A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat giv

Question

A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas $\_\_\_\_$ J.

Professor PC Thomas Classes · Answer

For an isobaric expansion, work done is $W = P \Delta V = nR\Delta T = 100	ext{ J}$. The heat supplied to the gas is given by $Q = nC_p\Delta T$. We know $C_p = \frac{\gamma R}{\gamma - 1}$. Therefore, $Q = n(\frac{\gamma R}{\gamma - 1})\Delta T = \frac{\gamma}{\gamma - 1} (nR\Delta T) = \frac{\gamma}{\gamma - 1} W$. Substituting $\gamma = 1.4$ and $W = 100	ext{ J}$, $Q = \frac{1.4}{1.4 - 1} 	imes 100 = \frac{1.4}{0.4} 	imes 100 = \frac{7}{2} 	imes 100 = 350	ext{ J}$.