Specific heat capacity calculator (ΔE = mcΔθ)

The specific heat capacity of a substance is the energy needed to raise the temperature of 1 kg of it by 1 °C. Water has a high value, about 4,200 J/kg °C, which is why it takes a long time to heat and is good at storing thermal energy. Metals have much lower values: aluminium is about 900 J/kg °C and copper about 390 J/kg °C.

• Energy: heating 2 kg of water by 10 °C. $\Delta E = 2 \times 4200 \times 10 = 84{,}000$ J (84 kJ).
• Specific heat capacity: 18,000 J raises a 0.5 kg block by 40 °C. $c = 18000 \div (0.5 \times 40) = 900$ J/kg °C, about right for aluminium.
• Temperature change: 21,000 J goes into 0.5 kg of water. $\Delta\theta = 21000 \div (0.5 \times 4200) = 10$ °C.

A common practical heats a metal block with an electric heater:

1. Measure the block's mass and starting temperature.
2. Heat it, measuring the energy supplied (with a joulemeter, or power × time).
3. Record the temperature rise and calculate $c = \dfrac{\Delta E}{m \Delta\theta}$.

The result is usually higher than the true value, because some energy heats the surroundings rather than the block. Insulating the block reduces this.

$\Delta\theta$ is the change: final temperature minus starting temperature. Heating water from 20 °C to 35 °C is a change of 15 °C. Using 35 °C by mistake is one of the most common errors in these questions.

• Using grams instead of kilograms.
• Using the final temperature instead of the change.
• Forgetting to convert kJ to J (multiply by 1,000).

See specific heat capacity explained for more practice.