Availability and Irreversibility Questions and Answers

Answer: A

The steady-flow availability function is \(b = h - T_{0}s\) per unit mass, where \(h\) is the enthalpy, \(T_0\) the temperature of the surroundings and \(s\) the entropy. It is the maximum useful work obtainable from a steady flow stream, and it is also called the Keenan function. The expression \(u + P_0 v - T_0 s\) is the non-flow availability function, which is the one for a closed system, so the third option is wrong, and the other two are not the standard availability functions.

Answer: C

The maximum power equals the rate of decrease in Gibbs free energy of the flowing fluid.

For a steady flow exchanging heat only with surroundings at \(T_{0}\), with kinetic and potential energy changes neglected, the maximum (reversible) work per unit mass is:

\[ w_{max} = (h_{1} - T_{0}s_{1}) - (h_{2} - T_{0}s_{2}) \]

When the fluid enters and leaves at the surroundings temperature, \(T_{1} = T_{2} = T_{0}\), so \(h - T_{0}s\) is exactly the Gibbs function \(g = h - Ts\) at each end. The maximum power is therefore the mass flow rate times the drop in g.

The Helmholtz function \(a = u - Ts\) plays this role for a closed system, not a flow. An increase in enthalpy would mean energy going into the fluid, and the drop in internal energy ignores both the flow work and the entropy term.

Answer: C

Exergy depends on the conditions of both the system and environment.

Exergy is the maximum useful work obtainable as a system is brought into equilibrium with its surroundings (the dead state). For a closed system,

\[ \begin{aligned} \phi &= (u - u_{0}) + p_{0}(v - v_{0}) \\ &\quad - T_{0}(s - s_{0}) + \frac{V^{2}}{2} + gz \end{aligned} \]

which contains both the system's state and the environment's \(T_{0}\) and \(p_{0}\). A hot block of metal has more exergy in a cold environment than in a warm one, and none at all when it is at the environment's temperature and pressure.

So it is not a property of the system alone, nor of the environment alone.

Answer: D

Availability is the maximum useful work obtainable as the system goes to dead state.

Availability (exergy) is the maximum useful work a system can deliver as it comes into equilibrium with its surroundings, the dead state, through reversible processes. It depends on both the system and the environment.

Because it depends on the surroundings it is not purely a property of the system. 'Goes to a process' is not defined, and availability is always less than the total energy, since part of the energy cannot be converted into work.