Question

Assume all gases in this problem are ideal.

What is the total translational kinetic energy of the air molecules (in J) in a room of volume 27 m³ if the pressure is 9.1 ✕ 10⁵ Pa (the room is at fairly high elevation) and the temperature is 24°C?

in J

Answer 1

Total translational kinetic energy of the gas containing N molecules at temperature T is

where is the Boltzmann constant.

Using ideal gas equation or

we get

Note that n is number of moles of gas, and N is total number of molecules in the gas. N=nN_{​​​​​A} where N_{​​​​​​A} is Avagadro's number. And