First Law of Thermodynamics

Conservation of Energy

The first law of thermodynamics states that the total energy of an isolated system is constant. Energy can change form — from heat to work, from chemical to kinetic, from potential to thermal — but it cannot be created or destroyed. This is the most fundamental bookkeeping rule in all of physics.

In thermodynamic terms: the change in internal energy of a system equals the heat added to the system minus the work done by the system on its surroundings.

Internal Energy

Internal energy (U) is the total microscopic energy of a system — the sum of kinetic and potential energies of all its atoms and molecules. It includes molecular translational, rotational, and vibrational motion, as well as the energy stored in chemical bonds and intermolecular forces.

Internal energy is a state function: it depends only on the current state of the system (temperature, pressure, composition), not on how the system reached that state. This means that ΔU between two states is always the same, regardless of the path taken.

Heat and Work: Two Ways to Transfer Energy

Heat (Q) is energy transferred between systems due to a temperature difference. Heat flows spontaneously from higher to lower temperature — a consequence of the second law. At the molecular level, heat transfer occurs through collisions between faster (hotter) and slower (cooler) molecules.

Work (W) is energy transferred when a force acts through a distance. In thermodynamics, the most common form is pressure-volume work: a gas expanding against a piston performs work W = ∫P dV. Electrical work, shaft work, and other forms are also included.

The crucial insight of the first law is that heat and work are interchangeable — they are both ways of transferring energy. James Joule demonstrated this in the 1840s by showing that mechanical work (stirring water with a paddle wheel) produced the same temperature increase as an equivalent amount of heat.

Applications of the First Law

Adiabatic Processes

When Q = 0 (no heat exchange), the first law gives ΔU = −W. Compressing a gas adiabatically does work on it, increasing its internal energy and temperature. This is why a bicycle pump gets hot when you compress air quickly.

Isothermal Processes

At constant temperature, ΔU = 0 for an ideal gas, so Q = W. All heat added is converted to work. This describes a gas expanding slowly enough to maintain thermal equilibrium with its surroundings.

Isochoric Processes

At constant volume, W = 0, so ΔU = Q. All heat added goes directly to increasing internal energy (and temperature). Heating a sealed, rigid container is an example.

Why Perpetual Motion Machines Cannot Exist

The first law rules out perpetual motion machines of the first kind — devices that produce work without any energy input. Such a machine would create energy from nothing, violating conservation of energy. Every proposed perpetual motion machine, when analysed carefully, either has a hidden energy source or does not actually work.

Historical Context

The first law emerged from the work of Julius Robert von Mayer (1842), James Prescott Joule (1843–1849), and Hermann von Helmholtz (1847). Joule's paddle-wheel experiment — in which falling weights stirred water and measured the resulting temperature rise — established the mechanical equivalent of heat and demonstrated that heat and work are interconvertible forms of energy.