A gas is filled in a vessel at 27 degree Celsius.To what temperature it should be heated in order that 1/3rd of the gas may escape out of the vessel?

Dear student
Let us consider that the gas is ideal gas.
Here, pressure is constant .
Volume is constant as volume of gas is actually volume of container which is not changing , gas is just escaping out .
So , no. of molecules changes if initially there were n molecules now 1/3 escape out so we are left with 2/3 molecules .
Hence , no. of molecules =2/3 n
Using , ideal gas equation we have ,
PV=nRT
from this eq we get that T is inversely proportional to n ( no. of molecules)
Hence , T1/T2=n2/n1
T1=27°C=273+27=300K
n2=(2/3)*n1
Put these values in the above eq we get 300/T2=n1/(2/3)*n1
Thus, T2=(300*3)/2 =450K =177°C
Regards
Arun (askIITians forum expert)

Approved