First Law of Thermodynamics
The first law of thermodynamics: ΔU = Q - W.
Energy cannot be created or destroyed, only transferred.
Explained with examples.
The Formula
The first law of thermodynamics is simply the law of conservation of energy applied to thermodynamic systems. It states that the change in internal energy of a system equals the heat added to the system minus the work done by the system.
Internal energy (U) represents all the microscopic kinetic and potential energy of the molecules in a system. Heat (Q) is energy transferred due to a temperature difference. Work (W) is energy transferred when a force moves through a distance — in thermodynamics, this usually means a gas expanding against a piston.
The sign conventions are critical: Q is positive when heat flows into the system, negative when heat leaves. W is positive when the system does work on its surroundings (expansion), negative when surroundings do work on the system (compression).
This law has profound implications. You cannot build a perpetual motion machine of the first kind — a device that produces more energy than it consumes. Every process must balance its energy books.
Different thermodynamic processes simplify the first law in different ways. In an isothermal process (constant temperature), ΔU = 0 so Q = W. In an adiabatic process (no heat exchange), Q = 0 so ΔU = −W. In an isochoric process (constant volume), W = 0 so ΔU = Q. In an isobaric process (constant pressure), W = pΔV and ΔU = Q − pΔV.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| ΔU | Change in internal energy | Joules (J) |
| Q | Heat added to the system | Joules (J) |
| W | Work done by the system | Joules (J) |
Example 1
A gas absorbs 500 J of heat and does 200 J of work expanding against a piston.
ΔU = Q − W = 500 J − 200 J
ΔU = 300 J (internal energy increased by 300 J)
Example 2
A gas is compressed, with 300 J of work done on it, and releases 100 J of heat.
Q = −100 J (heat leaves), W = −300 J (work done on system)
ΔU = −100 − (−300) = −100 + 300
ΔU = 200 J (internal energy increased)
When to Use It
- Analyzing heat engines, refrigerators, and heat pumps
- Engineering thermodynamic cycles (Rankine, Brayton, Otto)
- Chemistry: calculating enthalpy changes in reactions
- Any problem involving heat, work, and energy balance