Question #297966

Calculate the temperature at which root mean square speed of a gas molecules is double of its speed at 27°C pressure remaining constant

1
Expert's answer
2022-02-15T16:19:55-0500

The rms speed (u) is directly proportional to the square root of temperature.

uu=TT\frac{u'}{u}=\sqrt{\frac{T'}{T}}

2uu=T27+273\frac{2u}{u}=\sqrt{\frac{T'}{27+273}}

2=T3002=\sqrt{\frac{T'}{300}}

4=T3004=\frac{T'}{300}

T=1200KT'=1200K

Thus, at 1200 K would the rms speed of a gas molecule have twice its value at 27 deg C



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