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
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- the rate of increase in enthalpy of the flowing fluid
- the rate of decrease in Helmholtz energy of the flowing fluid
- the rate of decrease in Gibbs free energy of the flowing fluid
- the rate of decrease in internal energy of the flowing fluid
The Correct Option is C
Solution and Explanation
In a steady flow process, the maximum work (or power) that can be obtained from the system is related to the change in the available energy of the system. The available energy in a system is a function of its internal energy, enthalpy, and free energy. In thermodynamics, when a system is exchanging energy with its surroundings, the maximum work that can be obtained corresponds to the change in Gibbs free energy. This is because the Gibbs free energy represents the potential for reversible work in a system at constant pressure and temperature. When considering steady flow processes, the fluid enters and exits the system at the same temperature as its surroundings. This means that the process occurs under conditions of thermal equilibrium with the surroundings, and the changes in kinetic and potential energies are neglected. Gibbs free energy is defined as: \[ G = H - TS \] where \( G \) is the Gibbs free energy, \( H \) is the enthalpy, \( T \) is the temperature, and \( S \) is the entropy. In steady state flow processes, the system undergoes a transformation, and the maximum power that can be obtained is directly related to the decrease in Gibbs free energy. This decrease represents the maximum amount of energy that can be converted into useful work by the system, which is the power being extracted. - Option (A): The rate of increase in enthalpy is not the correct answer. Enthalpy is a measure of the total energy of the system, and while it plays a role in energy conservation, it is not directly related to the maximum work that can be extracted from the system in this case.
- Option (B): The rate of decrease in Helmholtz energy is also not correct in this context. Helmholtz free energy is used in systems at constant temperature and volume, but in steady flow processes, Gibbs free energy is the appropriate thermodynamic potential for determining maximum work.
- Option (D): The rate of decrease in internal energy is also not the correct choice. Internal energy change is a broader term that encompasses both useful and non-useful energy changes, and it does not specifically account for the maximum power obtainable in steady flow processes.
Therefore, the correct answer is: (C) the rate of decrease in Gibbs free energy of the flowing fluid
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