Consider an ideal monatomic gas that lives in a

Chapter 2, Problem 26P

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QUESTION:

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.

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QUESTION:

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.

ANSWER:

Step 1 of 3

The area of the gas is given to be A.

Let us consider a single gas atom with an energy of U.

The multiplicity will be proportional to area (A) and area of the momentum space \(\left(A_{p}\right)\). This can be expressed as follows.

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