Five moles of hydrogen initially at STP is compressed adiabatically so that its temperature becomes 673 ~K . The increase in internal energy of the gas, in kilo joule is (R=8.3 ~J / mol - K ; =1.4 for diatomic gas )

Step-by-step solution

Work done by an ideal gas is adiabatic expansion aligned & d U=n R -1 d T & d U=n R -1 (T₂-T₁ ) aligned Given aligned T₁ & =273 ~K T₂ & =673 ~K R & =8.3 ~J / mol - K n & =5 & =1.4 aligned aligned d U & =5 8.3 1.4-1 (673-273) & = 41.5 0.4 400 ~J & =415 100 ~J & =41.50 ~kJ aligned