The specific heat at constant pressure of a real gas obeying $\mathrm{PV}^2=\mathrm{RT}$ equation is :
JEE MAIN 2024, Diffcult
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$\mathrm{dQ}=\mathrm{du}+\mathrm{dW}$
$\mathrm{CdT}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}+\mathrm{PdV}$ $....(1)$
$\therefore \quad \mathrm{PV}^2=\mathrm{RT}$
$\quad \mathrm{P}=\text { constant }$
$\quad \mathrm{P}(2 \mathrm{VdV})=\mathrm{RdT}$
$\quad \mathrm{PdV}=\frac{\mathrm{RdT}}{2 \mathrm{~V}}$
Put in equation $(1)$
$\mathrm{C}=\mathrm{C}_{\mathrm{V}}+\frac{\mathrm{R}}{2 \mathrm{~V}}$
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