Five moles of Hydrogen gas initially at STP is compressed adiabatically so that its temperature becomes 673 ~K . The increase in internal energy of the gas is (R=8.3 ~J ~mol ⁻¹ ~K ⁻¹, =1.4 . for diatomic gas )

Step-by-step solution

Given, temperature, T₂=673 ~K initial temperature T₁=273 ~K rate of heat flow, R=8.3 ~J ~mol ⁻¹ ~K ⁻¹ =1.4 for diatomic gas, moles of hydrogen gas, n=5 Now, change in internal energy due to adiabatic process is or or or or U=n C_v T U=5 R -1 (T₂-T₁ ) ( . Specific heat, .C_v= R -1 )=5 8.3 1.4-1 (673-273)=5 8.3 0.4 400 U=41.5 ~kJ So, the increase in internal energy of the gas is U=41.54 ~kJ