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

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Let the P , V  and n be the pressure ,volume ,no of moles respectively initialy.
T= 27c= 27 +273 K=300Kelvin
therefore according to ideal gas equation we can write
PV = n R T
PV = n r 300      (T= 300)
n =PV/300r
Now since 1/3rd gas escaped remaining gas = 2n/3
now let T'' = new temperature
PV = 2n/3  rT''
after putting value of n we get 
PV = 2 PV/900r  r T''
Now eliminating PV from both sides and r r canceled we get
T'' = 900/2 = 450 Kelvin = 450 -273=177 celcius
So ans 450 kelvin or 177 celcius

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