Newton's Law of Cooling Calculator

Formula

The formula to calculate the final temperature (Tf) is:

\[ \text{Tf} = \text{Ta} + (\text{Ti} - \text{Ta}) \times e^{(- c \times t)} \]

Where:

\(\text{Tf}\) is the final temperature (°C)
\(\text{Ta}\) is the ambient temperature (°C)
\(\text{Ti}\) is the initial temperature (°C)
\(\text{c}\) is the cooling coefficient
\(\text{t}\) is the total time (seconds)

What is Newton's Law of Cooling?

Newton's law of cooling describes the rate at which an exposed body changes temperature through radiation, conduction, or convection. The law states that the rate of change of temperature is proportional to the difference between the object's temperature and the ambient temperature.

Example Calculation

Let's assume the following values:

Ambient Temperature (Ta) = 25 °C
Initial Temperature (Ti) = 100 °C
Cooling Coefficient (c) = 0.01
Total Time (t) = 600 seconds

Using the formula to calculate the final temperature (Tf):

\[ \text{Tf} = 25 + (100 - 25) \times e^{(-0.01 \times 600)} \approx 25 + 75 \times e^{-6} \approx 25 + 75 \times 0.0025 \approx 25.19 \text{ °C} \]

The final temperature (Tf) is approximately 25.19 °C.