How much heat changes a sample’s temperature?
You will be able to: Use sample, specific and molar heat capacities with consistent units.
How much heat changes a sample’s temperature?
Warming twice as much water through the same temperature change needs twice as much energy. The material’s heat capacity per gram stays the same, while the whole sample’s capacity doubles.
A useful starting point: Why is the final temperature not always the average? →
Words and symbols before equations
- Specific heat capacity, c
- Heat per gram per degree; J/(g·K).
- Molar heat capacity, Cm
- Heat per mole per degree; J/(mol·K).
- Mass, m / amount, n
- Sample size in grams / moles.
- ΔT
- Tf−Ti; a temperature change of 1 °C equals 1 K.
What this picture assumes
Single-phase liquid with supplied constant c=4.00 J/(g·K), initially 20 °C. Controls keep final temperature below 100 °C. No phase change, reaction or heat leak.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- 2400 J heats 75 g by 8 K. C=300 J/K; c stays 4.00 J/(g·K). Double mass at fixed q and c to halve ΔT.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
Within one phase and with approximately constant c, q=mcΔT. The units g × J/(g·K) × K reduce to joules.
For a known whole-sample capacity C, use q=CΔT. With molar capacity, use q=nCmΔT. Match grams with c and moles with Cm.
C=mc=nCm. For the same material, Cm=cM where M is molar mass in g/mol; neither c nor Cm is the capacity of an arbitrary whole sample.
Cooling gives ΔT<0 and q<0. These formulas describe temperature change and cannot alone supply the heat for a constant-temperature phase transition.
| Quantity | Units | Heat relation |
|---|---|---|
| Whole-sample C | J/K | q=CΔT |
| Specific c | J/(g·K) | q=mcΔT |
| Molar Cm | J/(mol·K) | q=nCmΔT |
A worked example, step by step
Warm 75.0 g of a liquid from 20.0 to 28.0 °C with c=4.00 J/(g·K). Find q and sample heat capacity.
- ΔT=28.0−20.0=8.0 K.
- C=mc=75.0×4.00=300 J/K.
- q=CΔT=300×8.0=2400 J=2.4 kJ.
- The positive sign means heat enters; no phase change and approximately constant c are assumed.
Do not multiply grams by a molar heat capacity. Match the amount unit to the capacity unit.
Must temperatures be converted to kelvin before finding ΔT from Celsius readings?
Compare with an explanation
No. Celsius and kelvin temperature differences have the same numerical size.
Predict. Change one thing. Explain.
Keep supplied heat and c fixed while changing mass. Predict the temperature rise and explain why doubling mass halves it.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
2400 J heats 75 g by 8 K. C=300 J/K; c stays 4.00 J/(g·K). Double mass at fixed q and c to halve ΔT.
Single-phase liquid with supplied constant c=4.00 J/(g·K), initially 20 °C. Controls keep final temperature below 100 °C. No phase change, reaction or heat leak.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using heat-flow signs, energy conservation, phase changes, bond inventories or the stated thermochemical path. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA material has c=0.80 J/(g·K), molar mass 50 g/mol and mass 25 g. Find Cm, sample C, and q when it cools by 12 K.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Cm=0.80×50=40 J/(mol·K).
- 1 point: C=25×0.80=20 J/K.
- 1 point: ΔT=−12 K, so q=20(−12)=−240 J.
- 1 point: The negative sign means the sample releases 240 J; no phase change is assumed.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What distinguishes c from C?
c is per gram; C describes the whole sample.
RECALL 2What unit pairs with Cm?
Moles.
RECALL 3When is mcΔT insufficient?
When phase change or other energy changes must be included.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How much heat changes a sample’s temperature?
- q=mcΔT=CΔT=nCmΔT within one phase.
- C=mc=nCm; Cm=cM.
Remember: Do not multiply grams by a molar heat capacity. Match the amount unit to the capacity unit.
Conditions: Single-phase liquid with supplied constant c=4.00 J/(g·K), initially 20 °C. Controls keep final temperature below 100 °C. No phase change, reaction or heat leak.
Refresh Kid · AP Chemistry Unit 6 · Objectives 6.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 6.4, objective 6.4.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 6: Thermochemistry, Topics 6.1–6.9. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Technical enthalpy/internal-energy distinctions and formal state-function terminology are not assessed in the current AP framework. Constant-pressure heat, conservation, phase-specific capacities, reaction amounts and Hess sums are taught here with explicit conditions. Supplied rounded data and original molecular geometry are teaching models, not experimental measurements. A phase transition preserves molecular identity; a bond-energy accounting path is not an actual reaction mechanism.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
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