Question

When an ideal diatomic gas undergoes adiabatic expansion, if the increase in its volume is 0.5%, then the change in the pressure of the gas is

• A. +0.5%
• B. -0.5%
• C. -0.7%
• D. +0.7%

Hint:

In adiabatic processes, pressure and volume are related by \(PV^\gamma = \text{constant}\). Use this relation to find pressure change for a given volume change.

Answer 1

The Correct Option is C

For adiabatic process: \[ PV^\gamma = \text{constant} \] where for diatomic gas, \(\gamma = \frac{7}{5} = 1.4\). Using differential form: \[ \frac{\Delta P}{P} + \gamma \frac{\Delta V}{V} = 0 \Rightarrow \frac{\Delta P}{P} = -\gamma \frac{\Delta V}{V} \] Given \(\frac{\Delta V}{V} = 0.5% = 0.005\), \[ \frac{\Delta P}{P} = -1.4 \times 0.005 = -0.007 = -0.7% \]