A mono - atomic ideal gas undergoes a process in which the ratio of  P  to  V  at any instant is constant and equals to 1. What is the molar heat capacity of the gas

In general, the molar heat capacity for any process is given by
$C=C_v+\frac{R}{1-n},$ when  $P{V}^n=$ constant
Here $\frac{P}{V}=1,i.e.P{V}^{-1}=$  constant
For monatomic  gas,  $C_v=\frac{3}{2}R$
$\therefore C=\frac{3}{2}R+\frac{R}{1-(-1)}=\frac{3}{2}R+\frac{R}{2}=\frac{4R}{2}=2R$.