Energy, Heat & Work

The vocabulary of energy — system, surroundings, and the crucial difference between heat and temperature.

High schoolIntro Gen ChemUni Year 1
⏱️ About 16 min

Touch a metal railing and a wooden bench on the same cold morning: the metal feels far colder, yet a thermometer says they're the same temperature. That puzzle is the whole point of thermochemistry — heat and temperature are not the same thing, and once you separate them, energy bookkeeping suddenly makes sense.

💡
The big idea: Energy is never created or destroyed — it only moves. We split the universe into the SYSTEM we care about and its SURROUNDINGS, then track energy crossing the boundary as heat (q) or work (w). A system's internal energy changes by exactly what flows in or out.
🎯 By the end, you'll be able to
  • Define the system, surroundings, and the boundary between them
  • Distinguish heat from temperature, and explain why heat flows from hot to cold
  • Recognise internal energy as a state function, and heat and work as path functions
  • Apply the first law ΔU = q + w with correct signs
📎 Helpful to know first

System, surroundings, and the boundary

To study energy we first draw a line. The system is the part of the universe we're focused on — the reacting chemicals, say. Everything else — the beaker, the air, the bench, the rest of the cosmos — is the surroundings. The imaginary line between them is the boundary, and energy is tracked as it crosses that line.

Energy crosses in just two forms: heat (q), the flow driven by a temperature difference, and work (w), energy transferred by a force acting through a distance (for gases, usually pushing back the atmosphere as they expand). Everything in this module is careful bookkeeping of those two flows.

🔑 Heat is not temperature
Temperature measures the average kinetic energy of the particles — how fast they jiggle on average. Heat is energy in transit from a hotter object to a cooler one. A bathtub of warm water holds far more total energy than a spark at 1000 °C, even though the spark is much hotter. Temperature is intensity; heat is a quantity that moves.

Heat always flows hot → cold

Here's a phrase to bury for good: "the cold from the freezer got into my hand." Cold is not a substance and it does not flow. What actually happens is the reverse — heat flows out of your warm hand into the cold air, and losing that energy is what your nerves register as "cold."

This is why the metal railing feels colder than the wooden bench at the same temperature: metal conducts heat away from your skin quickly, so heat leaves your hand faster. Same temperature, very different rate of heat flow.

✨ State functions vs path functions
A state function depends only on the current state, not on how you got there — like altitude on a mountain: the summit's height is the same whether you hiked the easy trail or the cliff. Internal energy (U) is a state function. But heat (q) and work (w) are path functions — the amounts depend on the route taken. Their sum, ΔU, does not.

The first law: energy is conserved

Internal energy (U) is the total energy stored in a system — the kinetic and potential energy of all its particles. We can't measure U directly, but we can measure how it changes. The first law of thermodynamics says the change equals the heat added plus the work done on the system:

\[ \Delta U = q + w \]
Sign convention: q > 0 = heat flows INTO the system; w > 0 = work done ON the system. A system that releases heat or does work on its surroundings gets a minus sign.
⚠️ Getting the signs right
Think from the system's point of view. Energy coming in is positive; energy going out is negative. Heat absorbed by the system: +q. Heat released: −q. Work done on the system (compressed): +w. Work done by the system (it expands and pushes out): −w.
📝 Worked example: A gas absorbs 500 J of heat from its surroundings and, as it warms, expands and does 200 J of work on the surroundings. What is ΔU?
  1. Heat is absorbed by the system, so q = +500 J.
  2. The system does work on the surroundings (it expands outward), so energy leaves: w = −200 J.
  3. Apply the first law: ΔU = q + w = (+500) + (−200).
  4. ΔU = +300 J.
✓ ΔU = +300 J — the system's internal energy rose by 300 J.
✏️ Practice: A system releases 350 J of heat to its surroundings while the surroundings do 120 J of work compressing it. What is ΔU (in joules)?
J
Solution
  1. Heat is released by the system, so q = −350 J.
  2. Work is done on the system (it is compressed), so w = +120 J.
  3. ΔU = q + w = (−350) + (+120).
  4. ΔU = −230 J — the internal energy fell by 230 J.

Check your understanding

1. A hot cup of coffee cools down in a cool room. What is actually happening?
Heat always flows from hotter to cooler. There is no "cold" moving in — energy (heat) leaves the coffee for the room, so the coffee cools.
2. Which statement about heat and temperature is correct?
Temperature = average kinetic energy (an intensity). Heat = energy in transit between objects at different temperatures. A big warm bath has more total energy than a tiny hotter spark.
3. Which quantity is a state function (independent of the path taken)?
Internal energy depends only on the current state. Heat and work are path functions — how much of each is exchanged depends on the route — but their sum, ΔU, is path-independent.
🔎 Related lessons
Next: Enthalpy & Calorimetry Entropy, Gibbs Energy & Spontaneity Collision Theory & Activation Energy
✅ Key takeaways
  • The system is what we study; the surroundings are everything else; energy is tracked crossing the boundary.
  • Temperature = average kinetic energy (intensity); heat = energy transferred because of a temperature difference.
  • Heat flows from hot to cold — "cold flowing in" is just heat flowing out.
  • Internal energy U is a state function; heat and work are path functions.
  • First law: ΔU = q + w, with energy IN positive and energy OUT negative.
➡️ Most chemistry happens in open beakers at constant (atmospheric) pressure, where the heat exchanged has a special name and symbol: enthalpy, ΔH. That's exactly what we measure — and how we measure it — next.
Want to test yourself on this? Try the Chemistry practice test →