If the RMS velocity of an ideal gas is v ms^ | vedclass

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(C) The root mean square $(RMS)$ velocity of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,w

Vedclass · Accepted Answer

$1600$

Vedclass · Answer

(C) The root mean square $(RMS)$ velocity of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,we can write: $\frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}}$.Given $T_1 = 127^{\circ} C = 127 + 273 = 400 \ K$ and $v_1 = v$.We want to find $T_2$ such that $v_2 = 2v$.Substituting the values: $\frac{v}{2v} = \sqrt{\frac{400}{T_2}}$.$\frac{1}{2} = \sqrt{\frac{400}{T_2}}$.Squaring both sides: $\frac{1}{4} = \frac{400}{T_2}$.$T_2 = 400 	imes 4 = 1600 \ K$.

If the $RMS$ velocity of an ideal gas is $v \ ms^{-1}$ at $127^{\circ} C$,at what temperature its $RMS$ velocity is doubled (in $K$)?

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