What is the total translational kinetic energy of the air in an empty room that has dimensions 7.00 m × 12.00 m × 4.00 m if the air is treated as an ideal gas at 1.00 atm?

The total translational kinetic energy of a gas is given by
(1)
where this equation is derived from the ideal gas law, and where P is the gas pressure and V its volume.

For the gas in our problem, the pressure is

while the volume is


Therefore, the total translational kinetic energy of the gas is (by using eq.(1))

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