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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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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$\begingroup$ You do have to assume that $V$ is constant, since this could change due to thermal expansion. $\endgroup$ Commented Jan 10, 2014 at 11:17
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$\begingroup$ @fibonatic The question specified in a sealed container. $\endgroup$– RubenCommented Jan 10, 2014 at 12:32
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$\begingroup$ Yes, but the container can expand due to the applied heat/temperature. $\endgroup$ Commented Jan 10, 2014 at 12:52