Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide.
Recap
- q is the energy transferred as heat, in J or kJ. Positive q: the system absorbs heat (its energy rises). Negative q: it releases heat (its energy falls).
- Specific heat capacity, c, is the energy to warm 1 g by 1 °C. Water: 4.18 J g⁻¹ °C⁻¹, unusually large.
- The same energy given to equal masses of different substances gives different temperature changes: the smaller c, the larger ΔT.
- Molar heat capacity is per mole; the heat capacity of an object is for the whole object.
- First law of thermodynamics: energy is conserved. In an insulated calorimeter, energy released by one part is absorbed by the rest.
- A system changes its energy by heating/cooling, phase changes (Topic 6.5) and reactions (Topic 6.6 on).
- Dissolution calorimeter: mixture warms → dissolving is exothermic; mixture cools → dissolving is endothermic.
Key relationships
| Relationship | Units | Use it to |
|---|---|---|
| q = mcΔT | q in J, m in g, c in J g⁻¹ °C⁻¹, ΔT in °C (or K) | heat for a mass of one substance |
| q = nC_mΔT, with C_m = c × M | C_m in J mol⁻¹ °C⁻¹ | heat for an amount in moles |
| q = CΔT, with C = mc | C in J °C⁻¹ | heat for a whole object or a calorimeter |
| ΔT = T(final) − T(initial) | °C or K (same size) | gives q its sign |
| q(lost) + q(gained) = 0 | J | any insulated calorimeter |
| q(process) = −q(solution) | J | energy of dissolving or a reaction in solution |
Assumptions behind the numbers
- No energy is exchanged with the air or bench (perfect insulation).
- The calorimeter absorbs negligible energy, unless its heat capacity is given.
- A dilute solution has c = 4.18 J g⁻¹ °C⁻¹; its mass is water plus solute.
- The final reading is the thermal-equilibrium temperature, after stirring.
Mistakes to avoid
- Sign of ΔT. Always final minus initial.
- Sign of q(process). It is opposite to q(solution).
- “High c heats fast.” High c heats slowly.
- Wrong mass. Use the mass of the substance whose temperature changes (for a solution, water + solute).
- Per gram vs per mole. Match c with grams and C_m with moles.
- Too many significant figures. ΔT, found by subtraction, often has fewer than the readings.
- Halfway final temperature. Only when the two heat capacities (mc) are equal.
Quick self-check
- Energy to warm 10.0 g of water by 5.0 °C? (209 J)
- 100.0 g of water and 100.0 g of copper each absorb 2.00 kJ. Which warms more? (Copper: about 52 °C against 4.78 °C.)
- In a calorimeter the solution’s q is −850 J. What is q for the process? Exothermic or endothermic? (+850 J; endothermic: the solution cooled.)
Next: practice questions.