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.

Question

Chemistry

Rashad Ochoa

8 August, 06:19

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.

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Kadence · Answer 1

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:

adiabatic process:

∴ Q = 0 ⇒ ΔU = W ... first law

⇒ ΔU = Cv*ΔT

⇒ W = P*dV ∴ P = nRT/V

⇒ ΔH = ΔU + P*ΔV = Cv*ΔT + nRT/V*ΔV

isothermally (T = constant):

∴ ΔT = 0 ⇒ ΔU = 0

⇒ Q = - W = nRTLn (V2/V1)

⇒ ΔH = PΔV = nRT/V*ΔV