Physics · Lesson 12

Heat, specific heat and latent heat

JAMBWAECNECO

What the syllabus asks

JAMB: temperature scales and thermometers, expansion, gas laws, quantity of heat, change of state, vapour, transfer of heat

WAEC: temperature and its measurement, thermometric properties, fixed points and scales, types of thermometer, thermal expansion of solids (linear, area, cubic expansivity) and liquids (real and apparent, anomalous expansion of water), gas laws (Boyle, Charles, pressure law, general gas law), heat capacity and specific heat capacity, latent heat, evaporation, boiling and vapour pressure, humidity,…

NECO: temperature and its measurement, thermometric properties, fixed points and scales, types of thermometer, thermal expansion of solids (linear, area, cubic expansivity) and liquids (real and apparent, anomalous expansion of water), gas laws (Boyle, Charles, pressure law, general gas law), heat capacity and specific heat capacity, latent heat, evaporation, boiling and vapour pressure, humidity,…

What you will learn

Distinguish heat from temperature and convert between Celsius and kelvin.
Explain how thermometers are calibrated and compare types of thermometer.
Calculate linear, area and volume expansion and explain applications and the anomalous expansion of water.
State and apply Boyle's law, Charles's law, the pressure law and the general gas law.
Use Q = mcΔθ and the method of mixtures.
Use Q = mL and explain evaporation, boiling, vapour pressure and humidity.
Describe conduction, convection and radiation and their applications (vacuum flask, land and sea breezes).

Key points

Temperature measures hotness (average particle KE); heat is energy in transit; T(K) = θ(°C) + 273.
θ = (X − X₀)/(X₁₀₀ − X₀) × 100; clinical thermometers have a constriction.
ΔL = αLΔθ; β = 2α, γ = 3α; bimetallic strips bend towards the less expansive metal.
γ_real = γ_apparent + γ_container; water is densest at 4 °C and expands on freezing.
Boyle PV = k; Charles V/T = k; pressure law P/T = k; P₁V₁/T₁ = P₂V₂/T₂ with kelvin.
Q = mcΔθ; water c = 4200 J/(kg K); electrical: VIt = mcΔθ.
Method of mixtures: heat lost = heat gained.
Q = mL; water L_f = 3.36 × 10⁵ J/kg, L_v = 2.26 × 10⁶ J/kg; temperature constant during change of state.
Evaporation cools; boiling when s.v.p. = external pressure; pressure cookers raise the boiling point.
Conduction (solids, free electrons), convection (fluids, density currents), radiation (infrared, no medium).
Dull black = best absorber and emitter; vacuum flask cuts conduction, convection and radiation.

Start here: Heat and temperature are not the same

Pour boiling water from a kettle into a cup, and also into a large bucket of cool water. The cup is hotter (higher temperature), but the bucket, even after warming slightly, contains far more thermal energy. Heat and temperature are related but very different.

Temperature is the degree of hotness or coldness of a body. On the particle level, it measures the average kinetic energy of the particles. Heat is the energy that flows from a hotter body to a colder body because of their temperature difference.

Heat	Temperature
A form of energy (in transfer)	A measure of hotness
Unit: joule (J)	Unit: kelvin (K) or °C
Depends on mass, material and temperature change	Does not depend on mass
Measured with a calorimeter (by calculation)	Measured with a thermometer

Heat always flows from higher to lower temperature, never the other way on its own. When two bodies reach the same temperature, the flow stops: they are in thermal equilibrium. That is why a thermometer must be left in the patient's armpit for a while before reading.

Temperature scales

The Celsius scale takes the melting point of pure ice as 0 °C and the boiling point of pure water at standard pressure as 100 °C. The Kelvin (absolute, thermodynamic) scale starts at absolute zero, the lowest possible temperature, where particles have their minimum energy. A change of 1 K equals a change of 1 °C.

T (K) = θ (°C) + 273

The Fahrenheit scale (still seen on some imported thermometers) uses 32 °F and 212 °F for the fixed points: F = 9θ/5 + 32.

Worked example 12.1

Convert (a) 27 °C to kelvin, (b) 373 K to °C, (c) body temperature 37 °C to °F.

(a) 27 + 273 = 300 K.
(b) 373 − 273 = 100 °C.
(c) 9 × 37/5 + 32 = 66.6 + 32 = 98.6 °F.

300 K; 100 °C; 98.6 °F

⚠️ Common mistake: writing "°K". Kelvin has no degree sign: 300 K.

Try it yourself. A temperature rises from 20 °C to 45 °C. What is the rise in kelvin?

Show solution

25 K — a change in kelvin equals the change in °C.

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Practice questions

1. Convert 57 °C to kelvin.

Show worked answer

330 K.

2. A thermometer reads 30 mm at 0 °C and 180 mm at 100 °C. Find the temperature at 120 mm.

Show worked answer

90/150 × 100 = 60 °C.

3. A 5 m aluminium rod (α = 2.4 × 10⁻⁵ K⁻¹) is heated through 50 K. Find its expansion.

Show worked answer

5 × 2.4 × 10⁻⁵ × 50 = 6 mm.

4. A gas at 120 kPa occupies 5 L. Find its volume at 200 kPa (constant temperature).

Show worked answer

600/200 = 3 L.

5. How much heat is needed to warm 3 kg of water from 20 °C to 60 °C?

Show worked answer

3 × 4200 × 40 = 504,000 J.

Key words

Temperature: The degree of hotness or coldness of a body; measured in °C or K.
Heat: Energy transferred from a hotter to a colder body; unit joule (J).
Thermometric property: A physical property that varies steadily with temperature, e.g. length of mercury, resistance, e.m.f.
Fixed points: Reproducible temperatures used to calibrate a thermometer: ice point (0 °C) and steam point (100 °C).
Absolute zero: The lowest possible temperature, 0 K = −273 °C.
Linear expansivity (α): Increase in length per unit length per kelvin rise in temperature.
Heat capacity: Heat needed to raise the temperature of a body by 1 K; unit J/K.
Specific heat capacity (c): Heat needed to raise 1 kg of a substance by 1 K; unit J/(kg K).
Specific latent heat (L): Heat needed to change the state of 1 kg of a substance without change of temperature; unit J/kg.
Evaporation: Escape of the faster molecules from a liquid surface at any temperature.
Boiling point: Temperature at which the saturated vapour pressure of a liquid equals the external pressure.
Saturated vapour pressure: Pressure exerted by a vapour in equilibrium with its liquid.

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