The molecules of air in the room where you ar | vedclass

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(B) The air molecules in a room are in constant random motion due to thermal energy. The average thermal energy of a molecule is given by $E_{th} \app

Vedclass · Accepted Answer

the gravitational potential energy $mgh$ is much lesser than the average thermal energy $kT$

Vedclass · Answer

(B) The air molecules in a room are in constant random motion due to thermal energy. The average thermal energy of a molecule is given by $E_{th} \approx kT$,where $k$ is the Boltzmann constant and $T$ is the absolute temperature.The gravitational potential energy of a molecule at a height $h$ is $U_g = mgh$,where $m$ is the mass of the molecule and $g$ is the acceleration due to gravity.For air molecules in a typical room (height $\approx 3 \ m$),the value of $mgh$ is extremely small compared to the thermal energy $kT$ at room temperature. Because $kT \gg mgh$,the random thermal motion dominates over the gravitational force,preventing the molecules from settling at the floor. Thus,the density remains nearly uniform throughout the room. Therefore,the correct option is $B$.

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