Kinetic Theory

JEE Main level, single correct, medium

126 of 168

Question 126 of 168

The temperature of a gas is −78∘C-78^{\circ} \mathrm{C} and the average translational kinetic energy of its molecules is K\mathrm{K}. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K2 \mathrm{~K} is :

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Answer: (B) 117∘C117^{\circ} \mathrm{C}

$\begin{aligned}& \mathrm{K} . \mathrm{E}=\frac{\mathrm{nf}_1 \mathrm{RT}}{2} \\& \mathrm{~T}_{\mathrm{i}}=-78^{\circ} \mathrm{C} \rightarrow 273+\left[-78^{\circ} \mathrm{C}\right]=195 \mathrm{~K}
\end{aligned}$

K.E
αT\alpha \mathrm{T}
To double the K.E energy temp also become double

$\begin{aligned}& \mathrm{T}_{\mathrm{f}}=390 \mathrm{~K} \\

& \mathrm{~T}_{\mathrm{f}}=117^{\circ} \mathrm{C}\end{aligned}$

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