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Say I have a box of volume $V$, with an ideal gas inside it with temperature $T_b$. I don't know the number of particles inside it. The box is surrounded by the room's environment, which has essentially infinite volume, the same kind of ideal gas, but a different temperature $T_a$, and atmospheric pressure $P_a = 1\text{atm}$.

Is it possible to calculate the pressure $P_b$ the box's walls experience? I'm also interested in how to describe the change in $P_b$ as heat is transferred from the box to the environment, and the temperatures equalize, if that is possible to calculate.

I tried to solve this with the $P V = N K_B T$ formula but it is weird how to treat the environment with it's infinite volume.

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  • $\begingroup$ Regarding your last paragraph, it may be helpful to note that $V=(Nm/\rho)$, where $m$ is the molecular mass and $\rho$ is the density. $\endgroup$
    – PM 2Ring
    Commented May 9 at 23:06
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    $\begingroup$ If you would like to know the gas pressure on the inside of the (rigid) box, you have a problem. With only the temperature and the volume, you cannot determine the pressure, you also need the number of moles of the ideal gas inside the box. $\endgroup$
    – freecharly
    Commented May 10 at 1:26

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