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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(bar(v^2)) prop sqrt(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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