A tool that judges the quality of energy, not just its quantity. Adjust the stream temperature, ambient reference temperature and energy rate to see, in real time, how much of that energy is exergy that can actually do work and how much is anergy that cannot — an intuitive way to grasp Second-Law (available-energy) thinking.
Parameters
Stream temperature T
K
Temperature of the fluid carrying the heat you want to use
Ambient reference temp T₀
K
Temperature of the surrounding environment used as the exergy reference
Energy rate Q
kW
Energy carried by this heat stream per unit time
Target
Select the type of energy stream to analyse
Results
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Exergy rate (kW)
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Anergy (unavailable energy) (kW)
—
Carnot factor (exergy factor)
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Exergy fraction (%)
—
Temperature ratio T₀/T
—
Energy quality
—
Energy stream split — exergy and anergy
The incoming energy stream splits into exergy (bright part) that can do work and anergy (dull part) that cannot. Watch the thermometer's stream temperature and the ambient-temperature marker.
Of the energy Q carried by a heat stream at temperature T, the exergy is the part that can do work and the anergy is the part that cannot. T₀ is the ambient reference temperature.
$$\text{Energy} = \text{Exergy} + \text{Anergy}$$
Energy splits into exergy plus anergy, and only the exergy can be converted into useful work. The total energy is conserved, but exergy is destroyed by irreversible processes.
$$\eta_{\text{Carnot}} = 1-\frac{T_0}{T}$$
The Carnot factor (exergy factor). It equals the efficiency of a reversible heat engine running between a source at T and the environment at T₀, and represents the exergy fraction itself.
What is Exergy?
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I have never heard the word "exergy" before. Is it something different from energy?
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Roughly speaking, energy measures quantity, while exergy measures quality. The First Law of thermodynamics says energy is conserved and can never disappear. But our everyday sense tells us the heat in lukewarm water is no longer "usable", right? The same number of joules in a hot furnace can run an engine, while in tepid water it does almost nothing. That "maximum work you could actually extract" is exergy.
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I see — so exergy is the "useful part" of energy. Then what decides how much of it is usable?
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For heat, it is decided by temperature. The hotter the heat, the larger the exergy fraction. That fraction is the Carnot factor 1 - T₀/T, where T₀ is the temperature of the surroundings. If you raise the "stream temperature T" slider on the left, you will see the exergy fraction climb steadily toward 100%. Conversely, as T approaches the ambient temperature T₀, no matter how many joules you have, none of it can do work — the exergy drops to nearly zero.
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Wait — if it is only slightly above ambient, you can't use it? Even though the heat is clearly there?
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Exactly, and that is what makes exergy interesting. To extract work you need a temperature difference, and once heat has reached the same temperature as the surroundings, nothing more can be taken out. So the remaining part — the heat that cannot become work — is called anergy. Energy = exergy + anergy. For example, 30 °C waste heat seen from a 20 °C environment has only about 3% exergy. That is exactly why low-temperature waste heat is called a "nuisance".
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I read that energy is conserved but exergy is "destroyed". What does that mean?
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Good question. The total amount of energy is always conserved. But exergy shrinks in every real, irreversible process. Friction, heat crossing a finite temperature difference, unrestrained mixing and expansion — each time one of these happens, exergy turns into anergy. That is "exergy destruction". Once destroyed, exergy can never do work again. Even just passing the heat of a hot flame through a boiler tube wall into water destroys a large amount of exergy, because the temperature difference is so large.
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So exergy analysis is what tracks that. How is it different from a First-Law analysis?
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A First-Law energy balance makes every component look loss-free, because energy is conserved. That tells you nothing about where to improve. Exergy analysis — also called Second-Law or availability analysis — lets you quantitatively trace which unit in a power plant, engine or chemical process is destroying the quality of energy. In practice, you target the place wasting the most quality, not the most quantity. That is the greatest value of exergy analysis.
Frequently Asked Questions
Energy is a measure of quantity; exergy is a measure of quality — how much of that energy can be turned into useful work. The First Law of thermodynamics says energy is conserved and never disappears. Yet the same joule of heat is highly useful inside a furnace but nearly useless in lukewarm water. Exergy is the maximum useful work the energy could deliver. It is always defined relative to the environment (reference state T₀) and grows as temperature rises.
The Carnot factor 1 - T₀/T is the fraction of heat at temperature T that is exergy. It equals the efficiency of a reversible heat engine (Carnot cycle) operating between a source at T and the environment at T₀. For T = 800 K and T₀ = 298 K it is 1 - 298/800 = 0.6275, meaning only 62.75% of that heat can ideally be converted to work and the remaining 37.25% must be rejected to the environment.
Anergy is the part of heat that cannot be converted to work, so that Energy = Exergy + Anergy. The key point is that while energy is always conserved, exergy is destroyed by every real, irreversible process — friction, heat flow across a finite temperature difference, and unrestrained mixing or expansion. Destroyed exergy becomes anergy and can never again be used to do work.
It pinpoints where the quality of energy is being wasted in a power plant, engine or chemical process. A First-Law energy balance can make every component look loss-free, but an exergy (Second-Law or availability) analysis reveals that specific units — combustion, the boiler, the condenser — destroy large amounts of exergy. The strength over a First-Law-only analysis is that you can target the component wasting the most quality, not merely the most quantity, of energy.
