First Law of Thermodynamics
The First Law of Thermodynamics is one of the most fundamental principles in all of physics: energy cannot be created or destroyed, only transferred or transformed. When applied to a thermodynamic system — any well-defined collection of matter we choose to study — this law says that the change in the system's internal energy equals the heat added to it minus the work it does on its surroundings. It is, at its core, a bookkeeping rule for energy, and it holds without exception from steam engines to living cells to the interior of stars. Think of internal energy like a bank account balance. Heat flowing into the system is a deposit, work done by the system is a withdrawal, and the balance at the end reflects all those transactions. If you add 500 J of heat to a gas but the gas expands and does 200 J of work pushing a piston, the internal energy rises by exactly 300 J — no energy mysteriously appears or vanishes. This is why perpetual-motion machines of the first kind (devices that produce energy from nothing) are physically impossible: they would violate this law. Historically, the First Law resolved a long-standing confusion between heat and work. Scientists in the early 19th century gradually realized both are forms of energy transfer, not fundamentally different substances. James Joule's famous paddle-wheel experiments in the 1840s quantified the mechanical equivalent of heat, proving that a precise amount of mechanical work always produces a precise amount of thermal energy — the ratio now embedded in the definition of the joule itself. Today the First Law underpins every heat engine, refrigerator, and chemical reaction analysis you will encounter in physics and chemistry.
- Defining the System and Surroundings
- Sign Convention
- Internal Energy and Microscopic Interpretation
- Work Done by a Gas
- Special Processes
Defining the System and Surroundings
Before applying the First Law you must clearly define your system (the gas inside a cylinder, a sample of water, etc.) and the surroundings (everything outside). Energy can cross the boundary as heat Q or as work W. Internal energy U is a state function — it depends only on the current state of the system, not on how it got there.
Sign Convention
Physics uses the convention ΔU = Q − W. Heat Q is positive when it flows INTO the system (warming it) and negative when it flows out. Work W is positive when done BY the system on the surroundings (e.g., gas pushing a piston outward) and negative when done ON the system. Chemistry courses sometimes write ΔU = Q + W with the opposite sign for W, so always check which convention is being used.
Internal Energy and Microscopic Interpretation
Internal energy U is the sum of all microscopic kinetic and potential energies of the particles in a system — random translational, rotational, and vibrational motion of molecules, plus intermolecular potential energy. For an ideal monatomic gas, U = (3/2)nRT, so temperature is a direct measure of internal energy. When you heat a gas, you are literally speeding up its molecules.
Work Done by a Gas
For a gas expanding against a constant external pressure P, the work done by the gas is W = PΔV, where ΔV is the change in volume. When a gas expands (ΔV > 0), it does positive work on the surroundings — useful work that can drive a piston, turn a turbine, or power an engine. When compressed (ΔV < 0), the surroundings do positive work on the gas, increasing its internal energy.
Special Processes
Four idealized processes illustrate the First Law clearly. (1) Isothermal (constant temperature): ΔU = 0, so Q = W — all heat input becomes work. (2) Adiabatic (no heat exchange): Q = 0, so ΔU = −W — internal energy changes only through work. (3) Isochoric (constant volume): W = 0, so ΔU = Q — all heat goes into changing internal energy. (4) Isobaric (constant pressure): both Q and W are non-zero and ΔU = Q − PΔV.
The Key Equation
- \Delta U — Change in internal energy (joule (J)): The net change in total microscopic kinetic and potential energy of all particles in the system. Positive ΔU means the system gained energy.
- Q — Heat transferred (joule (J)): Energy crossing the system boundary due to a temperature difference. Q > 0 means heat flows into the system; Q < 0 means heat flows out.
- W — Work done by the system (joule (J)): Energy transferred when the system exerts a force through a displacement. For gas expansion against pressure P, W = PΔV. W > 0 means the system does work on surroundings.
Worked Example
Problem. A gas in a cylinder absorbs 800 J of heat from a flame. At the same time, the gas expands and pushes a piston outward, doing 300 J of work on the piston. What is the change in internal energy of the gas?
Answer. The internal energy of the gas increases by 500 J.
Origins · 1 minJames Prescott Joule and how this was discovered
Joule conducted meticulous experiments in the 1840s demonstrating that mechanical work and heat are equivalent forms of energy. His famous paddle-wheel experiment measured the mechanical equivalent of heat by using falling weights to stir water and recording the precise temperature rise. His results showed that 4.18 J of mechanical work produces 1 calorie of heat — directly establishing the quantitative foundation of the First Law and the concept of energy conservation in thermodynamics. The SI unit of energy, the joule (J), is named in his honor. Joule was a brewer by trade, not a university professor. He conducted his groundbreaking experiments in the laboratory attached to his family's brewery, funding the research himself. He reportedly even measured the temperature difference in waterfalls during his honeymoon to test his energy-conservation ideas.
Related Concepts
- Second Law of Thermodynamics — The Second Law complements the First by specifying the direction in which energy transfers occur — heat naturally flows from hot to cold — introducing the concept of entropy as a measure of irreversibility.
- Internal Energy and Heat Capacity — Internal energy U is the central quantity in the First Law. Understanding heat capacity (how much heat is needed per degree of temperature rise) lets you calculate ΔU and Q for real substances.
- Thermodynamic Processes and PV Diagrams — PV diagrams graphically represent isothermal, adiabatic, isochoric, and isobaric processes, and the area under a PV curve equals the work W done by the gas — a direct application of the First Law.
- Heat Engines and Efficiency — Heat engines convert thermal energy into work. Their efficiency analysis is built directly on the First Law — the work output can never exceed the heat input — placing an upper bound on engine performance.