The temperature at which the r.m.s. velocity | vedclass

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Question

(B) The root mean square (r.m.s.) velocity of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, which implies $v_{rms} \propto \sqrt{T}$

Vedclass · Accepted Answer

$2184^{\circ} C$

Vedclass · Answer

(B) The root mean square (r.m.s.) velocity of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, which implies $v_{rms} \propto \sqrt{T}$, where $T$ is the absolute temperature in Kelvin.Let $v_0$ be the r.m.s. velocity at $T_0 = 0^{\circ} C = 273 \,K$.Let $v_T$ be the r.m.s. velocity at temperature $T$.According to the problem, $v_T = 3v_0$.Using the proportionality $v_{rms} \propto \sqrt{T}$, we have:$\frac{v_T}{v_0} = \sqrt{\frac{T}{T_0}}$$3 = \sqrt{\frac{T}{273}}$Squaring both sides:$9 = \frac{T}{273}$$T = 9 	imes 273 = 2457 \,K$.To convert this temperature to Celsius:$T(^{\circ} C) = 2457 - 273 = 2184^{\circ} C$.

The temperature at which the r.m.s. velocity of a gas triples its r.m.s. velocity at $0^{\circ} C$ is:

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