Question

The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is : $U=a+bPV$ Where a and b are constants. What is the value of the ratio of the specific heats?

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

Answer 1

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

let $U_1=a+b{P}_1{V}_1$ and

$U_2=a+b{P}_2{V}_2$

so $\Delta U=b(P_2{V}_2-P_1{V}_1)$....(1)

also for adiabatic $\Delta U=\frac{P_2{V}_2-P_1{V}_1}{\gamma -1}$ ...(2)

From equation 1 and 2

we get $b=\frac{1}{\gamma -1}\Rightarrow \gamma =\frac{b+1}{b}$