# Combined gas law in an open atmosphere

The question was asked about pressure vs. Volume increasing in an ideal gas as temperature is increased. My question then is this. What is the formula to determine how much volume and pressure will increase as temperature is increased?

Let me frame the question this way. PV/T=P2V2/T2 this formula works for a controlled system where more than one of these values can be maintained. If we apply a known amount of heat, say n, to the atmosphere, what formula would be used to calculate volume and pressure as the temperature is increased?

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Have you seen $PV=nRT$ – yankeefan11 Jul 29 '13 at 15:30
@JamesMaslek, that's how he got PV/T=P2V2/T2. – udiboy1209 Jul 29 '13 at 15:31

Technically speaking, If you managed to create a planet with an ideal gas atmosphere, the atmosphere would just float away. Why?

One of the approximations of an ideal gas is

• There are no attractive or repulsive forces between the molecules or the surroundings

This means that the gas wouldn't feel the force of gravity!
So if I had a jar of ideal gas, the pressure wouldn't increase as I went to a greater depth in the jar(It does increase in gasses too, just like it does in liquids).

I know this sounds strange but all it really means is that you cannot apply the ideal gas approximation to a system the size of our atmosphere. This approximation works well for small systems(A jar of ideal gas), because the effects of gravity are pretty negligible.

So to analyse effects of change in temperature on the whole atmosphere, you'll need a better model. Maybe considering the atmosphere a non-viscous fluid can help, I don't know. You should research on this.

Note that other approximations like the Van der Waals equation wouldn't help too because they too neglect the effect of gravity.

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At first I wanted to say that you should use the first law of thermodynamics. However both $P$, $V$ and $T$ are unknown if you would add a certain amount energy to an atmosphere.

I agree with udiboy that you should threat the atmosphere as an non-viscous fluid, which allows you to determine the pressure as a function of altitude. However for this to give an unique solution you still need to make some more assumptions, such as the temperature distribution, the molar mass of the gas, how fast the planet and atmosphere are rotating, ect.

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