Calculating different thermodynamic Quantities By Sayantan Bhattacharya
Contents .Ensembles Thermodynamics Quantities . Calculating Thermodynamic Quantities using Partition Function
Canonical Ensemble Canonical Ensemble: A system which can transfer energy with a reservoir but not partides is called the Canonical Ensemble. The corresponding probability distribution is called a canonical distribution.
Micro-Canonical Ensemble . If a system exchanges neither heat nor partides, it's said to be micro-canonical ensemble. The corresponding probability distribution is called the micro-canonical distribution.
Grand-Canonical Distribution A system which can exchange both energy and particles with a reservoir is called a Grand canonical Ensemble. The corresponding probability distribution is called
Thermodynamic Quantities In statistical mechanics we mainly calculate those thermodynamic quantities, using which we can completely describe a system . Example: Entropy, total and mean energy, Helmholtzfree energy, Enthalpy, Gibbs Potential, Pressure, Specific heat etc.
Calculation Of Thermodynamic Quantities We can calculate the Thermodynamic quantities ,previously described First we need to calculate the partition function. Then we can derive other quantities from it. Each system has different partition function: i.e. For a classical gas molecule, The Partition function is given by: z(2rmkT/2 .
Entropy . We know that s-k in , from this equation we can derive the value of Entropy in terms of Partition function for,any assembly of ideal gas molecules We get
Total Energy . We know for total number of particles Nif average energy is e .Then total energy E-N So,we have, . And, Total energy, E-Ne
. Helmholtz potential: F NKT loge Z . Enthalpy: . Gbbs Potential: 2 O(log Z) + RT -T(Nk log Z+Nk) 2 o(log Z) + RT - NTlog Z-3NkT
. The speific heat at constant volume can be expressed as: OE So,we get : OT OT
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