Question

The volume of one mole of an ideal gas with adiabatic exponent γ is varied according to the law TV = a where a is a constant. The amount of heat obtained by the gas in the process if the gas temperature gets increased by ΔT is
$\frac{nR\Delta T(2-\gamma )}{3(\gamma -1)}$. Then the value of $n\left(\text{integer}\right)$ is

Answer 1

For 1 mole gas
PV = RT
$P{V}^2=aR=\text{constant}\text{Compare with}P{V}^x=\text{constant}x=2\text{Molar heat capacity of gas}C=\frac{R}{\gamma -1}+\frac{-R}{x-1}\Rightarrow C=\frac{R}{\gamma -1}(2-\gamma )\therefore \Delta Q=nC\Delta T=\frac{R\Delta T}{\gamma -1}(2-\gamma )$