The heat supplied to one mole of an ideal mono atomic gas in increasing temperature from  $T_0{\text{ to 2T}}_{\text{0}}$ is 2RT₀. Find the equation of process to which the gas follows.

Heat supplied to the  gas $Q=nC\Delta T$  for poly tropic process molar heat capacity is given by

$\begin{array}{l}C=\frac{R}{(\gamma -1)}+\frac{R}{(1-N)}\\ =\frac{R}{\left(\frac{5}{3}-1\right)}+\frac{R}{(1-N)}=\frac{3}{2}R+\frac{R}{(1-N)}\\ Q=n\left[\frac{3R}{2}+\frac{R}{(1-N)}\right]\left[2T_0-T_0\right]\\ =\left(1\right)R{T}_0\left[\frac{5-3N}{2(1-N)}\right]=2R{T}_0 \left(given \right)\\ 5-3N=4(1-N)\end{array}$

N = -1
Hence equation of process,  $P{V}^{-1}=cons\tan t$