Food & cooking
Newton cooling & heating curve
Estimate time to a target temperature using a supplied first-order rate constant.
A clear answer. Here’s how.
Uses T(t)=Tambient+(Tinitial−Tambient)exp(−kt). A target equal to the initial temperature takes zero time; other finite-time targets must lie strictly between initial and ambient temperatures. The ambient value is approached asymptotically. Assumes a well-mixed/lumped body and constant rate parameter; no food-safety, phase-change, changing-ambient or spatial temperature prediction is made.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Initial temperature (°C)
- 80
- Constant ambient temperature (°C)
- 20
- Target temperature (°C)
- 40
- Supplied cooling/heating rate constant (1/min)
- 0.05
Example result
| Elapsed time (minutes) | Model temperature (°C) |
|---|---|
| 0 | 80 |
| 0.274653072167 | 79.1816725476 |
| 0.549306144334 | 78.3745060922 |
| 0.823959216501 | 77.5783484112 |
| 1.09861228867 | 76.7930493584 |
Constant ambient temperature and supplied first-order rate constant. This is a lumped mathematical model, without phase change or a food-safety prediction.