for the process `PT^(2)=` constant
D. for the process coefficient of volume expansion is `gamma=(2)/(T)`

Explanation

For the process, `P=(R )/(aT)`
So, work done by the gas `=200R "Joule"`
For the process, molar heat capacity `C=(3)/(2)R+(RT)/(V)2aT=(7R)/(2)`
Volume expansion coefficent `gamma=(1)/(V)(dV)/(dT)=(2)/(T)`