- #1
GeneralOJB
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Does [itex]pV = \dfrac 1 3 N m \left(c_{rms}\right)^2[/itex] apply in containers that aren't cuboids? The derivation I have seen uses a cuboid container so I'm not sure if or how this can be generalised.
The formula pV=1/3Nm(c_rms)^2 in non cuboids is used to calculate the average kinetic energy of gas molecules in a non-cuboid container. It takes into account the number of molecules (N), the root mean square speed of the molecules (c_rms), and the volume of the container (V).
This formula is different from the ideal gas law (PV=nRT) in that it takes into account the shape of the container. The ideal gas law assumes that the container is a cube, while the formula pV=1/3Nm(c_rms)^2 takes into account the varying dimensions of non-cuboid containers.
This formula is important in scientific research because it allows researchers to accurately calculate the average kinetic energy of gas molecules in non-cuboid containers. This can be useful in various fields, such as physics, chemistry, and engineering.
Yes, this formula can be applied to all types of non-cuboid containers as long as the dimensions of the container are known and the gas molecules inside are behaving according to the ideal gas law.
This formula is derived from the kinetic theory of gases, which states that the average kinetic energy of gas molecules is directly proportional to their temperature. By considering the dimensions of the container and the number of molecules, the formula pV=1/3Nm(c_rms)^2 is derived to calculate this average kinetic energy.