Calculate heat energy transferred using Q = mcΔT. Covers water, metals, gases, and all GCSE physics required practical concepts with worked examples.
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Specific heat capacity (c) is the amount of energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K). It quantifies how resistant a material is to temperature change.
Key Worked Example: Heat 2 kg of water from 20°C to 100°C:
Q = 2 × 4,200 × (100 − 20) = 2 × 4,200 × 80 = 672,000 J (672 kJ)
This is the energy needed to boil 2 kg (2 litres) of water in a kettle, equivalent to approximately 0.187 kWh of electrical energy.
These values are at standard conditions (approximately 25°C, 1 atm). Values can vary slightly with temperature and purity.
| Material | c (J/kg°C) | Notes |
|---|---|---|
| Water (liquid) | 4,200 | Highest of common liquids — excellent coolant and climate regulator |
| Ice | 2,100 | Half that of liquid water — used in calorimetry |
| Steam (water vapour) | 2,010 | At 100°C, 1 atm |
| Air (dry) | 1,005 | At constant pressure (Cp) |
| Aluminium | 900 | High for a metal — used in cookware and heat sinks |
| Glass | 840 | Varies with composition |
| Brick / concrete | 840 | Important for thermal mass in buildings |
| Steel | 502 | Common structural metal |
| Iron | 450 | Close to steel |
| Copper | 390 | Low for a common metal — excellent heat conductor |
| Brass | 380 | Copper-zinc alloy |
| Tin | 228 | Low specific heat — heats quickly |
| Silver | 235 | Best electrical conductor but expensive |
| Gold | 128 | Dense metal with low specific heat |
| Lead | 128 | Heavy, low specific heat |
| Mercury (liquid) | 140 | Used in thermometers (increasingly replaced) |
| Ethanol | 2,440 | Common organic solvent |
| Engine oil | 1,900 | Approx. value for mineral oil |
Water has one of the highest specific heat capacities of any common substance (4,200 J/kg°C). This has profound effects on climate, industry, and biology.
Oceans cover 71% of Earth's surface and absorb vast amounts of solar energy without large temperature changes, due to water's high specific heat. This stabilises global temperatures and explains why coastal areas have milder, more temperate climates than inland areas at the same latitude. Compare London (coastal-influenced, average range 5–24°C) with Moscow (continental, −10 to 24°C).
Water is the dominant coolant in power stations, car engines, and industrial processes because it can absorb large quantities of heat for relatively little temperature rise. A car cooling system may circulate 5–8 litres of water (plus antifreeze) to maintain engine temperature. An electric power station may use millions of litres per hour in its cooling towers.
The human body is approximately 60% water by mass. This high water content helps maintain a stable core temperature (37°C), buffering against rapid temperature swings from exercise or ambient temperature changes. Sweating uses water's high latent heat of vaporisation (2,260,000 J/kg) to provide powerful cooling.
Hot water central heating systems exploit water's high specific heat to distribute warmth efficiently around a building. A relatively small volume of hot water can deliver a large amount of thermal energy to radiators. Upgrading insulation reduces the temperature rise required and therefore the energy cost.
When a substance changes state (e.g., melts or boils), energy is transferred without any temperature change. This is specific latent heat.
| Substance | Latent Heat of Fusion (melting, J/kg) | Latent Heat of Vaporisation (boiling, J/kg) |
|---|---|---|
| Water | 334,000 (334 kJ/kg) | 2,260,000 (2,260 kJ/kg) |
| Ethanol | 108,000 | 841,000 |
| Iron | 247,000 | 6,090,000 |
| Aluminium | 397,000 | 10,900,000 |
| Nitrogen (liquid) | 25,700 | 198,000 |
Example: Melting 1 kg of ice at 0°C requires Q = 1 × 334,000 = 334,000 J (334 kJ) — without any temperature change.
Water's exceptionally high latent heat of vaporisation (2,260 kJ/kg) means sweating is very effective at cooling the body. Evaporating just 100 g of sweat removes 226 kJ of heat energy.
This is a compulsory practical in AQA, OCR, and Edexcel GCSE Physics and Combined Science courses.
True value: 900 J/kg°C. Typical experimental results: 850–1,050 J/kg°C depending on insulation quality. Percentage error = |experimental − true| ÷ true × 100%.
The formula is Q = mcΔT, where Q is heat energy in Joules, m is mass in kilograms, c is specific heat capacity in J/kg°C, and ΔT is the temperature change in °C (or K). Rearranging: c = Q ÷ (m × ΔT); m = Q ÷ (c × ΔT); ΔT = Q ÷ (m × c).
Water has a specific heat capacity of 4,200 J/kg°C. This is exceptionally high because water molecules form extensive networks of hydrogen bonds. A large amount of energy must be supplied to increase the motion of molecules (and thus temperature) before these bonds are disrupted. This is why the sea heats up and cools down much more slowly than the land.
Specific heat capacity (Q = mcΔT) describes energy transfer during a temperature change, with no change of state. Specific latent heat (Q = mL) describes energy transfer during a change of state (melting or boiling), with no temperature change. During melting or boiling, all energy supplied goes into breaking intermolecular bonds rather than increasing molecular kinetic energy (temperature).
The required practical involves using an electric immersion heater to heat a block of metal (usually aluminium) or a known volume of water. Energy supplied is measured using Q = VIt or a joulemeter, and temperature rise is recorded with a thermometer or data logger. Specific heat capacity is calculated as c = Q ÷ (mΔT). The main source of error is heat loss to the environment, which causes the calculated value to be higher than the true value.
1 kWh = 3,600,000 J (3.6 MJ). Divide the energy in Joules by 3,600,000 to get kWh. Example: heating 50 litres of water from 20°C to 70°C requires Q = 50 × 4,200 × 50 = 10,500,000 J = 10,500 kJ = 2.917 kWh. At the UK average electricity price of approximately 24p/kWh, this costs about 70p.
Heavy metals generally have the lowest specific heat capacities: gold (128 J/kg°C), lead (128 J/kg°C), mercury (140 J/kg°C), tin (228 J/kg°C). This means they heat up and cool down quickly for a given mass. By contrast, water (4,200 J/kg°C) and alcohols (2,000–2,500 J/kg°C) have very high values and resist temperature changes effectively.