Library / Foundations: Physics / FPH-15
Foundations: Physics
Specific heat capacity
Energy to change the temperature of a mass.
- Ref
- FPH-15
- Rev
- v1
- Field
- Foundations: Physics
- Result
- E [kJ]
Use specific heat capacity c for a temperature change. E in joules, m in kg, c in J/(kg·K), ΔT in K or °C change.
The energy needed to warm something depends on its mass, how stubbornly its material resists warming (c), and the temperature rise.
Calculator
- Energy in joules83,600 J
- Time at 1 kW heating83.6 s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Water has a very high specific heat, which is why it is a good coolant and heat store.
- The same energy warms a lighter object or low-c material faster.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kJ) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Mass | 0.01 to 100 kg | 1.672 | 16,720 | 16,720 | +10% | +10 % |
| ΔT Temperature change | 1 to 200 K | 2.09 | 418 | 415.9 | +10% | +10 % |
| c Specific heat capacity | 100 to 5,000 J/(kg·K) | 2 | 100 | 98 | +10% | +10 % |
Sweep of Temperature change
| Temperature change (K) | Thermal energy (kJ) |
|---|---|
| 1 | 2.09 |
| 1.939 | 4.053 |
| 3.761 | 7.86 |
| 7.293 | 15.24 |
| 14.14 | 29.56 |
| 27.42 | 57.32 |
| 53.18 | 111.2 |
| 103.1 | 215.5 |
| 200 | 418 |
Sweep one variable
Variables and how each one contributes
Thermal energy
What the equation gives you. Everything else feeds it.
Mass
Mass heated. Directly proportional.
Specific heat capacity
Water 4180, aluminium 900, steel 490. Directly proportional.
Temperature change
Rise in temperature. Directly proportional.
Worked example with the values above
- m × c = 0.5 × 4,180 = 2,090 J/K.
- Multiply by ΔT = 40 K: 83,600 J.
- E = 83.6 kJ.
Assumptions and limits
- No change of state.
- Constant specific heat over the temperature range.
Common mistakes
- Using grams with J/(kg·K).
- Ignoring heat lost.
Statistics and uncertainty
Heat losses to the surroundings make measured energy higher than this ideal value, often by 10% or more.
Where it is used
- Heating and cooling duty estimates.
- Thermal soak of equipment.
Maths you need
- Temperature and heat: difference between them
- Units: J, kg, K