5 moles of Hydrogen `(gamma =(7)/(5))` initially at STP are compressed adiabatically so that its temperature becomes `400^(@)C`. The increase in the internal energy of the gas in kilo-joule is `[R =8.30 J mol^(-1)K^(-1)]`

Options

A. `21.56`
B. `41.55`
C. `65.55`
D. `80.55`

Answer

B

Explanation

From first law of thermodynamics
`dQ = dU + dW`
`dU = dW` (`becaues` dQ = 0 in adiabatic process)
`dw = (nR(T_(1)-T_(2)))/(gamma-1)=(5xx8.30xx(400))/((7/(5)-1))=41.55 kJ`