Energy exists in many forms like kinetic energy, potential energy, electrical energy, heat energy etc. While it is possible to convert most of the energies like potential energy, kinetic energy, electricity etc. into work, only some part of heat energy can be converted into work. The part of energy that can be converted into work is Available energy and the remainder is Unavailable portion.
Availability is about work potential or quality of the energy. When thermal energy is used to do work entire heat energy cannot be converted to useful work as per the second law of thermodynamics. The part that can be converted to useful work is referred to as the Available energy or Availability or Energy. The quality of energy is measured by Availability. As energy is used in a process it loses quality, its availability or Energy decreases.
High/Low Grade of Energy:
Energies like electrical energy or potential energy which can be converted almost entirely to do work are high-grade energy. Heat on the other hand is low-grade energy since only a part of it can be converted into work. Heat is of the lowest grade in which energy exists in a very disordered state. The lower the temperature at which the heat energy exists the lower would be the grade of energy.
However low grade energy is used to produce high-grade energy. For example- electricity a high-grade energy is produced in thermal or nuclear power plants using heat a low-grade energy source.
Availability:
Available energy is that of energy which is available for doing work. It is either work or that portion of energy that can be converted wholly into work. Concept of availability comes from the Second Law of Thermodynamics where some portion of heat has to be rejected to a sink to produce work. The work has to be with reference to some datum. Generally earth’s atmosphere is taken as reference and is called the dead state designated by ‘0’. Dead state implies the temperature and pressure existing in the surroundings and are designated by T0 and P0.
Availability or Energy is the maximum portion of energy that can be converted into work by ideal process that reduces the system to dead state.
Any system that has temperature T and pressure P can do useful work till the temperature and pressure are reduced to T0 and P0. When the temperature and pressure are equal to that of the earth or dead state all transfer of energy, stops although the system contains internal energy which would be unavailable. When a system is in equilibrium with the surroundings its potential to do any work ceases. Thus when the pressure P of the system reduces to the atmospheric pressure P0, temperature T becomes equal to T0 and likewise the KE and PE become equal to that of the surroundings no more work can be obtained.
ADVERTISEMENTS:
The properties of the system in dead state are denoted by subscript 0 i.e., as P0, T0, H0, S0, U0, C0 etc. Generally dead state temperature is taken at 25°C (298 K) and P0 as 1.01325 bar unless otherwise indicated.
Availability of Various Systems:
We can study the availability of:
(a) Work Reservoir:
A work reservoir is a source of infinite work and it would not come to equilibrium with the surroundings. However the amount of W withdrawn from the work reservoir can be converted fully into useful work in the absence of any dissipative effects. Therefore Availability of work reservoir is A = ΔW.
ADVERTISEMENTS:
(b) Heat Reservoir:
(i) Infinite Heat Reservoir (at constant temperature).
(ii) Finite Heat Reservoir (where temperature changes).
Irreversibility:
Most of the real processes in nature are irreversible due to mixing, friction and heat transfers with finite temperature difference. In a reversible process there is no net increase in the entropy of the universe. In a reversible process the change in the entropy of a system equals the change in the entropy of the universe. However in the case of an irreversible process the reduction in the entropy of a system is less than the increase of entropy of the heat receiving system.
ADVERTISEMENTS:
This leads to loss of availability or an equivalent increase in unavailability— which however are equal. In any process, aim is always to get maximum work. In an expansion process we try to get the maximum work output. In compression process aim is to have minimum work input. Thus both in expansion as well as in compression processes aim is to maximize the work as per sign convention of work.
Maximum work (Wrev) during a process between two states can be obtained by reversible process. However in actual practice the actual work (Wact) between these two states is always less than the Wrev The difference between the two is called Irreversibility.
I = Wrev – Wact
In irreversibility (I)/Exergy destruction = wasted work potential in a process. It is lost opportunity to do work. The greater the irreversibility the greater is the loss of work that could have been performed. Thus irreversibility gives the quality of the process.
ADVERTISEMENTS:
Let there be two processes, one reversible and another irreversible between two states and let heat δQrev and δQ be added giving work output of Wrev and Wu respectively.
Effectiveness:
The effectiveness of a system is the ratio of the useful or actual work done to the maximum or reversible work.
Thus, Effectiveness = δW/δWrev
Second Law Efficiency:
So far we have been using the efficiencies and COP based on the First Law of Thermodynamics. Based on the increasing use of availability which gives indication about possibility of maximum work output or minimum work input if the process is carried out reversibly — concept of Second Law efficiency is being used these days. Second law efficiency is a measure of reversible operation.
Let us assume that an engine operating between say 1200 K and 300 K has – ƞth of 30% (by measuring brake power and dividing by the heat input—based on First Law of Thermodynamics).
However, had the work been done in a reversible manner i.e., by Carnot Cycle.
Importance of Availability/Irreversibility/Effectiveness/ƞII:
These concepts are based on the second law of thermodynamics and are applicable to both cycle and process. These indicate the departure of an actual process from an ideal or reversible process.
Helmontz and Gibbs Functions:
Both these functions are properties (based on combination of properties just like h = u + pv.
Helmontz Function F = U – TS
or f = u + Ts (per unit mass)
This function is useful for closed systems that undergo reversible, isothermal process. Decrease in the value of F equals the max work that can be done by system undergoing an isothermal process at temperature equal to that of the surroundings.
Gibbs Function:
G = H – Ts
or g = h – Ts (For unit mass)
Summary:
Availability of Energy is the maximum useful work that can be obtained from a system under ideal conditions by reducing it to the dead state. Availability A of various systems are –
Entropy Change ΔS:
The unavailable energy UA = T0 ΔS. Thus change in entropy during a process is required to find out availability and unavailability.
Availability of Heat Reservoir:
(a) Infinite Heat Reservoir:
In such a reservoir temperature remains constant when small amount of heat δQ is withdrawn from it.
Let a small quantity of heat δQ be withdrawn from the heat reservoir which is at average temperature T. For getting maximum work, let there be a Carnot engine operating between temperatures T and T0 (sink temperature being of the surroundings).
(b) Finite Heat Reservoir:
In this case when heat is added or withdrawn from the reservoir which has finite capacity the temperature does not remain constant.
Consider a small quantity δ heat being withdrawn from the reservoir (1) at temperature T and producing entropy change ds as shown. Using a Carnot engine to derive maximum work between T and T0 we have –
Integrating between 0 and 1 we would get –
For the heat reservoir where temperature does not remain constant we would use appropriate equation for entropy change as applicable.