So what is ‘energy’? Energy is a much used word but all too frequently also misused. Energy can be in many different forms, be it electrical, chemical, due to the effects of gravity, due to movement (rotational or translational), due to the temperature or pressure of a system, and many other forms.
We also talk of energy being ‘used’ but basic physics tells us that energy is neither created nor destroyed; it is simply converted from one form to another.
Thermodynamics also tells us that in a closed system energy can only flow in one direction, towards a state of higher disorder (higher entropy). This also tells us that while the efficiency of a process of energy transfer can approach 100% it can never attain it in a practical system, and it certainly cannot exceed it (though claims that violate this fundamental principle are still made).
We can however usefully determine the limiting behaviour of a system, one which is reversible or ideal, and use this as a benchmark to measure the efficiency of a process.
When we talk about how much energy a system has we mean (usually implicitly rather than explicitly) the energy relative to some other state, and often in some specific frame of reference. For example, we might talk about the kinetic energy of a car being zero at zero velocity, but this will be the velocity relative to a point on the earth’s surface. In thermodynamics we happily deal with the fundamental property of enthalpy even though it has no absolute value; its magnitude is simply the difference between the current state and an arbitrary reference state.
When we refer to the calorific value of a fuel, this is the thermal energy we can extract (it being in a defined state) when we combust it with oxygen (again in some defined state), and cool the products down, also to some defined state. For the evaluation of thermodynamic properties we are free to choose whatever reference state we want, though some are more convenient than others.
So the energy content of a fuel is not an absolute value but the difference in energy between two states. If we consider the standard heat of combustion of a hydrocarbon, we can take the end state for CO2 to be as a gas at 25C and 1 bar, since this is considered to represent the lowest energy state for CO2 we can achieve, given typical environment conditions.
As it happens, this is not actually the lowest energy state we could attain for CO2 in the environment, as we can react CO2 with serpentinite type rocks (of which there are large quantities in the earth’s crust) to form solid carbonates with a lower energy state. This is a reaction being seriously evaluated as a means of mineralizing CO2, but the normal assumption of rejecting CO2 into the environment as a gas is a pragmatic one, and the one by which we normally choose to judge a fuel’s ‘energy content’.
The oxygen produced by electrolysis is more or less pure, but if not recovered is discharged into an atmosphere that has only 21% oxygen; this is a lower energy state, so strictly we should use air as the reference state for oxygen (not pure oxygen) since we can in principle recover energy from the mixing process (due to the entropy change on mixing).
The effect is small; there is no effect on the heat of reaction (provided that we can consider the system to exhibit ideal or close to ideal behaviour) but the overall Gibbs Free Energy change is reduced by 1.9 MJ/kmole from 237.2 to 235.3 MJ/kmole. There is no established means of exploiting the effect so it is reasonable to ignore it.
There is a similar consideration for any stream rejected to the environment that is not at the same composition as the system receiving it; for example flue gases arising from hydrocarbon combustion contain much higher levels of CO2 and much lower levels of oxygen than the receiving air. There is an implicit acceptance that no useful energy can, in practice, be recovered; the effect is ignored.
But we have to measure energy not just by quantity, but also by its quality, and by this we mean its ability to do work.
This is most simply illustrated by considering a heat engine. From the study and understanding of heat engines, and in particular the steam engine, arose the science of thermodynamics (bearing in mind that the understanding came after the practical application of steam engines and not the other way around).
High temperature heat has an intrinsic value itself in terms of potential work. In 1824 Nicolas Carnot showed that for a heat engine working between two temperature reservoirs the maximum possible efficiency (Emax) is given by a very simple equation, namely:
where:
Tc = cold reservoir temperature (K)
Th = hot reservoir temperature (K)
Wmax = maximum possible work output
Q = heat transferred from the hot reservoir
This insight led to the development of the concept of entropy. Its relevance here is that a heat source has a work value dependent on its temperature. As the temperature of the hot reservoir approaches the cold reservoir, the potential work that can be recovered approaches zero; conversely, as Th becomes much larger than Tc, then the limiting efficiency tends to 1. For example, if we take Tc as 298.15K (25C) and Th as 373.15K (100C), then
If we set Th as 1373.15K (1000C), Emax rises to 78.3%.
The basic Carnot equation gives us the maximum possible work (Wmax) that can be extracted from a given quantity of heat (Q1) heat flowing from a constant temperature heat source (at T1) to a heat sink (at T2). This is the work we could theoretically extract if we had a machine with absolutely no energy losses - one which would then be reversible, i.e. if we put the work back in we could transfer heat back to the higher temperature source and return the system to its initial state. It should go without saying that this is in practice impossible, but it tells us the limiting properties of the system.
As we are extracting some of the energy as work, the heat flow into the sink (Q2) at T2 is lower than the heat flow from the source at T1, and equal to the heat input minus the energy extracted as work [ Q1-Wout ].
The concept of available work was developed by Keenan (1941) drawing on the earlier work of Willard Gibbs. Formerly termed ‘availability’, it is nowadays more commonly referred to ‘Exergy’.
For an open system, the Gibbs Free Energy (G) is given by:
G = H – T.S
The equation for Exergy has the same form, and is given by:
where
H = enthaply
T = system temperature (K)
To = temperature of reference state (K)
S = entropy
Exergy is the maximum possible work that can be obtained from the system relative to the reference state (at T0). The maximum possible work output for a system going from state 1 to state 2 is the change in exergy:
Since Exergy (and Gibbs Free Energy) is a function of enthalpy there is no such thing as absolute exergy, only the exergy relative to a defined reference state. For the sort of systems we are concerned with here the usual choice is STP (see previous article) relative either to the elements or to the combustion products, each in their standard states. When dealing with combustion systems the latter basis can make sense, but it can also make life awkward in most other cases.
Entropy (S) for any species is taken to have an absolute value, and is zero at zero K (absolute zero) for a perfect crystal. Otherwise all species have positive entropy, the value increasing with increasing temperature. Entropy is usually calculated by difference from the standard value at STP.
Any loss of exergy in a closed system is irreversible, and an exergy analysis of a process can be used to identify where inefficiencies occur and to establish what the limiting possible performance is of a given process. An early example of an exergy analysis of a chemical process (production of nitric acid from ammonia) was published in 1955 by K G Denbigh.
Where ideal or near ideal behaviour can be assumed, then calculation of Gibbs Free Energy and Exergy are straightforward, all we need is the basic data for each species consisting of the heat of formation, standard entropy and specific heat (as a function of temperature). Even with moderately non-ideal systems, high accuracy is often not required and treating the system as ideal can still be adequate.
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