Question

Q 16 Heat

​Q16. The internal energy of a gas in an adiabatic process is given by U = a + b PV, find $\gamma$ :-

(A) $\frac{\mathrm{a}+1}{\mathrm{a}}$ (B) $\frac{\mathrm{a}+1}{\mathrm{b}}$ (C) $\frac{\mathrm{b}+1}{\mathrm{a}}$ (D) $\frac{\mathrm{a}}{\mathrm{b}+1}$

Answer 1

Dear Student,

$$\begin{gathered} Given \\ U=a+bPV \\ ForidealgasPV=nRTHence,U=a+b\left(nRT\right) \\ DerivatebothsidewithrespecttoT \\ \frac{dU}{dT}=b\left(nR\right)------\left(1\right) \\ Beacause,\frac{dU}{dT}=n{C}_V------\left(2\right) \\ Hence,C_V=bRand{C}_P=(b+1)R \\ \gamma =\frac{C_P}{C_V}=\frac{b+1}{b} \end{gathered}$$

Regards