A rigid perfectly insulated vessel is divided in half by a v

A rigid, perfectly insulated vessel is divided in half by a valve. The left side initially contained 1 m^3 of air at 300 K and 1 atm; the right side (also 1 m^3) was evacuated. If I open the valve and cause the ideal gas to expand into the other side of the box, what is the change in internal energy of the air as it fills the entire volume if I assume that air is an ideal gas.

Solution

Given

The vessel is rigidly insulated. Hence net heat transfer, Q = 0

After the valve is opened, the gas undergoes free expansion. We know that during free expansion, work done W = 0 (no resistance to expansion of gas)

Let delta_U denote the change in internal energy of the gas during the free expansion process

From first law of thermodynamics,

Q = W + delta_U

delta_U = Q - W

= 0 - 0

delta_U = 0

Hence the change in internal energy of the air is zero.