Systems, States, and the First Law

Choosing the system

A fuel can warm a saucepan, turn an engine, or supply electrical energy through a cell. These effects look different, yet each involves energy being transferred or transformed. Thermodynamics studies such changes using the measurable properties of large collections of particles. Its starting point is a choice: exactly which part of the situation will we study?

For a reaction in a beaker, we might choose the reacting mixture as the system. The beaker, air, and laboratory then belong to the surroundings. A boundary separates the two. It can be a real wall or an imaginary surface around a chosen volume. Changing the selection changes the bookkeeping, so state it before discussing heat, work, or matter flow.

An uncovered reacting mixture is an open system because material may enter or leave and energy may cross the boundary. A sealed conducting vessel is closed: it keeps its matter but can exchange heat. An ideally sealed and insulated vessel is isolated. A real thermos approximates isolation for a limited time; no everyday container insulates perfectly.

Describing a state

Following the position and speed of every molecule would be impossible in a chemical calculation. Instead we describe a state using bulk properties such as pressure, volume, temperature, amount, and composition. At equilibrium these macroscopic properties remain steady. Thermodynamics relates equilibrium states and the energy changes between them; it does not by itself tell us how fast a reaction reaches its final state.

Not every state variable is independent. For a fixed amount of ideal gas, specifying its pressure and temperature fixes its volume through the gas equation. For a reacting mixture, the composition must also be known. Two samples at the same temperature need not have the same energy if they contain different amounts or different substances.

Internal energy, heat, and work

Atoms and molecules have energy associated with motion, interactions, and their internal structures. Internal energy, represented by $U$, includes the microscopic energy of the system. We usually cannot assign its absolute value experimentally. We can determine a change, $\Delta U=U_{\mathrm{final}}-U_{\mathrm{initial}}$, by measuring energy transferred to or from a suitably defined system.

Joule compared mechanical stirring of insulated water with electrical heating through a resistor. When equal amounts of work produced the same final state from the same initial state, the measured temperature changes agreed. The route for doing work differed, but the resulting internal-energy change was fixed by the endpoints. In an adiabatic experiment all the transferred energy is work, so $\Delta U=w_{\mathrm{ad}}$.

The chemical sign convention keeps the system at the centre of the account. Heat absorbed by it is positive; heat released is negative. Work done on it is positive; work done by it is negative. The signs describe direction, not whether an interaction is useful or desirable.

Conserving energy

A system can receive heat and work during the same process. Its net energy gain is the algebraic sum of both transfers. For a closed system with negligible changes in its overall kinetic and gravitational potential energies, the first law gives the internal-energy change in this form.

In an isolated system both transfers are zero, so its internal energy stays constant. Energy can still change form or redistribute inside it. For example, chemical energy can become thermal energy without energy appearing from nowhere. For a fixed pair of states, $q$ and $w$ may individually change with the route, but their sum must equal the same $\Delta U$.