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Liquid Cooling Time Calculator — result sheet
Estimate a liquid temperature after a time interval, the time to a target temperature, and heat removed using a Newton-cooling model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Newton cooling: T(t) = Tₐ + (T₀ − Tₐ)e^(−t/τ). For a reachable target, time = −τ ln((Ttarget − Tₐ)/(T₀ − Tₐ)); heat removed over the entered interval = mass × specific heat × (T₀ − T(t)).
The model uses a user-entered time constant to represent the combined container, surface, airflow, and heat-transfer conditions. It is useful for comparisons and experiments, but one time constant cannot certify food safety, a refrigerator cycle, a beverage temperature, or a commercial process.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Initial liquid temperature — °C; minimum -273.14; maximum 1000
- Ambient temperature — °C; minimum -273.14; maximum 1000
- Target temperature — °C; minimum -273.14; maximum 1000
- Elapsed time — min; minimum 0; maximum 1000000
- Cooling time constant — min; minimum 1.0E-6; maximum 1000000
- Liquid volume — L; minimum 1.0E-6; maximum 1000000
- Liquid density — kg/L; minimum 1.0E-6; maximum 100000
- Specific heat capacity — J/(kg·K); minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Initial liquid temperature | 90 |
| Ambient temperature | 22 |
| Target temperature | 40 |
| Elapsed time | 30 |
| Cooling time constant | 45 |
| Liquid volume | 1 |
| Liquid density | 1 |
| Specific heat capacity | 4184 |
After 30 min the model estimates 56.91 °C, reaches 40 °C in about 59.81 min, and removes about 138.44 kJ by the entered time.
Assumptions and limits
- The liquid and surrounding environment are represented by one uniform temperature each.
- The cooling time constant stays constant over the interval; real heat transfer can change as temperature, airflow, container geometry, and phase change change.
- The target must lie between the initial and ambient temperatures for a finite positive target time.
- Mass is estimated from litres × entered density, and heat capacity is treated as constant.
- The heat result is sensible heat only; evaporation, freezing, condensation, mixing, and container heat capacity are not included.
- Use a thermometer and applicable food-safety or process guidance when temperature affects health or product quality.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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