Multiplicity for an ideal monatomic gas.
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In problem 2.26 you found the multiplicity for an ideal monatomic gas that lives in a two-dimensional universe. It was (see attachment). As implied, the multiplicity is determined by the internal energy, the area occupied by the gas, and the number of particles in the gas. From these, determine the temperature, 'pressure', and chemical potential of this gas. (As a side note: in two dimensions, the 'pressure' is defined as force per length).
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Solution Summary
I have stated the general 3D form of microstates and then evolved that in 2D case as per your problem so that you can understand the cases. Then I illustrated basic mechanisms to determine pressure, temperature and entropy. Then I calculated entropy and pressure while I clearly hinted the form of temperature without hand calculation keeping this as your exercise. This is just one algebraic manipulation as I have stated differential form.
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I have stated the general 3D form of microstates and then evolved that in 2D case as per your problem ...
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