Kinetic Theory

JEE Main level, numerical answer, medium

91 of 168

Question 91 of 168

A monoatomic gas of mass 4.0u4.0u is kept in an insulated container. The container is moving with velocity 30ms−130m{s}^{-1}. If the container is suddenly stopped then a change in temperature of the gas (R=R=gas constant) is x3R\dfrac{x}{3R}. Value of xx is,

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Answer: 3600

Given that mass of gas is 4u4u hence its molar mass MM is 4gmol−14g{mol}^{-1}
∴12mv2=nCvΔT∴\dfrac{1}{2}m{v}^{2}=n{C}_{v}\Delta T
⇒12m×(30)2=mM×3R2×ΔT\Rightarrow \dfrac{1}{2}m\times {\left(30\right)}^{2}=\dfrac{m}{M}\times \dfrac{3R}{2}\times \Delta T
∴ΔT=36003R∴\Delta T=\dfrac{3600}{3R}

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