Thermodynamics of NVT ideal gases

We can determine the thermodynamic properties of an ideal gas using canonical ensemble statistical mechanical calculations. We follow the same steps as in the W E ideal gas. The Hamiltonian of an W T ideal 

as in Chapter 4, the 3N integrals / dq over the configurational part of the phase space yield the volume of the system for each particle. Furthermore, using Eq. 5.48 we can write 

The integral for each of the momenta degrees of freedom can be conveniently calculated with the help of the following formula  

Any quadratic term in the Hamiltonian can then be easily computed in the ATr probability density calculation with Eq. 5.51. 

We can define a new property called the thermal wavelength, which is constant for a specific type of particle at constant temperature, as follows  

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