Availability and Irreversibility Questions and Answers

Q: The exergy (or availability) of a system at a specified state

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.

Q: 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

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.

Q: Availability of a system at any given state is:

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.

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Note: Usual notations have been used for thermodynamic variables.

Useful Data: Unless otherwise specified, the following data may be assumed. Universal gas constant, \(\bar{R}\) = 8.314 kJ/kmol.K; Acceleration due to gravity, g = 9.81 m/s²; Molecular mass of air, M_air = 29 kg/kmol; Specific heat of air at constant pressure, c_p = 1.005 kJ/kg.K; Ratio of specific heats of air, γ = 1.4. Assume air to be a perfect gas unless specified otherwise.

The exergy (or availability) of a system at a specified state

A.depends on the conditions of the system alone
B.depends on the conditions of the environment alone
C.depends on the conditions of both the system and environment
D.depends neither on the conditions of the system nor the environment

Exam Year(s)

GATE XE - 2012,

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.

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Which property is called the steady-flow availability function?

A.\(b = h - T_{0}s\) (per unit mass)
B.\(b = u + h - T_{0}s\) (per unit mass)
C.\(b = u + P_{0}v - T_{0}s\) (per unit mass)
D.\(b = P_{0}v - T_{0}s\) (per unit mass)

Exam Year(s)

DSSSB - 2023,

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.

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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

Exam Year(s)

GATE XE - 2025,

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.

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Availability of a system at any given state is:

A.a property of the system
B.the maximum work obtainable as the system goes to a process
C.the total energy of the system
D.the maximum useful work obtainable as the system goes to dead state

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

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.

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Availability and Irreversibility Questions and Answers

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