Energy as a physical quantity: work, heat and the laws of thermodynamics

Framing

The headline number for the energy industry in any given year is a single quantity expressed in a single unit. In 2024 the world consumed approximately 592 exajoules of primary energy. That one number aggregates five billion barrels of oil, almost nine billion tonnes of coal, four trillion cubic metres of natural gas, thirty thousand terawatt-hours of electricity and the work of perhaps seventy million people in the industry.

To understand the energy business, the first thing to understand is how an aggregation of that kind is possible at all. It is possible because energy is a physical quantity and physical quantities can be added. A joule of chemical energy in a barrel of oil and a joule of electrical energy delivered to a house are, in a precise sense, the same thing. They differ in their form and in what they can be made to do, but as quantities of energy they are equivalent and additive.

This equivalence is the foundation of the entire commercial and statistical apparatus of the industry. It is also a non-trivial scientific claim, established only in the middle of the nineteenth century after nearly two hundred years of confusion about what energy actually is.

Key terms

These terms are introduced once. Later lessons reference them rather than redefining them.

1. Energy. A scalar physical quantity, conserved in any closed system, measured in joules. Operationally, energy is the capacity to do work. A kilogramme of petrol contains roughly 44 megajoules of chemical energy.
2. Work. The transfer of energy by the application of a force through a distance — the organised, directed form of energy transfer.
3. Heat. The transfer of energy between systems at different temperatures, by the random motion of particles — the disordered form of energy transfer.
4. Power. The rate at which energy is transferred or converted, measured in watts. One watt is one joule per second.
5. Temperature. A scalar quantity proportional to the average kinetic energy of the particles in a substance, expressed in kelvin (0 °C corresponds to 273.15 K). Differences in temperature drive the flow of heat.
6. First law of thermodynamics. Energy in a closed system is conserved. Energy can change form, but the total quantity is constant.
7. Second law of thermodynamics. In any process, the entropy of an isolated system never decreases. No process that converts heat into work can have an efficiency of 100%; some heat must be rejected to a colder reservoir.
8. Carnot efficiency. The theoretical maximum efficiency of any heat engine operating between a hot reservoir at temperature T_h and a cold reservoir at temperature T_c, equal to 1 − (T_c / T_h), with both temperatures in kelvin.
9. Exergy. The portion of an energy quantity that is, in principle, available for conversion into useful work. A joule of high-temperature heat has high exergy; a joule of low-temperature heat has low exergy.

What energy actually is

The clearest definition of energy is operational: energy is the capacity of a system to do work. A litre of petrol has energy because it can be made to push a piston. A reservoir held a hundred metres above a turbine has energy because the water, if released, can spin the turbine. In each case, the energy of the system is the answer to a single question: how much work can this system, in principle, do?

That definition took a long time to arrive at. For most of the seventeenth and eighteenth centuries, heat and mechanical work were thought of as different substances. The unification of heat and work into a single concept of energy was the achievement of a small group of mid-nineteenth-century physicists: James Prescott Joule, who measured the mechanical equivalent of heat in the 1840s; Hermann von Helmholtz, who in 1847 published the first general statement of energy conservation; and William Thomson (Lord Kelvin) and Rudolf Clausius, who in the 1850s formulated the second law and gave entropy its definition.

Energy is a scalar quantity — it has magnitude but no direction — and it is measured in joules. One joule is the work done when a force of one newton moves an object one metre. The joule is small: a single match holds about 1,000 joules; a car at motorway speed has around 500,000 joules of kinetic energy; a European household uses around 50 gigajoules a year; the world's annual demand is around 6 × 10²⁰ joules.

A scalar quantity is additive. A joule is a joule, whether it comes from a barrel of oil, a kilowatt-hour from a wind farm or a lithium-ion battery. The whole statistical apparatus of the industry rests on that property — and so does every commercial transaction. An LNG buyer pays per million British thermal units; a power purchase agreement is priced per megawatt-hour. Both are units of energy and it is the energy that is, in the end, bought and sold.

Work and heat: the two ways energy moves

Energy moves between systems in exactly two ways: as work, or as heat. The distinction is not trivial — it is what makes the second law necessary and the reason the energy industry exists in the form it does.

Work is the organised transfer of energy. A piston pushed by expanding gases, a turbine blade turned by steam, current flowing through a motor — in each case the energy moves in a directed, structured form and the transfer can in principle be reversed without loss.

Heat is the disorganised transfer of energy. When a hot body sits in contact with a cold one, energy passes through the random collisions of molecules. There is no direction at the microscopic level, only a statistical bias from hotter to colder. The transfer is irreversible in any practical sense; nothing in nature runs it backwards on its own.

