Question

A rigid, perfectly insulated container has a membrane dividing its volume in half. One side contains a gas at an absolute temperature and pressure , while the other half is completely empty. Suddenly a small hole develops in the membrane, allowing the gas to leak out into the other half until it eventually occupies twice its original volume. In terms of and , what will be the new temperature and pressure of the gas when it is distributed equally in both halves of the container? Explain your reasoning.

Short answer

Thetemperaturewill be same

The pressure will be halved

Step-by-step solution

Determine the ideal gas Equation

Equation for Ideal Gas is

Step 2:Determine the new temperature and pressure of the gas when it is distributed equally in both halves

When the gas move from one side to other and its volume is doubled apply the ideal gas law

the gas move from one side to other Ha s the same R and Number of moles

when the molecules move there will be nofrictionorincreasein thetemperaturedue to moving and the movement depend only on the velocity and mass othe the molecules where the kinetic energy equals

Therefore ,thetemperaturewill be same

By keeptemperaturesame and double the volume we will have the half of the pressure asvolumeis inverselyproportionalto pressure

So after moving The pressure will behalved

Therefore The pressure will be halved