Real-World Applications
Optimizing thermal and nuclear power plants: The energy efficiency of a thermal power plant is around 40%, but an exergy analysis shows that the largest exergy destruction is not the flue gas leaving the stack but combustion itself and the large-temperature-difference heat transfer inside the boiler. Looking at the First Law alone tempts you to "reduce stack losses", whereas exergetically it is far more effective to improve boiler combustion or raise steam pressure and temperature. Building a component-by-component exergy-destruction map is standard practice in power-plant retrofit design.
Evaluating cogeneration (combined heat and power): A cogeneration system that extracts both electricity and heat from the same fuel can exceed 80% overall efficiency on a First-Law basis. But seen through exergy, if the recovered heat is, say, 60 °C hot water, that heat carries little exergy and the verdict changes dramatically. Exergy analysis correctly handles the difference in quality — "electricity is high grade, low-temperature heat is low grade" — and supports rational equipment selection matched to how the heat will be used (domestic hot water versus an industrial process).
Deciding on waste-heat recovery: How far you should recover a factory's flue gas or waste hot water is judged by the exergy of that waste heat. Flue gas at 400 °C has a high exergy fraction and is worth sending to power generation (such as a binary cycle). Waste water at 40 °C, on the other hand, has almost no exergy, and bolting on a generator will not pay back the investment. If you switch the target in this tool to "low-temperature waste heat", you can see how the exergy collapses with only a small drop in temperature.
Designing chemical processes and HVAC systems: In chemical plants and HVAC systems with distillation columns, boilers and heat pumps, exergy is destroyed in every heating, cooling and compression step. Exergy analysis exposes quality mismatches — "are we heating a low-temperature target with high-temperature steam?", "are we cooling more than necessary?" — and quantifies the energy-saving room available through heat pumps or process integration (pinch analysis).
Common Misconceptions and Pitfalls
The biggest misconception is assuming that high energy efficiency means high exergetic performance. An electric heater converts almost 100% of the supplied electricity into heat, so its First-Law energy efficiency is about 100%. But electricity is the highest-grade exergy (fraction near 100%), while the heating output it produces is low-grade. In exergy efficiency terms, an electric heater scores only about 5-10%. A heat pump warming the same room has a far higher exergy efficiency, and the judgment that "converting high-grade electricity directly into low-grade heat is wasteful" can only be quantified with exergy analysis.
Next is the carelessness of assuming the ambient reference temperature T₀ can be chosen arbitrarily. Exergy is always a quantity relative to the environment (reference state), and its value changes with the choice of T₀. In this tool too, raising T₀ reduces the exergy of the same heat stream. In practice T₀ is usually taken as the annual mean temperature of the sink that the equipment rejects to (atmosphere or cooling water). For equipment whose T₀ differs by more than 10 °C between summer and winter, the exergy assessment can change by season. When comparing several components, you must use the same T₀, or the comparison is not fair.
Finally, the misconception that anergy is waste that can be reduced. Anergy is the part of heat that is "fundamentally impossible to convert to work", and it always exists as long as the temperature is finite. What can be reduced is not anergy itself but the "destruction of exergy" caused by irreversible processes. Even an ideal, reversible engine rejects anergy to the environment. The purpose of exergy analysis is not to drive unavoidable anergy to zero, but to find and reduce the avoidable exergy destruction — excessive temperature-difference heat transfer, throttling, unnecessary mixing and the like.
How to Use
Enter the stream temperature in Kelvin (e.g., 450 K for superheated steam) using streamTempNum or the range slider
Set ambient reference temperature (e.g., 298 K for standard conditions) via ambientTempNum
Input energy rate in kW (e.g., 500 kW heat transfer) using energyRateNum
The simulator calculates exergy rate, anergy, Carnot factor, and energy quality metrics automatically
Observe how exergy fraction changes as you adjust T₀/T ratio to understand thermodynamic irreversibilities
Worked Example
Consider a waste heat recovery system: stream temperature T = 673 K (400°C exhaust gas), ambient reference T₀ = 298 K (25°C), energy rate = 800 kW. The Carnot factor = 1 − (298/673) = 0.557. Exergy rate = 0.557 × 800 = 445.6 kW (quality energy available for work). Anergy = 800 − 445.6 = 354.4 kW (irreversible heat loss). Exergy fraction = 55.7%. Temperature ratio T₀/T = 0.443. If stream cools to 473 K, Carnot factor drops to 0.369, reducing exergy rate to 295.2 kW—demonstrating how temperature separation controls exergy availability.
Practical Notes
Refrigeration cycles: use T₀ = 298 K and cold stream T = 263 K; negative exergy indicates work input required
Power plant condensers: high anergy (kW) at T₀ ≈ T reveals low-quality waste heat unsuitable for cascading processes
Industrial furnaces: compare exergy rates at different burner outlet temperatures to optimize fuel conversion efficiency and identify exergy destruction zones
Cryogenic systems: small T₀/T ratios (e.g., 0.02 at 15 K) yield high Carnot factors, justifying expensive cooling infrastructure