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

Sagot :

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

Calculation ,

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

[tex]V_{rms}[/tex] =√3RT/M

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

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

Equalize equation  ( i ) and ( ii )

√3R[tex]T_{1}[/tex]/[tex]M_{He}[/tex] = √3R[tex]T_{2}[/tex]/[tex]M_{N_{2}[/tex]  

[tex]T_{1}[/tex]/[tex]M_{He}[/tex]  = [tex]T_{2}[/tex]/[tex]M_{N_{2}[/tex]  

[tex]T_{1}[/tex] = [tex]M_{He}[/tex] × [tex]T_{2}[/tex]/[tex]M_{N_{2}[/tex]  =  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 [tex]N_{2}[/tex] molecules at 25°C .

To learn more about  He atoms

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