In thermodynamics, energy is the capacity of a system to produce change, whether that means heating its surroundings, pushing a piston, or driving a chemical reaction. The central quantity is called internal energy (symbolized U), which accounts for all the microscopic motion and interactions of the molecules inside a system. Every law of thermodynamics is ultimately a statement about how this energy is stored, transferred, or constrained.
Internal Energy: The Core Concept
Internal energy is the total energy associated with the random, disordered motion of molecules inside a substance. You can’t measure it with a thermometer or a pressure gauge alone, but it’s there in the constant jostling, spinning, and vibrating of every particle in the system.
What contributes to internal energy depends on what you’re looking at. For a simple gas made of single atoms (like helium), internal energy is almost entirely translational kinetic energy: atoms flying in straight lines and bouncing off each other like tiny billiard balls. For gases made of multi-atom molecules (like oxygen or carbon dioxide), internal energy also includes rotational energy from molecules spinning around their centers and vibrational energy from atoms within each molecule oscillating back and forth like tiny springs. In liquids and solids, there’s an additional layer: potential energy stored in the attractive forces holding neighboring molecules together.
One critical property of internal energy is that it’s a state function. That means its value depends only on the current condition of the system (its temperature, pressure, volume, and composition), not on how the system got there. Think of it like your elevation on a mountain: whether you hiked up the north face or took the cable car, your altitude at the summit is the same. The change in internal energy between two states is always ΔU = U(final) − U(initial), regardless of the route.
How Energy Moves: Heat and Work
A system’s internal energy can change in exactly two ways: heat and work. These are not types of energy stored inside the system. They are modes of transfer, the verbs of thermodynamics rather than the nouns.
Heat is energy that flows between a system and its surroundings because of a temperature difference, and only because of a temperature difference. Place a hot metal block in cool water and energy moves from block to water as heat until both reach the same temperature. Work, on the other hand, is every other way of transferring energy. When a gas expands and pushes a piston, it does work on the piston. When you compress a gas with a pump, you do work on the gas. Stirring a fluid, passing electric current through a resistor, stretching a rubber band: all work.
Unlike internal energy, heat and work are path functions. The amount of heat transferred and the amount of work done depend on exactly how you carry out the process. You can take a gas from one temperature and pressure to another along many different paths (heating first then compressing, or compressing while heating gradually), and each path will involve different amounts of heat and work, even though the change in internal energy is the same every time.
The First Law: Energy Is Conserved
The first law of thermodynamics ties these ideas together with a simple equation:
ΔU = Q − W
Here, Q is the heat added to the system and W is the work done by the system. If you add 500 joules of heat to a gas and it does 200 joules of work expanding against its surroundings, the internal energy rises by 300 joules. The equation is really just a statement of conservation of energy: energy doesn’t appear from nothing or vanish into nothing. It flows in as heat, flows out as work (or vice versa), and whatever is left over changes the system’s internal energy.
The sign conventions matter. Heat flowing into the system is positive Q; heat leaving is negative. Work done by the system on its surroundings is positive W; work done on the system is negative. These conventions keep the bookkeeping consistent across every thermodynamic problem.
Energy Depends on the Type of System
How freely energy moves depends on the boundaries you draw. Thermodynamics classifies systems into three types based on what those boundaries allow.
- Isolated systems exchange neither energy nor matter with their surroundings. Total internal energy stays constant. A perfectly insulated sealed container is the textbook example (though no real container is perfectly insulated).
- Closed systems exchange energy (as heat or work) but not matter. A sealed piston-cylinder setup is a classic case: the gas inside can expand, doing work, and heat can flow through the cylinder walls, but no gas escapes.
- Open systems exchange both energy and matter. A boiling pot without a lid, a jet engine, or your body are all open systems. Energy flows in and out freely alongside the material that crosses the boundary.
Most real-world engineering problems involve open or closed systems, where tracking energy transfers is the whole point of the analysis.
Enthalpy: Internal Energy at Constant Pressure
Many processes, especially chemical reactions in open containers, happen at constant pressure rather than constant volume. In those situations, some of the energy released or absorbed goes into expanding or compressing the system against atmospheric pressure. To account for this automatically, thermodynamics defines a related quantity called enthalpy (H):
H = U + PV
The PV term represents the energy associated with the system maintaining its volume against the surrounding pressure. Enthalpy is what you’re actually measuring when you look up the “energy released” by burning a fuel or mixing two chemicals at atmospheric pressure. It’s not a fundamentally different kind of energy. It’s internal energy plus the pressure-volume work baked in, packaged for convenience.
Why Not All Energy Is Available for Use
Knowing a system’s total internal energy doesn’t tell you how much useful work you can actually extract from it. This is where entropy, the measure of molecular disorder, enters the picture.
At any given temperature T, a portion of the internal energy is “locked up” by the system’s disorder and can’t be converted into work. The energy that remains available depends on which conditions are held fixed. At constant temperature and volume, the useful energy is captured by the Helmholtz free energy: F = U − TS, where S is entropy. At constant temperature and pressure (the most common real-world scenario), the useful energy is the Gibbs free energy: G = H − TS.
This distinction matters enormously. A chemical reaction might release a large amount of total energy, but if it also creates a great deal of disorder, the portion available to do useful work is smaller. Equilibrium, the state a system naturally settles into, occurs at the minimum of the appropriate free energy, not at the minimum of internal energy alone. That is why minimizing U or H alone isn’t enough to predict what a system will do. Nature doesn’t just seek low energy; it seeks the best trade-off between low energy and high disorder.
The Joule: Measuring Energy
Energy in thermodynamics is measured in joules (J) in the SI system. The unit is named after James Prescott Joule, who demonstrated in the 1840s and 1850s that mechanical work and heat are interchangeable forms of energy. In his most famous experiment, falling weights turned a paddle wheel inside an insulated container of water, and the resulting temperature rise let him calculate the precise exchange rate: raising one pound of water by one degree Fahrenheit required the equivalent of 772 foot-pounds of mechanical work. The modern accepted value is 778.0 foot-pounds per British thermal unit.
Joule’s work proved that heat is not a separate substance (as scientists of his era believed) but a form of energy transfer, subject to the same conservation laws as any mechanical process. That insight is the experimental foundation of the first law, and the reason the SI unit of energy bears his name. You encounter joules constantly: every nutrition label lists food energy in kilojoules alongside calories, and both are simply different-sized units for the same underlying quantity.