3.2 When the number of particles changes in a thermodynamic transformation, it is important to use the correct form of entropy for an ideal gas, as given by the Sacker-Tetrode equation (2.49). (a) Use the Sacker-Tetrode equation to calculate A(V, T) and G(P, T) for an ideal gas. Show, in particular, that A(V,T) = NkT[In(nλ³)-1], where it is the density, and λ =√√2h²/mkT is the thermal wavelength. (b) Obtain the chemical potential for an ideal gas from (24/3N)v.r and (AG/AN)P.T. Show that you get the same answer μ=kT ln(nλ³).

3.2 When the number of particles changes in a thermodynamic transformation, it is important to use the correct form of entropy for an ideal gas, as given by the Sacker-Tetrode equation (2.49). (a) Use the Sacker-Tetrode equation to calculate A(V, T) and G(P, T) for an ideal gas. Show, in particular, that A(V,T) = NkT[In(nλ³)-1], where it is the density, and λ =√√2h²/mkT is the thermal wavelength. (b) Obtain the chemical potential for an ideal gas from (24/3N)v.r and (AG/AN)P.T. Show that you get the same answer μ=kT ln(nλ³).

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Concept explainers

Boltzmann statistics of Ideal gas

In statistical mechanics and thermodynamics, Maxwell - Boltzmann statistics explains the statistical distribution of the energies of the classic gas molecules over different states in thermal equilibrium. Maxwell Boltzmann statistics helps us to derive the Maxwell - Boltzmann distribution of ideal gas molecules, which is the result of the kinetic theory of gases.

Question

3.2 When the number of particles changes in a thermodynamic transformation,
it is important to use the correct form of entropy for an ideal gas, as given by the
Sacker-Tetrode equation (2.49).
(a) Use the Sacker-Tetrode equation to calculate A(V, T) and G(P, T) for an ideal
gas. Show, in particular, that
A(V,T) = NkT[In(nλ³) — 1],
where it is the density, and λ = √2h²/mkT is the thermal wavelength.
(b) Obtain the chemical potential for an ideal gas from (2A/3N)v.7 and
(ƏG/AN)P.T. Show that you get the same answer
μ = KT ln(nλ³).

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Step 1: calulation of A(V,T) and G(P,T) using sacker-Tetrode equation

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