# A closed vessel contains 0.1mole of a monoatomic ideal gas at 200K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium tempertaure (in K) of the gas in the vessel will be close to _______ Option: 1 10 Option: 2 267 Option: 3 35 Option: 4 100

The work done on gas is zero. (As the vessel is closed)

and Assuming the heat supplied to the gas is zero. (as no information on the heat supplied to the gas is given in the question)

So The total internal energy of gases remains the same.

\begin{aligned} &\mathrm{u}_{1}+\mathrm{u}_{2}=\mathrm{u}_{1}^{\prime}+\mathrm{u}_{2}^{\prime}\\ &\Rightarrow \text { (0.1) } \mathrm{C}_{\mathrm{v}}(200)+(0.05) \mathrm{C}_{\mathrm{v}}(400)=(0.15) \mathrm{C}_{\mathrm{v}} \mathrm{T}\\ &\Rightarrow \mathrm{T}=\frac{800}{3} \mathrm{k}=266.67 \mathrm{k} =267 \ \mathrm{k}\end{aligned}

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