Heat: specific heat capacity and heat transfer

Lesson page: echoesof.science/school/heat/ages-15-16/ · Pupil worksheet: echoesof.science/school/heat/ages-15-16/print/

Learning aims

Convert between °C and K and know that ΔT is the same in both.
Use Q = m·c·ΔT and compare specific heat capacities.
Apply energy conservation to mixing (thermal equilibrium).
Relate conduction rate to area, temperature difference and thickness; evaluate uncertainty.

Lesson plan

Time	Activity
5 min	Starter: why does sand on a beach get hot faster than the sea?
10 min	Read the text; work through the aluminium-pan example.
25 min	Method-of-mixtures experiment with predictions.
5 min	Compare predictions and measurements; discuss heat losses and uncertainty.
5 min	Quiz, or the game as homework.

Materials for the experiment

Polystyrene cups with lids (two nested cups)
Thermometer or temperature probe (±0.5 °C or better)
Balance (±1 g)
Warm tap water and cold tap water (iced if available)
Stirrer

Safety: Use warm tap water only, not boiling water from a kettle. Wipe up spills at once; glass thermometers break easily.

Common misconceptions

Pupils may think…	Actually…
Heat and temperature are the same.	Temperature is a property of the object; heat is energy transferred because of a temperature difference.
All materials heat up equally quickly.	The temperature rise for the same Q depends on c: water warms about 11 times less than copper.
A temperature of 20 °C is 'twice as hot' as 10 °C.	Ratios only make sense in kelvin: 293 K is only about 3.5% more than 283 K.

Worksheet answers

Warm water's line falls and the cold water's line rises until they meet at the same temperature (thermal equilibrium) and stay level.
T_f = (0.20 × 40 + 0.10 × 10)/(0.30) = 9.0/0.30 = 30 °C.
Heat lost to the cup, the thermometer and the air; the warm water cooled before mixing; thermometer reading too early. Improvement: use a lid and nested cups, measure T₂ just before mixing, use a digital probe.
Water's specific heat (4186 J/(kg·°C)) is about 4.7 times aluminium's (900), so the same mass of water needs about 4.7 times more heat for the same temperature rise.

Quiz answers

How much heat raises 2.0 kg of water by 10 °C? (c = 4186 J/(kg·°C)) About 84 kJ. Q = 2.0 × 4186 × 10 ≈ 83 700 J ≈ 84 kJ.[2]
What is 25 °C in kelvin? 298 K. T(K) = 25 + 273.15 ≈ 298 K.[1]
The same heat goes into 1 kg of water and 1 kg of copper. Which warms up more? The copper, about 11 times more. ΔT = Q/(m·c), and c for copper (387) is about 11 times smaller than for water (4186).[2]
How much heat warms a 0.500 kg aluminium pan from 20 °C to 80 °C? (c = 900 J/(kg·°C)) 27 kJ. Q = 0.500 × 900 × 60 = 27 000 J.[2]
You double the thickness of an insulating wall. The rate of heat conduction… halves. H is inversely proportional to the thickness l.[4]
Why can the Sun's heat reach us through space? Radiation needs no medium. Radiation is electromagnetic and needs no material.[2]

Going further

Use the method of mixtures to estimate the specific heat capacity of a metal: heat a metal block in warm water, transfer it to cold water and use m_metal·c_metal·ΔT_metal = m_water·c_water·ΔT_water. Compare with the OpenStax table value.

Sources used in this lesson

[1] Physics, 11.1 Temperature and Thermal Energy (OpenStax, Rice University): reliability High
[2] Physics, 11.2 Heat, Specific Heat, and Heat Transfer (OpenStax, Rice University): reliability High
[3] The Transfer of Heat Energy (NOAA National Weather Service, JetStream): reliability High
[4] Thermal conduction (Encyclopaedia Britannica): reliability High
[5] Insulation (Science Learning Hub – Pokapū Akoranga Pūtaiao, University of Waikato (New Zealand)): reliability High

Full list with links and a note on each source's reliability: echoesof.science/school/heat/sources/

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