NEET Physics Question - Thermal Physics

For a certain gas the ratio of specific heats is given to be $\gamma = 1.5$. For this gas: (1990)

$C_v = 3R/J$

$C_p = 3R/J$

$C_p = 5R/J$

$C_v = 5R/J$

Solution:

Given $\gamma = \frac{C_p}{C_v} = 1.5 = \frac{3}{2}$. In work units, $C_p - C_v = \frac{R}{J}$. Substituting $C_v = \frac{2}{3}C_p$, we get $C_p - \frac{2}{3}C_p = \frac{R}{J}$, leading to $\frac{C_p}{3} = \frac{R}{J}$, or $C_p = \frac{3R}{J}$.

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