# Determining heat capacity of gasses

I need a little help on answering a question which popped into my head while I was reading about gas laws:

Suppose that I have three canisters, each holding a different gas of unknown identity [let's call them gasses A, B, and C] . I also happen to have another tank of a different volume in which these gasses can be mixed as I please, and a pump to remove the gasses from the mixing tank afterwards. Each of these containers is fitted with a pressure and temperature gauge. Furthermore, I have a heating apparatus which can be used to heat or cool the gasses inside any of the containers. I want to determine the molar heat capacity of each of the gasses. Assuming that no energy is lost to heating of the containers, is it possible to determine the molar heat capacities of gasses A, B, and C using this setup? If so, how? If not, why not?

I presume that yes, it is possible to do so. I'm thinking that, for instance, gas A at room temperature could be pumped into the mixing chamber, then the amount of moles of gas A in the mixing tank could be calculated using the PV=nRT formula. Then, gas B could be heated up to a certain temperature and pumped into the tank. Based on the fact that we know the amount of moles of gas A in the tank and the change in temperature and pressure, we can calculate the amount of moles of gas B. Afterwards, the mixing tank can be purged and a different combination of gasses can be pumped in. Rinse and repeat. Afterwards,I would get a system of equations that looks something like the following:

AF=BG

BH=CJ

CN=AL

Where A, B, and C are the heat capacities of each of the gasses, and F,G,H,J,N, and L each equal the amount of moles of a particular gas multiplied by the observed change in temperature and are known. Solving for A, B, and C would yield the molar heat capacity of each gas.

Is my reasoning correct?

• That is a very detailed and complex scenario that "popped into" your head. Does the heating device tell you how much heat it delivers? – Karsten Theis Nov 19 '19 at 14:07
• @KarstenTheis No. – user73910 Nov 19 '19 at 22:03
• I think if you know the heat capacity of one gas, you could figure out the heat capacity of the others. However, I don't think your set of equations is able to get absolute values (i.e. if I find a solution and then multiply all heat capacities by 2, it would still be a solution to the equations). – Karsten Theis Nov 20 '19 at 20:10