Specific Heat Formula
Calculate heat energy to change an object's temperature using Q=mcΔT.
Covers specific heat values for water, metals, and common materials with examples.
Need to calculate, not just reference? Use the interactive version.
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The Formula
Q = m × c × ΔT
The specific heat formula calculates the thermal energy needed to change the temperature of a substance. Different materials require different amounts of energy to heat up — water requires much more than metal.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Heat energy transferred | Joules (J) |
| m | Mass of the substance | kg (or grams) |
| c | Specific heat capacity | J/(kg·°C) |
| ΔT | Change in temperature (T_final - T_initial) | °C or K |
Common Specific Heat Values
| Substance | c (J/kg·°C) |
|---|---|
| Water | 4,186 |
| Aluminum | 897 |
| Iron | 449 |
| Copper | 385 |
| Air | 1,005 |
Example 1
How much energy to heat 2 kg of water from 20°C to 100°C?
Q = m × c × ΔT = 2 × 4186 × (100 - 20)
= 2 × 4186 × 80
= 669,760 J ≈ 670 kJ
Example 2
A 0.5 kg aluminum pan absorbs 4,000 J. How much does its temperature rise?
ΔT = Q / (m × c) = 4000 / (0.5 × 897)
= 8.9°C
When to Use It
Use the specific heat formula when:
- Calculating energy needed to heat water, food, or materials
- Designing heating and cooling systems
- Performing calorimetry experiments in chemistry
- Estimating energy costs for industrial heating processes
Key Notes
- Formula is Q = mcΔT: Q is heat energy (J), m is mass (kg), c is specific heat capacity (J/kg·°C), and ΔT is the temperature change. A positive Q means heat is absorbed.
- Water has unusually high specific heat: Water's specific heat of 4,186 J/kg·°C is much higher than most substances. This is why oceans moderate coastal climates and why water is used as a coolant.
- Phase changes are excluded: This formula only applies while the substance stays in the same phase. During melting or boiling, use Q = mL (latent heat) instead — temperature stays constant during phase changes.
- Specific heat varies with temperature: The value of c is approximately constant over moderate temperature ranges but changes significantly at extreme temperatures. Tables usually give values at 25°C.
- Use consistent units: Specific heat is often given in J/g·°C (per gram) in chemistry and J/kg·°C (per kilogram) in physics. Always match units to your mass unit to avoid errors by a factor of 1,000.