A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it, the final equilibrium temperature (in $K$ ) of the gas in the vessel will be closed to
JEE MAIN 2020, Medium
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As work done on gas and heat supplied to the gas are zero,
total internal energy of gases remain same
$u _{1}+ u _{2}= u _{1}^{\prime}+ u _{2}^{\prime}$
$(0.1) C _{ v }(200)+(0.05) C _{ v }(400)=(0.15) C _{ v } T$
$T =\frac{800}{3} k =266.67 k$
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