Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio $\frac{C_P}{C_V}$ for the gas is

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

Answer 1

The correct option is D $\frac{3}{2}$

It is given that: $P\propto T^3$

From ideal gas equation, $PV\propto T$

$⟹P\propto (PV{)}^3$

$⟹P^2{V}^3=constant$

$⟹P{V}^{3/2}=constant$

For an adiabatic process, $P{V}^{\gamma }=constant$

Hence, $\gamma =\frac{C_P}{C_V}=3/2$