Physics - Heat & Thermo Question with Solution | TestHub

For the adiabatic process $P{V}^{\gamma }=$ constant: $V^{\gamma }\frac{dp}{dV}+P\gamma V^{\gamma -1}=0$. Pressure at point P: $P=\frac{nR{T}_0}{V_0}$. From the given condition $T{V}^{\gamma -1}=$ constant, differentiating w.r.t. $\mathrm{T}:V^{\gamma -1}+T(\gamma -$ 1) $V^{\gamma -2}\frac{dV}{dT}=0$. From the tangent in the figure $\frac{dV}{dT}=\frac{V_0/T_0}{-2T_0}\times T_0$ giving $\gamma -1=1,\gamma =2$. Bulk modulus $B=\gamma P=\frac{2nR{T}_0}{V_0}$.