The absolute temperature of a gas

Prove that the average kinetic energy of a molecule of an ideal gas is directly proportional to the absolute temperature of the gas.

If the pressure and the absolute temperature of a given mass of gas are doubled, the new volume will be..............of the initial volume.

An ideal gas in a thermally insulated vessel at internal pressure = P_(4) , volume = V_(1) and absolute temperature = T_(1) expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P_(2), V_(2) and T_(2) , respectively. For this expansion.

A gas follows a process TV^(n-1) = constant, where T = absolute temperature of the gas and V = volume of the gas. The bulk modulus of the gas in the process is given by

The critical temperature of a gas is that temperature

If the equation of state of a gas is expressed as (P + a/(V^2)) (V - b) = RT where P is the pressure, V is the volume and T the absolute temperature and a, b , R are constants, then find the dimensions of 'a' and 'b' ?