Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio $\frac{C_p}{C_v}$ for the gas is :

• A. $\frac{5}{3}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. $\frac{2}{1}$

Answer 1

Answer: (B)

$\frac{3}{2}$

In an adiabatic process $P{V}^{\gamma }=constant$ .....(1)

Given, $P\alpha T^3$

$\therefore P=b{T}^3$, where, b is a constant.

$\therefore P=b(\frac{PV}{R}{)}^3$

$\therefore P^2{V}^3=constant$

$\therefore P{V}^{\frac{3}{2}}=constant$ .....(2)

Comparing eqn(2) with eqn(1) we get $\gamma =\frac{3}{2}$

We know that, $\frac{C_p}{C_v}=\gamma$

$\therefore \frac{C_p}{C_v}=\frac{3}{2}$

Note that, in successive steps constants are different.