# What controls the room pressure?

The following question is here Bidon, Energy of room. Ideal gas law : URL (version: 2018-10-27)

Although my question is a little bit different.

I’m currently studying Thermal Physics and I am reading “Concepts in Thermal Physics”, by Blundell. And when I was trying to solve some problems, I found this one:

Mr Fourier sits in his living room at 18ºC. He decides he is rather cold and turns the heating up so that the temperature is 25ºC. What happens to the total energy of the air in his living room?

I made some calculations and I just got the expression Bidon got in his question:

$$E = \frac{3}{2}NKT$$

Where $$E$$ is the total energy of the room, $$N$$ is the number of particles, $$K$$ the Boltzmann constant and $$T$$ the temperature.

I read that the pressure is constant, because it’s atmospheric pressure, the volume of the room is assumed constant (and closed!) and what changes is the distribution of the particles in the volume (density), $$E$$ would be constant with $$T$$ increasing.

This doesn’t make any sense to me, I know that when $$T$$ increases, the mean kinetic energy will increase, but then the total energy kinetic of the room will increase too, right? Also I think this is wrong because the pressure will increase if the volume is constant.

What should be the answer to this situation?

As the room heats up from 18 C to 25 C the number of atoms in the room decreases. By $$PV=nRT$$ since $$P$$, $$V$$, and $$R$$ are constant as $$T$$ increases $$n$$ must decrease proportionally.