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if the pressure remains constant, find t...

if the pressure remains constant, find the temperature at which root mean square speed of a gas is half of its value at `27^(@)C`.

Text Solution

Verified by Experts

At constant pressure, rms speed depends only on the temperature.
`v_(rms)=sqrt(overline(v^(2)))propsqrt(T)`
`(V_(rms))/(V_(rms)')=sqrt((T_(1))/(T_(2)))`
`(V_(rms))/((V_(rms))/(2))=sqrt((300)/(273+t))`
`2=sqrt((300)/(273+t))`
Squaring both sides, we get
`4=(300)/(273+t)`
`1092+4t=300`
`4t=-1092+300=-792`
`t=-(792)/(4)=-198^(@)C`
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