Arigid tank contains 7 kg of an ideal gas at 5 atm and 30c. a valve is opened, and half of mass of the gas can escape. the final pressure in the tank is 1.5 atm. calculate the final temperature in the tank.

The equation of state for an ideal gas is

where p is the gas pressure, V the volume, n the number of moles, R the gas constant and T the temperature.

The equation of state for the initial condition of the gas is
(1)
While the same equation for the final condition is
(2)

We know that in the final condition, half of the mass of the gas is escaped. This means that the final volume of the gas is half of the initial volume, and also that the final number of moles is half the initial number of moles, so we can write:


If we substitute these relationship inside (1), and we divide (1) by (2), we get


And since the initial temperature of the gas is , we can find the final temperature of the gas:

That would be kinetic energy