echoesof.science · Ages 15–16
Heat: specific heat capacity and heat transfer
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Temperature is related to the kinetic energy of the particles of a substance. On the Kelvin scale, 0 K is absolute zero and T(K) = T(°C) + 273.15; water freezes at 273.15 K and boils at 373.15 K. A temperature change of 1 °C equals a change of 1 K.
Heat is energy transferred because of a temperature difference, from the hotter object to the colder one, until both reach the same temperature (thermal equilibrium).
The heat needed to change the temperature of a mass m is Q = m·c·ΔT, where c is the specific heat capacity in J/(kg·°C). Values: water 4186, ice 2090, wood 1700, air 1015, aluminium 900, glass 840, iron/steel 452, copper 387, lead 128.
Experiment: Method of mixtures: predict the final temperature
- Measure about 100 g of cold water into the nested polystyrene cups. Record its mass m₁ and temperature T₁.
- Measure about 100 g of warm tap water in a second cup. Record m₂ and T₂ just before mixing.
- Predict the final temperature, assuming heat lost by the warm water = heat gained by the cold water: T_f = (m₁·T₁ + m₂·T₂)/(m₁ + m₂).
- Pour the warm water into the cold water, put the lid on, stir and record the highest steady temperature T_f.
- Repeat with different mass ratios (for example 50 g + 150 g and 150 g + 50 g).
- Compare measured and predicted T_f. Estimate the uncertainty from the thermometer and from your repeats, and explain any systematic difference.
| m₁ cold (kg) | T₁ (°C) | m₂ warm (kg) | T₂ (°C) | T_f predicted (°C) | T_f measured (°C) |
|---|---|---|---|---|---|
Questions
Sketch a graph of temperature against time for the warm water and the cold water during mixing. Mark where thermal equilibrium is reached.
🍎0.20 kg of water at 40 °C is mixed with 0.10 kg of water at 10 °C. Predict the final temperature.
Your measured final temperature was 1.5 °C below the prediction. Give two reasons and suggest one improvement.
Why does a pan of water take much longer to heat up than an empty aluminium pan of the same mass? Use specific heat capacity.
Sources for every fact on this sheet: echoesof.science/school/heat/sources/