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  4. The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at 180°C is

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Q. The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at 180$^{\circ}$C is

Kinetic Theory

Solution:

Kinetic energy of a gas is directly proportional to its temperature.
$\therefore \frac{K_1}{K_2} = \frac{T_1}{T_2} $
$\Rightarrow \frac{K}{K/3} = \frac{273 + 180}{T_2}$
$\Rightarrow 3 = \frac{453}{T_2}$
$ T_2 = 151 K$
$ T_2 = 151K - 273 = -122^{\circ}C$