Energy and Heat

1. Kinetic vs. Potential Energy

Kinetic energy is the energy of motion, depending on mass and speed. Potential energy is stored energy of position or composition — a stretched spring, a ball on a shelf, or chemical bonds. In any chemical sample the molecules are always moving (kinetic energy), while electrostatic attractions between nuclei, electrons, and neighboring molecules store potential energy. Reactions are useful precisely because they convert bond potential energy into heat and work.

2. System and Surroundings

The system is the substance or reaction under study; the surroundings are everything else. An open system exchanges both matter and energy (a boiling pot); a closed system exchanges energy but not matter (a sealed bottle); an isolated system exchanges neither (an ideal thermos). Energy crosses the boundary in only two forms: heat (q) or work (w).

3. State Functions and the First Law

Internal energy E is the total kinetic plus potential energy of the particles in a system. We cannot measure E itself, only ΔE = E_final - E_initial. Crucially, E is a state function: its value depends only on the current state, not on how the system got there. The first law of thermodynamics is conservation of energy applied to a system: ΔE = q + w. Heat and work are path functions, but their sum equals the change in the state function E.

How it works

1. Choose the system and draw a boundary around it; everything else is the surroundings.
2. Identify each energy transfer across that boundary as heat q, work w, or both.
3. Assign signs: energy entering the system is positive; energy leaving is negative.
4. Sum them using ΔE = q + w.
5. If a gas changes volume against constant pressure, compute w = -PΔV and convert units.
6. Interpret the sign of ΔE: positive means the system gained energy, negative means it lost energy.

Common confusions

Memory aids

"In is +, Out is −" — any energy (heat or work) entering the system carries a plus sign, and anything leaving carries a minus sign. Then ΔE = q + w always balances the ledger.

Quick review

Topic Recap

Energy is the capacity to do work or transfer heat, existing as kinetic or potential energy. We track it by defining a system and its surroundings; energy crosses the boundary only as heat q or work w. Internal energy is a state function, and the first law says energy is conserved: ΔE = q + w. Consistent signs — positive for energy in, negative for energy out — make every calculation reproducible, and w = -PΔV quantifies pressure–volume work.

Knowledge Check

1. Which quantity is a state function? A) heat q B) work w C) internal energy E D) path length
2. A system absorbs 40 J of heat and has 15 J of work done on it. ΔE is: A) 25 J B) 40 J C) 55 J D) −25 J
3. A gas expands, doing work on its surroundings. The sign of w for the system is: A) positive B) negative C) zero D) depends on pressure only
4. Which system exchanges energy but not matter with its surroundings? A) open B) closed C) isolated D) none of these
5. A gas is compressed from 4.0 L to 2.0 L at a constant external pressure of 2.0 atm. The work (L·atm) is: A) −4.0 B) +4.0 C) −8.0 D) +8.0

Answers and Rationales

1. C — Internal energy depends only on the state of the system; heat and work depend on the path.
2. C — ΔE = q + w = (+40 J) + (+15 J) = 55 J. Both terms are positive because heat and work both entered the system.
3. B — The system loses energy doing expansion work, so w is negative (w = -PΔV with ΔV > 0).
4. B — A closed system exchanges energy but not matter; an isolated system exchanges neither.
5. B — ΔV = 2.0 - 4.0 = -2.0 L, so w = -(2.0 atm)(-2.0 L) = +4.0 L · atm. Compression means work is done on the system (positive).