This carries an asymmetry that shapes every power plant. Work can be converted entirely into heat — every time a brake pad heats up, kinetic energy becomes thermal energy, fully. But heat cannot be converted entirely into work; some must be rejected to a colder reservoir. The cooling-tower plume is the visible signature of the second law.

The first law: energy is conserved

The first law states that in any process the total energy of an isolated system is constant. Energy can change form — chemical to thermal, thermal to mechanical, mechanical to electrical — but the total is preserved.

For the industry, the first law is the foundation of the energy balance. Every facility, portfolio and national economy can be analysed by writing one: total energy in must equal total energy out, plus the change in energy stored. The IEA's World Energy Outlook and the Statistical Review of World Energy are, at root, energy balances at the global and national level.

The first law also dictates a habit of thought. When an engineer says the energy has to go somewhere, she is invoking it. If a plant burns coal with 24 gigajoules per tonne and the electrical output accounts for only 10 of those gigajoules, the remaining 14 are not gone — they have left in some other form and the question is which. It is also a hard constraint on commercial claims: any device that purports to produce more energy than it consumes is, by the first law, impossible.

The second law: the direction of every process

The second law is the more subtle and the more consequential. It states that in an isolated system a quantity called entropy never decreases. For the industry the operational consequence is what matters: heat flows spontaneously from hot to cold, never the other way; and no cyclic process can extract heat from a single reservoir and convert it entirely into work.

The practical implication is the Carnot limit. Sadi Carnot, working in Paris in the 1820s, showed that the maximum efficiency of any heat engine operating between a hot reservoir at T_h and a cold reservoir at T_c is 1 − (T_c / T_h), independent of engineering detail. Drag the sliders below to feel it:

This is why the industry has spent two centuries pushing combustion temperatures higher. A 1950s subcritical coal plant ran at peak steam temperatures around 540 °C, with a real efficiency near 35%. A modern ultra-supercritical plant runs at 600–620 °C and reaches 45%. A combined-cycle gas turbine, with turbine inlet temperatures above 1,500 °C, reaches 60–64%. Each step is bought with more exotic materials — the history of thermal power generation is in large part the history of metallurgy.

The second law also explains why low-temperature heat is, in a precise sense, less valuable than high-temperature heat. A joule of heat at 1,000 K can in principle yield 0.7 joules of work; a joule at 350 K, only 0.14. The two joules are the same quantity of energy by the first law, but not equivalent in their capacity to do useful work. The concept of exergy — the work-equivalent of a given quantity of energy, given the available cold reservoir — is the formal expression of this difference.

From physics to industry

The two laws together give the industry its structure. The first says energy must be accounted for. The second says high-temperature heat is the most valuable form of it, that work is more useful than heat and that the universe runs in one direction: from concentrated, high-quality energy in fuels, sunlight and gravitational potential, towards low-temperature, dispersed heat in the atmosphere and oceans.

Every energy business is a particular intervention in this one-way process. Upstream extracts concentrated chemical energy from geological reservoirs. Midstream moves it. Downstream refines it. The power business converts fuels — or wind, or sunlight — into electricity, the most useful and concentrated form of energy we handle at scale. End-use industries extract whatever fraction of the available exergy they can before discarding the rest as low-grade heat.

This framing is not a metaphor. A start-up promising an internal combustion engine of 70% efficiency, or a cycle that exceeds the Carnot bound, is not pushing a frontier — it is making a claim the laws of thermodynamics admit no exception to.

Worked example: a tonne of coal through a supercritical power station

To make the laws concrete, follow a single tonne of bituminous coal through a modern 600 MW supercritical station. It carries about 24 gigajoules of chemical energy. Watch where each joule goes:

The example illustrates every point of the lesson. The first law balances: the 24 GJ leaves as electricity, flue-gas heat, cooling-tower heat, ash heat and small radiative losses and the numbers add up. The second law constrains the conversion: only about 43% becomes electricity, the rest rejected as low-temperature heat. The Carnot limit underlies it — with a hot reservoir around 870 K and a cold reservoir at 300 K, the ceiling is about 65% and the real plant achieves roughly two-thirds of that. And the energy–exergy distinction explains why electricity is worth more than the same joules of cooling-tower heat: electricity is essentially pure work, while the rejected heat has almost zero exergy and almost zero value.

The same logic, with different numbers, applies to a gas turbine, a diesel engine, a fuel cell, a solar panel and a wind turbine. Every energy conversion is an exercise in extracting useful work before the second law claims its share.

Key insight. Energy is conserved by the first law of thermodynamics; its capacity to do useful work — its exergy — is not. Every industrial energy conversion is a managed degradation of exergy. The job of the energy industry is to manage that degradation profitably.