If two moles of an ideal monatomic gas at temperature T₀ are mixed with 4 moles of an ideal diatomic gas at temperature 2T₀, then the temperature of the mixture is

$\mathrm{U}=\frac{1}{2}\mathrm{nfRT}$ where n : number of moles & f : degree of freedom
$\begin{array}{l}{\mathrm{U}}_1=2\frac{3}{2}{\mathrm{RT}}_0\mathrm{\&}{\mathrm{U}}_2=4\frac{5}{2}\mathrm{R}\left(2{\mathrm{T}}_0\right)\\ 2\times \frac{3}{2}{\mathrm{RT}}_{\mathrm{mix}}+4\left(\frac{5}{2}\right){\mathrm{RT}}_{\text{mix }}=2\frac{3}{2}{\mathrm{RT}}_0+4\frac{5}{2}\mathrm{R}\left(2{\mathrm{T}}_0\right)\\ 3{\mathrm{RT}}_{\text{mix }}+10{\mathrm{RT}}_{\text{mix }}=3{\mathrm{RT}}_0+20\mathrm{R}\left({\mathrm{T}}_0\right)13{\mathrm{T}}_{\text{mix }}=23{\mathrm{T}}_0\Rightarrow {\mathrm{T}}_{\text{mix }}=\frac{23}{13}{\mathrm{T}}_0\end{array}$