$\text{Laws Of Thermodynamics}$

Here ,

$C_V= \dfrac{3R}{2} \text{(for ideal monoatomic gas) and :}$ $\large\color{#3D99F6}{PV^{-1}=constant}$ $\text{For the general polytropic process:}$ $\color{#D61F06}{PV^x=constant}$ $\text{We know}$ $\large \color{#69047E}{C=C_V + \dfrac{R}{1-x} }$ $\text{Plugging in x=-1 and the value of : } C_V , \text{we get}$ $C=\dfrac{3R}{2} + \dfrac{R}{1+1} = \color{#D61F06}{2R}$ $\text{Now heat supplied to the gas is :}$ $\large \color{#3D99F6}{\Delta Q=nC \int_{T_0}^{2T_0} dT=1\cdot 2R\cdot (2T_0 - T_0)= 2RT_0 }$