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Using statistical mechanics and the partition function, we can now calculate the thermodynamic properties of the monoatomic ideal gas. Let's look at a few key ones. **Pressure** is a measure of the force the gas exerts on the walls of its container. In the quantum picture, the pressure arises from the momentum transfer of the atoms as they collide with the walls. The **internal energy** is the total energy of the gas, which is the sum of the kinetic energies of all the atoms. The internal energy is directly related to the temperature of the gas. **Entropy** is a measure of the disorder or randomness of the gas. The higher the entropy, the more ways the atoms can be arranged in different energy states. These properties are all interconnected, and the quantum theory gives us a precise way to calculate them. We see how the microscopic behavior of the atoms determines the macroscopic properties of the gas. The values of these thermodynamic properties can be calculated using the partition function and statistical mechanics. The quantum theory provides a consistent framework for understanding the thermodynamic behavior of the monoatomic ideal gas.
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