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Q. 2.39

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Found in: Page 81

### An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

# Compute the entropy of a mole of helium at room temperature and atmospheric pressure, pretending that all the atoms are distinguishable. Compare to the actual entropy, for indistinguishable atoms, computed in the text.

The actual entropy indistinguishable atoms is

See the step by step solution

## Step: 1

The Sackur-Tetrode formula by ideal gas is

Where,represents volume, represents energy, represents the number of molecules, represents the mass of a single molecule, and represents Planck's constant.These are some of the assumptions used to generate this formula is that the molecules are indistinguishable, therefore altering any of the molecules makes no change in any arrangement of the molecules in position and momentum space. This assumption inserts the component into the multiplicity function's denominator.

The logarithm factor loses its , we get

## Step: 2 Finding degree of freedom:

The mole mass of helium is ,the mass of helium molecule is

From ideal gas law, the pressure of and temperature of one mole occupies a volume of

The monatomic gas of internal energy is

Helium is monatomic gas so .

## Step: 3

By degree of freedom,

Substituting the values of , we get

Because there are many more molecular orbitals accessible to the system if the molecules are distinct, the entropy is substantially larger.