Heat: specific heat capacity and heat transfer
Temperature scales and kelvin, Q = m·c·ΔT and specific heat capacity, thermal equilibrium, and the rate of conduction. With a method-of-mixtures experiment that tests the predictions.
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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.[1][2]
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).[2]
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.[2]
Example: heating a 0.500 kg aluminium pan holding 0.250 kg of water from 20.0 °C to 80.0 °C takes 0.250 × 4186 × 60.0 ≈ 62.8 kJ for the water plus 0.500 × 900 × 60.0 = 27.0 kJ for the pan: 89.8 kJ in total.[2]
The rate of heat flow by conduction is proportional to the area A and the temperature difference ΔT, and inversely proportional to the thickness l: H = k·A·ΔT/l. Copper has a high thermal conductivity k; wood's is thousands of times lower, so wood is a good insulator.[4]
Convection transfers heat by the bulk movement of a fluid; radiation transfers it by electromagnetic waves and needs no medium, which is how the Sun heats the Earth.[2][3]
Try it: Method of mixtures: predict the final temperature
You need
- 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.
What to do
- 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.
What happens, and why?
Heat flows from the warm water to the cold water until they reach thermal equilibrium. Because both are water, c cancels and energy conservation gives T_f = (m₁T₁ + m₂T₂)/(m₁ + m₂). The measured T_f is usually slightly lower than predicted, because some heat is transferred to the cup, the thermometer and the air. Polystyrene, which contains trapped air, keeps these losses small.[2][5]
Play: How much heat?
Calculate Q = m·c·ΔT (water 4186, aluminium 900, copper 387, iron 452, concrete 840 J/(kg·°C)) and pick the closest value.
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Quiz
Other ages: Ages 6–7 · Ages 10–11