A gas is filled in a container of volume v at 121 degrees celsius to what temperature should it be heated in order that 1/4th off the gas may escape out of the vessel

Ideal gas equation is PV=nRT. Initially T=121+273=394 k so PV=nR(394)....(1) After since 1/4 of the gas is escaped so n`=n-1/4n =3n/4 so PV=(3n/4)RT`....(2)now equating equations we get nR394=3n/4RT` we get T`=525k=252`c here v remains same because the remaining gas also occupies whole of the container volume.(since gas have infinite expandability).

Dear Student,
Please find below the solution to your problem.

Ideal gas equation is PV=nRT.
Initially T = 121 + 273 = 394k
so PV = nR(394)....(1)
After since 1/4 of the gas is escaped so
n`=n-1/4n =3n/4
so PV=(3n/4)RT`....(2)
now equating equations we get
nR394=3n/4RT`
we get T`=525k
=252`c
here v remains same because the remaining gas also occupies whole of the container volume.(since gas have infinite expandability).

Thanks and Regards