# Does heat increase the volume of a gas, and in turn its pressure?

Lets say you have 1 liter of hydrogen in a sealed container, at 100 psi. If 50 cm^2 of the containers surface area is heated to a 1000 degree Celsius, will the psi increase over time? What would be the formula to figure this out in terms of the amount of pressure added and the time frame it takes? No need to do the math for me, I'm capable of that, but I do need help with understanding which formula to use. Disregard the heat loss of the container for now.

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## 1 Answer

The system will eventually reach thermal equilibrium so heat received by the gas is the same as heat lost by the container. So: $m c (T_f-T_i) + m c(T_f-T_i) = 0$. Hence you need to know the specific heat capacity of the materials, and the mass, as well as the initial temperatures.

The formula relating pressure, volume, amount of moles and temperature is: $PV = nRT$, where R is the gas constant (which depends on what units you use). From this you derive $P_1/T_1 = P_2/T_2$ so by inputting $P_1$, $T_1$, and $T_2$ you can calculate the final pressure.

EDIT: I do not believe you can easily calculate the time this takes.

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You do have to assume that $V$ is constant, since this could change due to thermal expansion. –  fibonatic Jan 10 '14 at 11:17
@fibonatic The question specified in a sealed container. –  Ruben Jan 10 '14 at 12:32
Yes, but the container can expand due to the applied heat/temperature. –  fibonatic Jan 10 '14 at 12:52