Find an expression for the entropy of the two-dimensional ideal gas considered in below Problem. Express your result in terms of U, A, and N.

Problem:

Consider an ideal monatomic gas that lives in a two-dimensional universe (“flatland”), occupying an area A instead of a volume V. By following the same logic as above, find a formula for the multiplicity of this gas, analogous to equation 2.40.

Problem 32P

Solution 32P

Step 1:

In this question, we need to find an expression for entropy of two dimensional ideal gas and we need to express the equation in terms of U,A and N