Question

The internal energy, pressure, and volume of an ideal gas are related as U = 3pv/4.

Answer 1

The ratio of specific heats is 7/3.

Answer 2

For an ideal gas, $U = nC_vT$ and $PV=nRT$, leading to $U = \frac{C_v}{R}PV$. Given $U = \frac{3}{4}PV$, comparing these yields $\frac{C_v}{R} = \frac{3}{4}$, so $C_v = \frac{3}{4}R$. Using Mayer's relation $C_p - C_v = R$, we find $C_p = \frac{7}{4}R$. The ratio of specific heats is $\gamma = \frac{C_p}{C_v} = \frac{7/4 R}{3/4 R} = \frac{7}{3}$.