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## Main Question or Discussion Point

Hello,

I'm still trying getting familiar with the concepts of statistical mechanics and thermodynamics , and there's this equation for S of an ideal system, which somehow perplexes me. Suppose the ideal gas is composed of N indistinguishable atoms , then :

[tex]S = \frac{U - U_{0} }{T} + k Ln \frac{q^N}{N!}[/tex]

At T = 0 this expression becomes :

[tex]S = \frac{3}{2} Nk + k Ln \frac{{g_0}^N}{N!}[/tex]

where g

Is there anything wrong with this ? If not , why doesn't the entropy equal to zero at T = 0 kelvin ? Doesn't that contradict the 3rd law of thermodynamics ?

S = kLnW = 0 because at T = 0 , W = 1 .

What am I doing wrong ?

I'm still trying getting familiar with the concepts of statistical mechanics and thermodynamics , and there's this equation for S of an ideal system, which somehow perplexes me. Suppose the ideal gas is composed of N indistinguishable atoms , then :

[tex]S = \frac{U - U_{0} }{T} + k Ln \frac{q^N}{N!}[/tex]

At T = 0 this expression becomes :

[tex]S = \frac{3}{2} Nk + k Ln \frac{{g_0}^N}{N!}[/tex]

where g

_{0}is level of degeneracy of the ground state.Is there anything wrong with this ? If not , why doesn't the entropy equal to zero at T = 0 kelvin ? Doesn't that contradict the 3rd law of thermodynamics ?

S = kLnW = 0 because at T = 0 , W = 1 .

What am I doing wrong ?