Question

At what temperature will he atoms have the same crms value as N2 molecules at 25°c?

Answer 1

At  -230 °C temperature will He atoms have the same rms value as $N_{2}$ molecules at 25°C .

Calculation ,

Given temperature =  25°C  =  25+273  = 298 K

$V_{rms}$ =√3RT/M

$V_{rms}$ =√3R$T_{1}$/$M_{He}$      ......( i )

$V_{rms}$ =√3R$T_{2}$/$M_{N_{2}$      ......( ii )

Equalize equation  ( i ) and ( ii )

√3R$T_{1}$/$M_{He}$ = √3R$T_{2}$/$M_{N_{2}$  

$T_{1}$/$M_{He}$  = $T_{2}$/$M_{N_{2}$  

$T_{1}$ = $M_{He}$ × $T_{2}$/$M_{N_{2}$  =  4 ×298 K/28 = 42.57 K

Temperature in°C = 42.57 - 273  = -230 °C

Therefore , at  -230 °C temperature will He atoms have the same rms value as $N_{2}$ molecules at 25°C .

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