Heat, Work & Internal Energy
Every system — whether a gas in a cylinder, a cup of water, or a steel rod — possesses an internal energy U, which is the total kinetic and potential energy of all its microscopic particles. Unlike temperature, which measures the average kinetic energy per particle, internal energy is an extensive quantity: double the amount of gas and you double U. The central question of thermodynamics is: how does U change? The answer involves exactly two mechanisms — heat and work. Heat (Q) is energy transferred between a system and its surroundings purely because of a temperature difference, like warmth flowing from your hand into a cold metal railing. Work (W) is energy transferred by a macroscopic force acting through a displacement — for example, a piston being pushed into a gas compresses it and does work on it. Neither heat nor work is 'stored' inside the system; they are energy in transit. Once the transfer is complete, the system simply has a new internal energy U. The First Law of Thermodynamics ties these ideas together in one of the most powerful conservation laws in physics: the change in internal energy equals the heat added to the system minus the work done by the system. This single equation underlies steam engines, refrigerators, biological metabolism, and atmospheric science. Understanding its sign convention and physical meaning is the foundation for all further study of thermodynamics.
- Internal Energy (U)
- Heat (Q) — Energy Transfer by Temperature Difference
- Work (W) — Energy Transfer by Force
- The First Law: Putting It Together
- Special Cases Worth Knowing
Internal Energy (U)
Internal energy U is the sum of all microscopic kinetic energies (translational, rotational, vibrational motion of molecules) and all intermolecular potential energies. For an ideal monatomic gas, U = (3/2)nRT, where n is the number of moles and R is the gas constant. Crucially, U is a state function — its value depends only on the current state (temperature, pressure, volume) of the system, not on how the system got there. ΔU = U_final − U_initial.
Heat (Q) — Energy Transfer by Temperature Difference
Heat is not a substance; it is the process of energy flowing spontaneously from a hotter region to a cooler one via conduction, convection, or radiation. By convention used in most physics courses (IUPAC/physics convention): Q > 0 means heat flows INTO the system (endothermic), and Q < 0 means heat flows OUT of the system (exothermic). Think of Q as your bank deposit — positive means money coming in.
Work (W) — Energy Transfer by Force
For a gas, the most common form of work is pressure-volume (PV) work. When a gas expands against an external pressure P_ext, it does work W = P_ext ΔV on the surroundings. Convention: W > 0 means work done BY the system (gas expands, pushes piston out), and W < 0 means work done ON the system (gas compressed). This is the physics/IUPAC convention. Note: some chemistry textbooks flip the sign of W, so always check which convention is in use.
The First Law: Putting It Together
ΔU = Q − W. If you add 500 J of heat to a gas (Q = +500 J) and the gas expands doing 200 J of work on a piston (W = +200 J), the internal energy rises by only 300 J. The remaining 200 J was 'spent' pushing the piston. Think of it like earning £500 but spending £200 on bills — your savings (internal energy) only grow by £300. This accounting always balances; energy is never created or destroyed.
Special Cases Worth Knowing
Four idealized processes appear constantly. (1) Isothermal: ΔT = 0, so for an ideal gas ΔU = 0, meaning Q = W. (2) Adiabatic: Q = 0, so ΔU = −W; the system's energy changes only through work. (3) Isochoric (constant volume): W = 0 (no PV work), so ΔU = Q; all heat goes into internal energy. (4) Isobaric (constant pressure): W = PΔV, and both Q and W are nonzero. These cases let us make predictions without integrating complex equations.
The Key Equation
- \Delta U — Change in internal energy (J (joules)): The increase or decrease in total microscopic energy of the system. Positive ΔU means the system gained energy internally.
- Q — Heat transferred to the system (J (joules)): Energy entering the system due to a temperature difference. Positive when heat flows in; negative when heat flows out.
- W — Work done by the system (J (joules)): Energy leaving the system via mechanical work (e.g., gas expanding against a piston). W = P_ext ΔV for constant-pressure processes.
Worked Example
Problem. A gas inside a cylinder absorbs 800 J of heat from a heater. At the same time, the gas expands and pushes a piston outward, doing 320 J of work on the piston. (a) What is the change in internal energy of the gas? (b) If the gas is then compressed adiabatically, requiring 150 J of work to be done ON the gas, what is the new change in internal energy for this second process?
Answer. Part (a): ΔU = +480 J. Part (b): ΔU = +150 J.
Origins · 1 minJames Prescott Joule and how this was discovered
Joule performed meticulous experiments in the 1840s demonstrating that mechanical work could be converted into heat in a precise, reproducible ratio — the 'mechanical equivalent of heat'. By using a falling weight to turn paddle wheels inside water and measuring the temperature rise, he showed that 4.18 J of work produced the same temperature change as 1 calorie of heat. His experiments provided the crucial experimental foundation for the First Law of Thermodynamics and the principle of energy conservation. The SI unit of energy, the joule (J), is named in his honour. Joule was so dedicated to measurement that, according to legend, he spent part of his honeymoon in the Alps measuring the temperature difference between the top and bottom of a waterfall — testing his own theories about energy conversion in nature.
Related Concepts
- Specific Heat Capacity — Specific heat capacity determines how much heat Q is needed to change a substance's temperature, directly linking Q to ΔU in constant-volume processes.
- Thermodynamic Processes (Isothermal, Adiabatic, Isobaric, Isochoric) — These four special processes are defined by constraints on Q, W, or ΔU, and are the main applications of the First Law equation.
- Kinetic Theory of Gases — Kinetic theory explains internal energy at the molecular level, giving U = (3/2)nRT for ideal gases and justifying why temperature determines internal energy.
- Entropy and the Second Law of Thermodynamics — The Second Law constrains which energy transfers are possible, complementing the First Law's accounting of how much energy is transferred.