5 moles of Hydrogen ( = 7 5 ) initially at S.T.P. are compressed adiabatically so that its temperature becomes 400^ C . The increase in the internal energy of the gas in kilo-joules is (R=8.30 ~J ~mol ⁻¹ ~K ⁻¹ )

Step-by-step solution

Initial temperature T₁=0^ C Final temperature T₂=400^ C Work done aligned & W= R -1 t = & 5 8.31 7 5 -1 (400-0) = & 5 8.31 400 2 / 5 ~J = & 5 5 8.31 400 2 ~kJ = & 41.55 ~kJ aligned For adiabatic process, Increase in internal energy = work done =41.55 ~kJ