As a chemical engineer, you have the option of operating a reversible flow compressor either adiabati- cally or isothermally. by comparing suitable partial derivatives, determine which condition will lead to a greater increase in the enthalpy of the working fluid. assume a > 0 in general.

As can be seen in the explanation, there will be a greater increase in the enthalpy of the working fluid in the adiabatic process than in the isothermal process, since in the adiabatic process the change of internal energy is added; In the isothermal process there is no change in internal energy that is added to the value of enthalpy.

Explanation:

∴ Q = 0  ⇒ ΔU = Wfirst law

⇒ ΔU = Cv*ΔT

⇒ W = P*dV  ∴ P = nRT/V

⇒ ΔH = ΔU + P*ΔV = Cv*ΔT + nRT/V*ΔV

∴ ΔT = 0 ⇒ ΔU = 0

⇒ Q = - W = nRTLn(V2/V1)

⇒ ΔH = PΔV = nRT/V*ΔV

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