A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200, K . If 0.05 mole of same gas at

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11.Thermodynamics

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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

A

$269.5$

B

$260.6$

C

$250.5$

D

$266.67$

(JEE MAIN-2020)

Solution

As work done on gas and heat supplied to the gas are zero,

total internal energy of gases remain same

$u _{1}+ u _{2}= u _{1}^{\prime}+ u _{2}^{\prime}$

$(0.1) C _{ v }(200)+(0.05) C _{ v }(400)=(0.15) C _{ v } T$

$T =\frac{800}{3} k =266.67 k$

Standard 11

Physics

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