Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Specific heat c is the energy needed to raise 1 kg of a material by 1 K. It is intrinsic: the same for a bead and a block of the same material.
- c depends on the atoms: how many particles are in a kilogram and how many ways they can store energy.
- For solids and liquids W ≈ 0, so the energy supplied by heating becomes internal energy: ΔU ≈ Q.
- Thermal conductivity k measures how easily a material conducts energy. Metals (free electrons) have high k; non-metal solids lower; still gases very low.
- In an isolated system, objects in thermal contact reach a common temperature, and the total energy is conserved.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| Q = mcΔT | Q in J, m in kg, c in J/(kg·K), ΔT in K or °C | find the energy for a temperature change, or c, m or ΔT |
| Q = PΔt | P in W, Δt in s | find the energy from a heater |
| slope of T against Q = 1/(mc) | K/J | read c from a graph |
| slope of T against t = P/(mc) | K/s | read c from heater data |
| Σ mcΔT = 0 | for an isolated system | find a final (equilibrium) temperature |
| Q/Δt = kAΔT/L | rate in W, k in W/(m·K), A in m², L in m | find the rate of conduction through a slab |
Factor-of-change reminders for conduction: double A → rate × 2; double ΔT → rate × 2; double L → rate × ½.
Assumptions behind the numbers
- c is independent of temperature (the course model).
- No change of state during heating or cooling.
- Mixing problems: the container is insulated, so no energy leaves the system.
- Conduction: steady state, uniform slab, energy flows straight through.
Mistakes to avoid
- Reading high c as “heats quickly”. High c means slow temperature change.
- Adding 273 to ΔT. A change of 10 °C is a change of 10 K.
- Taking the simple average as the final temperature when the mc values differ.
- A final temperature outside the starting range. That signals a sign error.
- Thinking a thicker slab conducts more. Rate ∝ 1/L.
- Calling k the rate. k is the material property; the rate also needs A, ΔT and L.
- Saying metal “is colder”. At the same temperature, metal only feels colder because it conducts faster.
Quick self-check
- How much energy warms 0.50 kg of aluminium (c = 900 J/(kg·K)) by 40 K? (18,000 J)
- A rod’s length is halved; A and ΔT stay the same. What happens to the rate of conduction? (It doubles)
- Equal masses of the same liquid at 60 °C and 20 °C are mixed in an insulated flask. Final temperature? (40 °C, because the two mc values are equal)
Next: practice questions.