Question

The inlet and outlet temperatures of the flowing fluid during a steady state flow process are the same as that of the surroundings. If the changes in kinetic and potential energies are neglected, the maximum power that can be obtained is equal to

• A. the rate of increase in enthalpy of the flowing fluid
• B. the rate of decrease in Helmholtz energy of the flowing fluid
• C. the rate of decrease in Gibbs free energy of the flowing fluid
• D. the rate of decrease in internal energy of the flowing fluid

Hint:

For steady-flow devices exchanging heat with the surroundings: \[ W_{max} = -\Delta G \] Remember: Helmholtz free energy applies to closed, isothermal–isochoric systems; Gibbs free energy applies to steady flow at constant temperature and pressure.

Answer 1

The Correct Option is C

Step 1: Recall maximum work principle.
For steady-flow systems exchanging heat with surroundings at temperature \(T_0\): \[ W_{max} = - \Delta G \] where \(G\) is Gibbs free energy.

Step 2: Given condition.
Inlet and outlet temperatures of fluid = temperature of surroundings. Thus, the maximum useful work is equal to the decrease in Gibbs free energy of the fluid.

Step 3: Eliminate wrong options.
(A) Enthalpy change is not the correct measure.
(B) Helmholtz energy applies for closed systems at constant \(T, V\).
(D) Internal energy decrease is not the criterion for max work. Final Answer:
\[ \boxed{(C) \; \text{Rate of decrease in Gibbs free energy of the flowing fluid}} \]