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A glass vessel is filled with air at 30^...

A glass vessel is filled with air at `30^@C`. Up to which temperature should the vessel the heated kepping the pressure constant so that `1/3rd` of the initial volume of air is expelled? `gamma_p=1/273^@C^-1`.

Text Solution

Verified by Experts

Let initial volume of air =`V_1`
`therefore` Final volume of an equal mass of air,
`V_2=V_1+V_1/3+4/3V_1` [as volume of a expelled air `=1/3 V_1`]
Initial temperature `T_1=273+30=303K` let the required temperature be `T_2K`.
As pressure is constant
`V_1/T_1=V_2/T_2orV_1/303=(4/3V_1)/T_2`
or,`T_2=4/3times303=404K=(404-273)^@C=131^@C`
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