The r.m.s. speed of a certain gas is v at 400 | vedclass

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(B) The $r.m.s.$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $v_{rms} \propto \sqrt{T}$

Vedclass · Accepted Answer

$1600$

Vedclass · Answer

(B) The $r.m.s.$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $v_{rms} \propto \sqrt{T}$.Given,at $T_1 = 400\,K$,the speed is $v_1 = v$.We want to find the temperature $T_2$ at which the speed becomes $v_2 = 2v$.Using the proportionality $v_{rms} \propto \sqrt{T}$,we have $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the given values: $\frac{2v}{v} = \sqrt{\frac{T_2}{400}}$.Squaring both sides: $2^2 = \frac{T_2}{400}$.$4 = \frac{T_2}{400}$.Therefore,$T_2 = 4 	imes 400 = 1600\,K$.

The $r.m.s.$ speed of a certain gas is $v$ at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times,will be ...... $K$.

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