For certain system the number of accessible states is given by Ω = Aer(VU)1/2,  where A and r are constants, V is volume and U is the internal energy. The temperature would be :

1
\(\mathrm{T}=\frac{2 r(\mathrm{UV})^{\frac{1}{2}}}{\mathrm{~K}_{\mathrm{B}}}\)
2
\(\mathrm{T}=\frac{2 r}{\mathrm{~K}_{\mathrm{B}}} \cdot\left(\frac{\mathrm{U}}{\mathrm{V}}\right)\)
3
\(\mathrm{T}=\frac{2 \mathrm{U}^{1 / 2}}{\mathrm{~K}_{\mathrm{B}} \sqrt{\mathrm{V}^{1 / 2}}}\)
4
\(\mathrm{T}=\frac{r^2(\mathrm{UV})}{\mathrm{K}_{\mathrm{B}}}\)
5
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