# Is it possible for temperature to cause a change in the density of air in a closed isochoric system?

I am taking a meteorology chair as part of a airline transport pilot course and while discussing atmospheric pressure and density the professor claimed that an increase in the temperature of the air causes an increase in it's density.

When I pushed him for clarification, he clearly said that if I heat up a closed system at a constant volume, the density of the air inside will increase.

I do not believe this to be true as the notion of density ($$ρ$$) that I have is mass ($$m$$) per unit volume ($$V$$):

$$ρ = \frac{m}{V}$$

and in a closed system, no matter what we do, the number of air molecules will remain constant. So if we don't change the volume, the density will remain constant.

He then explained density as a statistical value of how many molecules are in a given volume at a specific time, and that if we increased the temperature, the velocities of the molecules would increase, thus making it more probable to find a greater amount of molecules in the same volume.

I gave the example of heating a perfectly sealed pressure cooker with nothing but air inside: the pressure would increase but surely not the density or it would become heavier.

He claimed that yes, the density would increase and the weight too, we just couldn't feel it / measure it with a kitchen scale because it was a small amount.

I asked him if he would agree that he is saying that increasing the temperature of air in a closed isochoric system will cause an increase in its density. He confirmed.

He has also justified this by saying that an increase in pressure implies an increase in density. And thus if the pressure builds up inside the cooker, so does the air density.

I believe this to be wrong but I was unable to find a simple, clear proof in the past couple of hours due to my lack of general physics knowledge regarding this area. I have also searched this Stack Exchange and the closest I found was this question:

Is it possible to change Pressure without changing Density?

where by looking at the $$ρ=\frac{P}{RT}$$ equation provided for ideal gases, I take that density would remain constant because in a isochoric process, a temperature increase would cause an equal increase in pressure, which would cancel out because they are on different sides of the fraction.

Am I completely wrong or is there a simple, unequivocal way to show that what he is saying makes no sense?

• Have you asked the professor why the precision of a kitchen balance is relevant when a closed system is defined as m=constant, an isochoric process is defined as V=constant, and density is defined as m/V? – Cell Oct 2 at 22:08
• @Cell Yes, that makes sense to me but he countered by talking about this "statistical definition" of density I mentioned in the 4th paragraph which, so far, I have been unable to find any reference to online. – secknv Oct 2 at 23:25
• Because it makes no sense. The volume is the boundary of the system. The mass is the product of the moles of molecules within the boundary and their molar mass. Both are fixed. – Cell Oct 2 at 23:46