Question

A rigid, insulated container is divided into three equal compartments and contains an ideal gas. All are at a constant temperature of 25 deg C. Compartment 1 is at a pressure of 1 bar, Compartment 2 is at a pressure of 2 bars and Compartment 3 is at a pressure of 6 bars. The partitions between compartments are removed suddenly and the gas is allowed to reach equilibrium pressure in the container. What will be temperature and pressure reached? Explain with calculations.  

Answer 1

since, the container is insulated and all the three deprtment has equal temperature
so, temperature remains same
final temperature = 25 oC

use,
n = (P*V)/(R*T) for each compartment having volume V
so,
n1 = (1*V)/(R*T)
= V/(R*T)
n2 = (2*V)/(R*T)
= 2V/(R*T)
n3= (6*V)/(R*T)
= 6V/(R*T)

let final pressure be P
final volume will be 3V
from ideal gas law
P*3V = (n1+n2+n3)*R*T
P*3V = {V/(R*T) + 2V/(R*T) + 6V/(R*T)}*R*T
P*3V = 9V
P = 3 bar
so, final pressure = 3 bar