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# Use the Sackur-Tetrode equation to calculate the entropy

## Problem 33P Chapter 2

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition

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Problem 33P

Use the Sackur-Tetrode equation to calculate the entropy of a mole of argon gas at room temperature and atmospheric pressure. Why is the entropy greater than that of a mole of helium under the same conditions?

Step-by-Step Solution:

Step 1 of 5</p>

In the given problem, the entropy of a mole of helium at room temperature and pressure is . We need compare the entropy of monatomic argon gas with the helium. The entropy of the argon gas can be calculated using Sackur Tetrode equation.

The Sackur Tetrode equation gives the entropy of a monatomic gas molecule as,

……….1

Where S is entory, N is avogadro number, k and h are constants, m is mass of argon atom, V is volume and U is internal energy.

Step 2 of 5</p>

In order to calculate, the entropy of argon gas first we need to calculate volume , internal energy and mass of argon atom using ideal gas laws.

To calculate Volume occupied by 1 mole of argon gas at STP

At STP,  pressure , Temperature T=300 k and for one mole n=1

Using ideal gas law volume is given by,

Substituting  , T=300 k,  n=1 and R=8.314 J/mol.k

Step 3 of 5</p>To calculate the internal energy of monatomic gas of one mole,

For one mole of monatomic gas, the internal energy is given by

Using PV=nRT

Substituting T=300 k,  n=1 and R=8.314 J/mol.k

Step 4 of 5

Step 5 of 5

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