The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. In any system, the total amount of energy stays constant. What changes is the form that energy takes: heat can become motion, motion can become heat, and stored energy can become either one. This principle is one of the most fundamental rules in all of physics.
The Core Idea: Energy In, Energy Out
Think of any system (an engine, a balloon full of gas, your own body) as having an energy bank account. Energy can flow in through heat, and energy can flow out through work. Whatever is left over changes the balance of the account, which physicists call the system’s internal energy. The first law simply says: the change in your energy balance equals the heat that flows in minus the work that flows out.
Written as an equation, it looks like this: ΔU = Q − W. Here, ΔU is the change in internal energy, Q is the net heat transferred into the system, and W is the net work done by the system. If you add 100 joules of heat and the system does 40 joules of work, the internal energy increases by 60 joules. The math always balances because energy has nowhere else to go.
There’s a small but important note about sign conventions. The version above (ΔU = Q − W) treats work done by the system as positive. The modern IUPAC convention flips this, writing ΔU = Q + W, where W is positive when work is done on the system. Both describe the same physics. If you’re reading a textbook or solving problems, just check which convention is being used.
What Internal Energy Actually Means
Internal energy is the total energy stored inside a substance at the microscopic level. It includes the kinetic energy of atoms and molecules as they vibrate, rotate, and move around, plus the potential energy stored in the bonds between them. A hot cup of coffee has more internal energy than a cold one because its molecules are moving faster.
Crucially, internal energy does not include the energy of the system’s interaction with its surroundings. If you lift a gas cylinder to a high shelf, its gravitational potential energy increases, but its internal energy stays the same because the molecules inside haven’t changed their behavior. Internal energy is purely about what’s happening inside.
Heat and Work: Two Ways to Transfer Energy
Heat and work are not types of energy that a system “has.” They are processes, ways that energy moves across a boundary. Heat is energy transferred because of a temperature difference. Work is energy transferred by a force moving through a distance. A flame under a pot transfers energy as heat. A piston compressing gas transfers energy as work.
This distinction matters because the first law tracks both pathways. You could raise the internal energy of a gas by heating it, by compressing it, or by some combination of the two. The final change in internal energy depends only on how much total energy entered and left, not on which pathway delivered it.
How It Applies to Common Processes
The first law simplifies in useful ways depending on the conditions of a process. Four classic cases show up repeatedly in physics and engineering.
- Constant pressure (isobaric): The work done by the system equals the pressure multiplied by the change in volume. Heating a gas in a cylinder with a freely moving piston is a good example. The gas expands, doing work against the piston, while also gaining internal energy.
- Constant volume (isochoric): If volume doesn’t change, no expansion or compression work is done (W = 0). All heat added goes directly into raising internal energy. This is what happens when you heat a rigid, sealed container.
- Constant temperature (isothermal): For an ideal gas held at constant temperature, internal energy doesn’t change (ΔU = 0). That means all the heat added to the gas is converted entirely into work. The gas expands, doing work, but never gets hotter.
- No heat transfer (adiabatic): When a system is perfectly insulated so no heat flows in or out (Q = 0), the change in internal energy equals the negative of the work. Compress the gas and it heats up. Let it expand and it cools down. This is why air gets warmer when you pump a bicycle tire.
Open, Closed, and Isolated Systems
The first law applies to every type of system, but the equation looks a little different depending on whether matter can cross the boundary. In a closed system, no material enters or leaves, so you only track heat and work. A sealed piston-cylinder setup is the classic example, and the standard ΔU = Q − W equation applies directly.
An open system allows matter to flow in and out, like a turbine or a jet engine. Because the incoming and outgoing material carries energy with it, the equation has to account for that flow. Engineers use a property called enthalpy (which bundles internal energy together with the energy needed to push fluid through the boundary) to keep the bookkeeping straight.
An isolated system exchanges neither energy nor matter with its surroundings. No heat in, no work out, no material crossing the boundary. The first law simplifies to: internal energy stays constant, period.
Your Body Follows the Same Rule
Human metabolism is a living demonstration of the first law. Your body converts the chemical energy in food into heat, mechanical work, and a stored energy molecule called ATP. The food you eat is the energy input. The heat you radiate, the physical work you do, and the energy stored in body tissues are the outputs. The balance always holds.
Not all of that food energy becomes useful work, though. Metabolic efficiency varies by fuel source. Carbohydrates convert to usable energy at roughly 35% efficiency, fats at about 32%, and amino acids (protein) at only around 10%. The rest is released as heat, which is why you warm up during exercise and why eating itself raises your body temperature slightly.
What the First Law Cannot Tell You
The first law is powerful, but it has a blind spot: it says nothing about direction. Consider a hot cup of coffee sitting on a counter. It cools down as heat flows into the cooler room. The first law would be equally satisfied if the coffee spontaneously got hotter by absorbing heat from the room, because the total energy would still be conserved. But that never happens.
Explaining why processes go one way and not the other requires the second law of thermodynamics, which introduces the concept of entropy. A process will only occur if it satisfies both laws. The first law ensures the energy books balance. The second law ensures the process runs in a direction that nature actually permits. Together, they form the foundation for understanding everything from engines to ecosystems.