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Question
Calculate the temperature at which the rms velocity of a gas triples its value at S.T.P. (standard temperature T1 = 273 K)
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Solution
At STP temperature T1 = 273 K
RMS velocity of a gas, (vrms)1 = v
New RMS velocity of a gas, at temperature (T2)
New temperature T2 = ?
vrms = `sqrt((3"RT")/"M")`
`("v"_"rms")_1/("v"_"rms")_2 = sqrt("T"_1/"T"_2)`
T2 = `[("v"_"rms")_2/("v"_"rms")_1]^2 xx "T"_1`
= `((3"v")/"v")^2 xx 273`
= 9 × 273
T2 = 2457 K
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