Formula & Calculator
Specific Heat Capacity
Calculates the heat required to change the temperature of a given mass of material by a specified amount.
Interpretation
Q = m·c·ΔT. Heat energy required to raise temperature. c is specific heat (J/kg·K). Used in thermal calculations, process heating, and energy balance.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Q | Heat energy | J |
| m | Mass | kg |
| c | Specific heat capacity | J/kg.K |
| delta_T | Temperature change | K |
What it means
Specific heat capacity (c) is the amount of heat per unit mass needed to raise the temperature by one degree Celsius (or Kelvin). The equation Q = m c ΔT gives the heat energy Q required to change the temperature of a mass m by ΔT. This property is used in thermal design, heating and cooling processes, and in energy‑balance calculations. Materials with high specific heat (like water) can store more thermal energy. In engineering, c is used to size heaters, coolers, and heat exchangers, and to analyse transient thermal behaviour. It also appears in the definition of enthalpy and in the first law of thermodynamics. Understanding specific heat is essential for process engineers, HVAC designers, and energy analysts.
Worked example
Specific Heat Capacity – Two Examples
Real‑World| Parameter | Value |
|---|---|
| m | 1 kg |
| c | 900 J/kg·K |
| ΔT | 50 K |
| Parameter | Value |
|---|---|
| m | 0.5 kg |
| c | 4180 J/kg·K |
| ΔT | 20 K |
Common mistakes
- Specific heat capacity c: The amount of heat required to raise the temperature of 1 kg of a substance by 1 K – in J/(kg·K).
- Mass m: In kg.
- Temperature change ΔT: In K or °C (same magnitude).
- Heat Q: In joules (or kJ if using kJ/kg·K).
- Assumption: c is constant over the temperature range – if not, use an average value.
Applications
Specific heat capacity (c) is defined by Q = m·c·ΔT, relating the heat required to change the temperature of a mass m by ΔT. It is crucial for thermal design, energy storage, and process heating/cooling. Engineers use c to calculate the energy needed for heating or cooling materials, to size heat exchangers, and to design thermal storage systems (e.g., sensible heat storage). In metallurgy, it is used in heat treatment calculations. In aerospace, it helps predict the thermal response of structures. Understanding specific heat capacity allows engineers to manage energy consumption and ensure that thermal processes are efficient and controlled.
- Sizing of heaters, chillers, and heat exchangers
- Thermal energy storage system design (e.g., solar thermal, molten salt)
- Heat treatment process energy calculations
- Thermal management of automotive and electronic systems
- Material selection for thermal insulation and heat transfer fluids
Frequently Asked Questions
Specific heat capacity (c) is the amount of heat required to raise the temperature of one unit mass of a material by one degree. The formula is Q = m · c · ΔT, where Q is heat energy, m is mass, and ΔT is temperature change.
In SI, it is J/(kg·K). Other units include cal/(g·°C) or Btu/(lb·°F). The conversion is 1 cal/(g·°C) = 4.184 J/(g·°C) = 4184 J/(kg·K).
Treating specific heat as constant through a phase change. During phase changes (melting, boiling), latent heat is required, and specific heat does not apply. The formula Q = m·c·ΔT is valid only for a single phase.
- Water: 4.18 J/(g·K) (very high).
- Aluminium: 0.90 J/(g·K).
- Iron: 0.45 J/(g·K).
- Copper: 0.385 J/(g·K).
For most solids, specific heat increases with temperature, approaching the Dulong‑Petit limit (3R per mole) at high temperatures. At low temperatures, it follows the Debye T³ law.
c_p is the heat required per unit mass to raise temperature at constant pressure; c_v is at constant volume. For gases, c_p > c_v; for solids and liquids, the difference is small.
Using Q = m·c·ΔT. For example, to heat 2 kg of water from 20°C to 80°C: Q = 2 × 4180 × 60 = 501,600 J = 501.6 kJ.
Materials with high specific heat can absorb more heat without large temperature rises, making them useful for thermal storage (e.g., water in radiators). Low specific heat materials respond quickly to temperature changes.
- Only for a single phase.
- Assumes c is constant over the temperature range.
- Does not account for heat losses.
Using calorimetry: a known mass of the material is heated and placed in a calorimeter, and the temperature change of the water is measured. Alternatively, using differential scanning calorimetry (DSC).