3 moles of an ideal gas at a temperature of 27^ ^ ^ C are mixed...

Energy possessed by the ideal gas at $27^{{}^{{}^{\circ}}} \mathrm{C}$ is E_{1}=3\left(\frac{3}{2}$R$\times300\right)=\frac{2700 R}{2}$Energy possessed by the ideal gas at$227^{{}^{{}^{\circ}}} \mathrm{C}$is$\mathrm{E}_{2}=2\left(\frac{3 \mathrm{R}}{2} \times500\right)=1500 $\mathrm{R}$If $\mathrm{T}$ be the equilibrium temperature, of the mixture, then its energy will be $\mathrm{E}_{\mathrm{m}}=$5 \left(\frac{3 \mathrm{R} \mathrm{T}}{2}\right)$Since, energy remains conserved,$\mathrm{E}_{\mathrm{m}}=\mathrm{E}_{1}+\mathrm{E}_{2}$or$\quad 5\left(\frac{3 R T}{2}\right)=\frac{2700 R}{2}+1500 R$or$\quad \mathrm{T}=380 \mathrm{~K}$or$107^{{}^{{}^{\circ}}} \mathrm{C}