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[NOTES/SM-06003] Grand Canonical Ensemble

In this article various thermodynamic functions are expressed in terms of the grand canonical partition function.

 kapoor's picture 24-04-07 12:04:27

[NOTES/SM-04018] Boltzmann Entropy from Canonical Partition Function

We derive the Boltzmann relation for entropy using the canonical partition function. This derivation uses the fact that the number of micro states \(\Omega(E)\) as a function energy has a sharp peak around the mean energy.

 kapoor's picture 24-04-06 19:04:11

[NOTES/SM-04019] Properties of an Ideal Gas

Several properties such as internal energy, entropy etc. of perfect gases are calculated using the canonical partition function.

 kapoor's picture 24-04-06 17:04:28

[NOTES/SM-04009] The Imperfect Gas

The ideal gas equation \(pV=NkT\) is good approximation for low densities. In this section a scheme of obtaining corrections to the ideal gas equation is discussed.

 kapoor's picture 24-04-05 23:04:46

[NOTES/SM-04015] Equilibrium of a System with a Heat Reservoir

For a system in equilibrium with a heat bath at temperature \(T\) the energy is not constant. We start with the Boltzmann relation \(S=k\log \Omega\). It will be shown that if of a microstate has energy \(E_r\), its probability \(p_r\) is proportional to \(e^{-\beta E_r}\) and is given by
\[p_r = \frac{\exp(-\beta E_r)}{Z} \]
where \(Z\) is function of \(T,V,N\), called the canonical partition function and is given by
\[Z = \sum_{\text{MS }r} \exp(-\beta E_r).\]

 kapoor's picture 24-04-05 13:04:19

[NOTES/SM-04005] Applications of Canonical Ensemble to Paramanetism

In this section the method of canonical ensemble is applied to paramagnetism. For a paramagnetic substance the variation of paramagnetic susceptibility with temperature is derived.

 kapoor's picture 24-04-05 13:04:43

[NOTES/SM-04010] Classical Theory of Specific Heat of Gases

In this lecture we derive law of equipartition of energy under the assumption that the energy is quadratic function of some variable such as coordinates and momenta. As an application, the classical theory of specific heat of gases is given.

 kapoor's picture 24-04-05 07:04:53

[NOTES/SM-04011] Specific Heat of Diatomic Gases --- Quantum Effects

The quantum effect of  vibrations on specific heat of diatomic gases is presented. The results are in agreement with experimentally observed facts.

 kapoor's picture 24-04-05 07:04:53

[NOTES/SM-04014] Partition Function of an Ideal Gas

In this section the classical canonical partition function of an ideal gas is computed.

 kapoor's picture 24-04-04 16:04:55

[NOTES/SM-04008] `Distribution of Molecules under Gravity

Distribution function of molecules in presence of gravity is as function of height is derived. 

 kapoor's picture 24-04-04 13:04:46

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