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Question
5 moles of Hydrogen (γ=75) initially at S.T.P. are compressed adiabatically so that its temperature becomes 400oC. The increase in the internal energy of the gas in kilo - joules is: (R=8.30Jmol−1 K−1)
5 moles of Hydrogen (γ=75) initially at S.T.P. are compressed adiabatically so that its temperature becomes 400oC. The increase in the internal energy of the gas in kilo - joules is: (R=8.30Jmol−1 K−1)
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Solution
The correct option is B 41.5
Given T1=0oC=273K, T2=400oC=673 K
Work done W=nR(γ−1)(T2−T1)=5×8.3×400(75−1)=41500 J=41.5 kJ
By convention, the work done on the gas is taken to be negative, i.e. W = - 41.5 kJ. From the first law of thermodynamics dQ = dU + dW. For an adiabatic process, dQ = 0. Hence dU = - dW = - ( - 41.5 ) = 41.5 kJ. The positive sign of dU implies that the internal energy increases.
Given T1=0oC=273K, T2=400oC=673 K
Work done W=nR(γ−1)(T2−T1)=5×8.3×400(75−1)=41500 J=41.5 kJ
By convention, the work done on the gas is taken to be negative, i.e. W = - 41.5 kJ. From the first law of thermodynamics dQ = dU + dW. For an adiabatic process, dQ = 0. Hence dU = - dW = - ( - 41.5 ) = 41.5 kJ. The positive sign of dU implies that the internal energy increases.
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