Question

A piston divides a closed gas cylinder into two parts. Initially, the piston is kept pressed such that one part has pressure P and volume 5V and the other part has pressure 8P and volume V. The piston is now left free. The new pressure if the process is isothermal:

• A. \( \frac{13}{6} P \)
• B. \( \frac{8}{13} P \)
• C. \( \frac{13}{8} P \)
• D. \( \frac{8}{6} P \)

Hint:

Isothermal processes maintain constant temperature, leading to direct proportionality between pressure and volume changes inversely.

Answer 1

The Correct Option is A

Step 1: Apply the ideal gas law and isothermal condition. 
Total initial moles: \[ n_1 = \frac{P \times 5V}{RT} + \frac{8P \times V}{RT} = \frac{13PV}{RT}. \] Since the process is isothermal and the volume after the piston is free is \(6V\): \[ P_{final} \times 6V = \frac{13PV}{RT} \times RT. \] Step 2: Calculate the final pressure. \[ P_{final} = \frac{13P}{6}. \]