Question

If the relation of the absolute temperature (T) and volume (V) of an ideal gas which expands adiabatically is T ∝ 1 / √V, then the ratio of the specific heat capacities of the gas is:

• A. 1.3
• B. 1.5
• C. 1.67
• D. 2.0

Hint:

In adiabatic processes, use the relation $T V^{\gamma - 1} = {constant}$. Compare the given relation with this form to find $\gamma$.

Answer 1

The Correct Option is B

For an adiabatic process, $T V^{\gamma - 1} = {constant}$, where $\gamma$ is the ratio of specific heats ($C_p/C_v$).
Given $T \propto \frac{1}{\sqrt{V}}$, rewrite as $T = k V^{-1/2}$.
So, $T V^{1/2} = {constant}$. Comparing with $T V^{\gamma - 1} = {constant}$, we get $\gamma - 1 = \frac{1}{2}$.
Thus, $\gamma = 1 + \frac{1}{2} = 1.5$.