Use eqn 35.22 to derive the energy density of a gas of (i) non-relativistic particles ( $γ = \frac{5}{3}$ ) and (ii) relativistic particles ( $γ = \frac{4}{3}$ ).

$u =\frac{p}{γ −1}$ . (35.22)

Question

Use eqn 35.22 to derive the energy density of a gas of (i) non-relativistic particles ([latex]γ = \frac{5}{3}[/latex]) and (ii) relativistic particles ([latex]γ = \frac{4}{3}[/latex]).

[latex]u =\frac{p}{γ −1}[/latex]. (35.22)

Accepted Answer

Straightforward substitution into eqn 35.22 yields

[latex]u =\frac{3}{2} p for γ = \frac{5}{3} ,[/latex] (35.23)

[latex]u =3 p for γ = \frac{4}{3} ,[/latex] (35.24)

in agreement with eqns 6.25 and 25.21.

[latex]p = \frac{2}{3} u.[/latex] (6.25)

[latex]p = \frac{u}{3},[/latex] (25.21)

Question 35.2: Use eqn 35.22 to derive the energy density of a gas of (i) n......

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