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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

MGIMS WardhaMGIMS Wardha 2010

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}}=151K=151-273=-{{122}^{o}}C $