Question

If $\Delta Q$ is the heat supplied and $\Delta W$ is the work done by the gas at constant pressure, then the ratio $\dfrac{\Delta Q}{\Delta W}$ is ($\gamma$ = specific heat ratio)

• A. $\gamma$
• B. $\gamma - 1$
• C. $\dfrac{\gamma}{1 + \gamma}$
• D. $\dfrac{\gamma}{\gamma - 1}$

Hint:

Use $\Delta Q = nC_p \Delta T$ and $\Delta W = nR \Delta T$ under constant pressure to find their ratio.

Answer 1

The Correct Option is D

At constant pressure, $\Delta Q = nC_p \Delta T$, and $\Delta W = nR \Delta T$
Also, $C_p = \dfrac{\gamma R}{\gamma - 1}$ ⇒ $\Delta Q = n \cdot \dfrac{\gamma R}{\gamma - 1} \cdot \Delta T$
So, $\dfrac{\Delta Q}{\Delta W} = \dfrac{n \cdot \dfrac{\gamma R}{\gamma - 1} \cdot \Delta T}{nR \cdot \Delta T} = \dfrac{\gamma}{\gamma - 1}$