Question

The relation between U, p and V for an ideal gas in an adiabatic process is given by relation U = a+ bpV. Find the value of adiabatic exponent $\gamma$ of this gas.

• A. $\frac{b+1}{b}$
• B. $\frac{b+1}{a}$
• C. $\frac{a+1}{b}$
• D. $\frac{a}{a+b}$

Answer 1

The correct option is A $\frac{b+1}{b}$

In an adiabatic process $dQ=0=dU+PdV$
$\therefore dU=-PdV$ ....(1)
Given:
$U-a-bPV=0$
$\therefore dU=bPdV+bVdP$ ...(2)
Comparing (1) and (2)
$-PdV=bPdV+bVdP$
$\therefore (b+1)PdV=-bVdP$
$\therefore \frac{dP}{dV}=-\left(\frac{b+1}{b}\right)\frac{P}{V}$ ...(3)
Comparing (3) with the equation of adiabatic process
$\gamma =-\frac{V}{P}\frac{dP}{dV}$
we get
$\gamma =\frac{b+1}{b}$