An insulated container is divided into two equal portions. One portion contains as ideal gas at pressure `P` and tenperature `T`. The othe portion is a perfect vaccume. If a hole is opened between the two portions, claculate
a. the change in internal energy.
b. the change in temperature.

Explanation

The system being thermally insulated, `q = 0`. The gas expands through the hole in other portion is show free expansion, i.e.
`w =- int P DeltaV = 0` (Since, `P = 0)`
Also from the first law of thermodynamics,
`q = DeltaU +w`
Since, `q = 0, w = 0 ( :' DeltaU = 0)`
Also internal enegry `U = 3//2 RT`. Since, the internal enegry remains same `( :' DeltaU = 0)`, thus the temperature will also remain constant.