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  4. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take R = 8.3 J/ K mole]

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Q. A $15\, g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ}C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about :
[Take R = 8.3 J/ K mole]

JEE MainJEE Main 2019Kinetic Theory

Solution:

$Q = nC_v \Delta T$ as gas in closed vessel
$Q = \frac{15}{28} \times\frac{5 \times R}{2} \times\left(4T -T\right) $
$ Q = 10000\, J = 10\, kJ$