General Chemistry I · Thermochemistry
Energy, Systems, and Surroundings
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In 30 seconds
Thermodynamics is the study of energy and its transformations. To analyze any process, chemists divide the universe into the system (the part under study — a reaction, a beaker of water, a gas in a cylinder) and the surroundings (everything else). Energy flows between them as heat (q) or work (w). The First Law says that energy is conserved: it is neither created nor destroyed, only transferred. This single idea organizes all of thermochemistry.
Why this matters
Every calorie you burn, every engine that runs, every battery that powers a phone, and every explosion is a statement of the First Law. Medicine relies on it directly: the heat your body produces is the energy released from food oxidation, and calorimetry (the measurement of heat) is how nutrition labels are determined. Understanding system/surroundings and sign conventions is the prerequisite for every later topic in thermochemistry — enthalpy, calorimetry, Hess's law, and Gibbs free energy.
The college version
Key Ideas
- Kinetic energy (KE) is energy of motion: KE = ½mv², where m is mass and v is velocity. Atoms and molecules are always in motion (translation, rotation, vibration), so they always possess kinetic energy.
- Potential energy (PE) is stored energy that depends on position or arrangement. A ball held above the floor has gravitational PE; two oppositely charged ions separated by a distance have electrostatic PE. Chemical bonds store chemical potential energy.
- Thermal energy is the total kinetic energy of all particles in a sample — the random motion of atoms and molecules. It is related to, but not identical with, temperature: temperature is the average kinetic energy, while thermal energy depends on the amount of substance as well.
- Chemical energy is the potential energy stored in the arrangement of atoms within molecules (bond strengths, electrostatic attractions). When bonds rearrange in a reaction, chemical energy is converted to or from heat.
- Internal energy (E) is the sum of all kinetic and potential energies of the particles in a system. We cannot measure absolute E, only changes in it (ΔE).
- The First Law: ΔE = q + w. Here ΔE is the change in internal energy, q is heat, and w is work.
Equations and Variables
| Symbol | Meaning | Units |
|---|---|---|
| KE | Kinetic energy | J |
| m | Mass | kg (for KE) |
| v | Velocity | m/s |
| E | Internal energy | J |
| ΔE | Change in internal energy | J |
| q | Heat transferred | J |
| w | Work done | J |
- KE = ½mv²
- ΔE = q + w (energy of system = heat into system + work on system)
Sign conventions (chemistry convention): q > 0 means heat is added to the system (endothermic direction); q < 0 means heat leaves the system (exothermic direction). w > 0 means work is done on the system (compression); w < 0 means the system does work on the surroundings (expansion). A system that loses energy to its surroundings has a negative ΔE; one that gains energy has a positive ΔE.
How It Works
Pick a boundary. Everything inside is the system, everything outside is the surroundings. For a reaction in a beaker, the chemicals are the system and the beaker + air + table are the surroundings. Energy crosses the boundary as heat (because of a temperature difference) or work (because of a force acting through a distance, e.g., a gas pushing a piston).
Because energy is conserved, any energy lost by the system is gained by the surroundings and vice versa. This is written compactly as q_system = −q_surroundings for processes where only heat is exchanged. If a reaction releases 100 J of heat, the surroundings gain exactly 100 J.
State vs. path functions. A state function depends only on the current state of the system, not on how it got there — like altitude: your elevation depends only on where you are, not on the route you hiked. Internal energy E and enthalpy H are state functions, so ΔE depends only on initial and final states. Heat (q) and work (w) are path functions: how much heat you must add depends on the route taken. This is why chemists prefer to work with ΔE and ΔH rather than q and w alone.
Worked Example
A gas absorbs 500 J of heat from its surroundings and does 200 J of work on the surroundings. What is ΔE?
Use ΔE = q + w. Heat is absorbed by the system, so q = +500 J. The system does work on the surroundings, so w = −200 J.
ΔE = (+500 J) + (−200 J) = +300 J.
The system's internal energy increased by 300 J. (Notice the two sign conventions in one problem: heat in is positive, work out is negative.)
Second example — kinetic energy. A 0.500 kg object moves at 2.00 m/s. Its kinetic energy is:
KE = ½mv² = ½ (0.500 kg)(2.00 m/s)² = 0.250 × 4.00 = 1.00 J.
Common Confusions
- q and w signs. Students often flip them. Memorize: energy entering the system is positive; energy leaving the system is negative. "Doing work on the surroundings" = w is negative (system loses energy).
- Temperature vs. thermal energy. A cup of boiling water and a bathtub of warm water can be at different temperatures, yet the tub contains far more thermal energy because it holds far more molecules.
- Heat vs. temperature. Heat (q) is energy transferred; temperature is a measure of average kinetic energy. Adding heat usually raises temperature, but not always (e.g., during a phase change).
- State vs. path functions. Don't say "Δq" as if q were a state function — q depends on path; only E and H have meaningful Δ values that are path-independent.
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine energy is money, and you keep it in different wallets. Sometimes your money is moving fast in your hand (kinetic energy — it's moving). Sometimes it's sitting in a savings account waiting to be used (potential energy — it's stored). The system is you, and the surroundings are everyone else in the world. When you buy something, money leaves your wallet and goes to someone else's — the total amount of money in the world didn't change, it just moved. That's the First Law: energy moves from one place to another, but it's never created or destroyed. If you spend $5, someone else is $5 richer. If a reaction "spends" 100 J of heat, the surroundings are 100 J warmer. Same idea.
Key takeaways
- Energy is conserved (First Law); it changes form but is never created or destroyed.
- ΔE = q + w with the chemistry sign convention (q in = +, w on = +).
- q_system = −q_surroundings (heat lost by one is gained by the other).
- E (internal energy) and H (enthalpy) are state functions; q and w are path functions.
- Temperature reflects average KE; thermal energy reflects total KE (depends on mass too).
- KE = ½mv² — kinetic energy grows with the square of velocity.
- Write the First Law equation and define each term.
- A system has 150 J of work done on it and releases 60 J of heat. Find ΔE.
- Why is heat a path function while internal energy is a state function?
- KE = ½mv²: if you double the speed, by what factor does KE increase?
- Answers: (1) ΔE = q + w; (2) ΔE = (+150 J) + (−60 J) = +90 J; (3) the amount of heat transferred depends on the specific route, whereas E depends only on initial/final state; (4) by a factor of four (v²).
Study tools & related lessonsYou’ll learn to · Related
You’ll learn to
- Distinguish kinetic, potential, thermal, and chemical energy.
- Define the system and the surroundings, and identify open, closed, and isolated systems.
- State the First Law of Thermodynamics and use ΔE = q + w with correct sign conventions.
- Differentiate state functions from path functions.
Sources & references
- OpenStax, *Chemistry 2e*, Ch. 5 "Thermochemistry," §5.1 Energy Basics.
- OpenStax, *Chemistry 2e*, §5.2 Calorimetry.
- NIST — Thermodynamics and thermochemistry reference data.
- IUPAC, "Gold Book" — definitions of energy, heat, work, system.
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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