Since gas is going to escape,the container must be open. Hence, due to any increase in temperature, there will be no effect on pressure. So, P=constant. Also, whatever gas is going to be left in container, so it will take the same volume.

V = constant. But the number of molecules will change as 1/3 of gas is not here. If initial no. of moles be N, then remaining no. of moles is 2/3 N. Then, through Ideal gas law, no. of moles is inversely proportional to Temperature. For initial temperature Ti and final Temperature Tf, and initial no. of moles Ni and final nno. of moles Nf, we get an equation Ni / Nf = Tf / Ti

Fot Ti = 300 K, Ni = N, Nf = 2/3 N , we get Tf = 450 K i.e. 177 °C which is the hike in temperature required.