One mole of an ideal monatomic gas at temperature T₀ expands slowly according to the law $\frac{\mathrm{P}}{\mathrm{V}}= \mathrm{constant}$. If the final temperature is 2T₀ heat supplied to the gas is

heat supplied (Q)= nC$∆$T

for polytropic process  

molar heat capacity (C )= $\frac{\mathrm{R}}{\mathrm{\gamma }-1}+\frac{\mathrm{R}}{1-\mathrm{x}}$

monoatomic gas $\mathrm{\gamma }$=$\frac{5}{3}$

given PV^-1 = constant and $∆$T = 2T₀ - T₀ = T₀

C = $\frac{\mathrm{R}}{{\displaystyle \frac{5}{3}}-1}+\frac{\mathrm{R}}{1-(-1)}=\frac{3\mathrm{R}}{2}+\frac{\mathrm{R}}{2}=2\mathrm{R}$

Heat supplied = 1 x 2R xT₀ = 2RT₀