What you'll be able to do: Define the system and surroundings for a chemical change and assign the correct sign to heat transferred.
Almost every thermochemistry mistake is a sign mistake, and almost every sign mistake comes from not deciding what the system is. This lesson sets up that vocabulary once so the calculations later stay clean.
These are recommended, not required. You can start this lesson at any time.
The system is the part of the universe you are studying, normally the chemicals reacting. The surroundings are everything else that can exchange energy with it: the solvent, the container, the air. Deciding this first is what fixes every sign that follows.
The system boundary is a choice that must remain consistent. In reaction calorimetry, one useful convention treats the chemical transformation as the system and the solution plus cup as the thermal surroundings. You could instead define the entire cup and contents as the system, but the energy crossing that larger boundary would be different. An open system exchanges matter and energy; a closed one exchanges energy but not matter; an isolated idealization exchanges neither. These labels describe the chosen boundary, not whether a chemical reaction occurs.
Energy cannot be created or destroyed, only moved or converted. For a chemical change this means the energy released by breaking and forming bonds has to appear somewhere else, usually as warmer water.
Written out, the internal energy change of the system equals the heat added plus the work done on it.
DE = q + w
Signs are written from the point of view of the system. Heat entering the system is positive, so an endothermic change has q > 0 and the surroundings cool.
Heat leaving the system is negative, so an exothermic change has q < 0 and the surroundings warm.
Temperature is an intensive property related to microscopic energy distributions; for an ideal gas it is proportional to mean translational kinetic energy. Heat is an amount of energy transferred. A bathtub of warm water at 40 C holds far more thermal energy than a cup at 90 C even though the cup is hotter.
Two samples at the same temperature can have different internal energies because they contain different amounts or kinds of material. Temperature determines the direction of spontaneous heat flow: heat passes from the hotter body to the colder one when they are thermally connected. “Heat contained in a body” is imprecise; heat is energy during transfer. Internal energy includes microscopic kinetic and potential contributions, so temperature alone does not specify it. Temperature is directly proportional to mean translational kinetic energy for an ideal gas, rather than being identical to energy for every material.
Breaking bonds always costs energy and forming bonds always releases it. A reaction is exothermic when the bonds formed in the products are collectively stronger than the bonds broken in the reactants. That single idea will return in the bond enthalpy lesson.
The first law is ΔU = q + w for a system. Heat entering the system is positive q; expansion against an external pressure is negative work because the system transfers energy to the surroundings. A temperature change alone does not identify the entire internal-energy change when work also occurs. Define the system and sign convention before adding energy terms.
For pressure-volume work, w = −PextΔV at constant external pressure. Expansion has ΔV > 0 and negative w; compression has ΔV < 0 and positive w. With Pext = 1.00 atm and expansion by 2.00 L, w = −2.00 L·atm = −203 J, using 1 L·atm = 101.325 J. If the gas also absorbs 300 J, ΔU = +300 − 203 = +97 J. “Does 203 J of work” reports a positive magnitude in words but contributes −203 J to this sign convention.
At constant volume with no other work, qv = ΔU. At constant pressure with only pressure-volume work, qp = ΔH. An adiabatic process has q = 0, but work can still change internal energy. Thus an expanding insulated gas can cool without losing heat. Heat and work are path dependent; ΔU and ΔH depend on endpoints.
The chemicals or process under study; everything else is the surroundings.
Energy transferred because of a temperature difference, measured in joules.
q is positive when heat flows into the system and negative when heat flows out.
The system releases heat, q(system) < 0, and the surroundings get warmer.
The system absorbs heat, q(system) > 0, and the surroundings get cooler.
DE = q + w
q(system) = -q(surroundings)
A solid dissolves in water and the water temperature falls from 22.0 C to 18.4 C. Is dissolving endothermic or exothermic, and what is the sign of q for the dissolving process?
Try it first: Decide which part is the system before looking at the thermometer.
0 of 4 steps revealed.
Burning 1.00 g of methane in a calorimeter raises the water temperature. State the signs of q(reaction) and q(water), and explain why they differ.
0 of 3 steps revealed.
A gas absorbs 300 J of heat while doing 100 J of work on its surroundings. Find ΔU.
Try it first: Assign signs from the gas system's point of view.
0 of 3 steps revealed.
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Quoting the reaction enthalpy as positive because the temperature went up. | A rising thermometer describes the surroundings, not the system. | Water warms means the reaction released heat, so the reaction q is negative. |
| Treating heat and temperature as the same quantity. | Temperature is intensive; heat depends on how much material there is. | Ask whether the quantity would change if you doubled the sample. |
| Changing the system boundary midway through a calorimetry calculation. | The usual reaction-calorimetry convention counts solution and cup as thermal surroundings; a different consistent boundary is possible but changes the balance. | State and keep one system boundary; for the standard reaction-calorimetry convention use the chemical transformation as the system. |
| Saying an endothermic reaction feels warm. | It draws heat out of its surroundings, including your hand. | Endothermic feels cold to the touch. |
Scroll horizontally if needed to read all columns.
After the lesson · Question bank
Work through new problems on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
34 topic questions across 3 difficulty levels.
Loading practice questions…
Energy is conserved: whatever the system loses, the surroundings gain. The system is the reacting chemicals, the surroundings are everything else, usually the water and the calorimeter. Heat flowing into the system is positive, heat flowing out is negative. An exothermic reaction releases heat, so q(system) is negative while the surrounding water warms up. Endothermic is the reverse. Temperature measures average kinetic energy; heat is energy in transit because of a temperature difference. The two are not the same thing.
Lesson: Not marked completed
Marking a lesson completed records that you finished reading it. Practice establishes mastery separately. Saved on this device.
Try a short set of different questions to check what you can do independently.
An optional video to support this lesson.
Loading video resources…
External resources belong to their respective creators. Chem Help is not affiliated with or endorsed by these providers. Links open the original provider; their terms apply.
Lesson-specific rights and provenance need review.
The current online Chemistry 2e edition lists CC BY-NC-SA 4.0. The source version used for this lesson and its applicable rights remain unverified.
Recorded use: reference. This describes the stored citation, not verified authorship or reuse permission.
Recorded attribution / license claim (applicability unverified): Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0.
Source rights and review status