Question:
A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200 \mathrm{~K}$. If $0.05$ mole of the same gas at $400 \mathrm{~K}$ is added to it, the final equilibrium temperature (in $\mathrm{K}$ ) of the gas in the vessel will be closed to
Solution:
As work done on gas and heat supplied to the gas are zero,
total internal energy of gases remain same
$\mathrm{u}_{1}+\mathrm{u}_{2}=\mathrm{u}_{1}^{\prime}+\mathrm{u}_{2}^{\prime}$
$(0.1) \mathrm{C}_{\mathrm{v}}(200)+(0.05) \mathrm{C}_{\mathrm{v}}(400)=(0.15) \mathrm{C}_{\mathrm{v}} \mathrm{T}$
$\mathrm{T}=\frac{800}{3} \mathrm{k}=266.67 \mathrm{k}$