Five moles of hydrogen \(\gamma = \frac{7}{5}\), initially at STP, is compressed adiabatically so that its temperature becomes 400^oC. The increase in the internal energy of the gas in kilojoules is (R = 8.30 J/mol-K) : 

41.50

\(\frac{C_P}{C_V} = \gamma = \frac{7}{5}\)

Work done = \(\frac{\mu R}{\gamma - 1} \Delta T = \frac{8.3*400*5}{\frac{7}{5}-1}\)

  = 41.5 J

Work done = change in internal energy

\(\text{ As } \Delta Q = 0 \text{ adiabatic process }\)

Therefore, change in internal energy = 41.5 kJ.