Cooling Constant Calculator

Formula

The formula to calculate the cooling constant is:

\[ k = \frac{\ln\left(\frac{T_i - T_a}{T_f - T_a}\right)}{t} \]

Where:

k is the cooling constant (1/minutes)
Ti is the initial temperature (°C)
Tf is the final temperature (°C)
Ta is the ambient temperature (°C)
t is the time (minutes)

What is a Cooling Constant?

The cooling constant is a value that represents the rate at which an object cools down towards the ambient temperature. It is a key parameter in Newton’s law of cooling, which describes the cooling of a warmer object to the cooler temperature of the environment. The cooling constant is specific to the object and its environment and can be used to predict how long it will take for the object to reach a certain temperature.

Example Calculation

Example 1:

Initial Temperature (Ti): 80°C
Final Temperature (Tf): 40°C
Ambient Temperature (Ta): 20°C
Time (t): 30 minutes

Step 1: Calculate the cooling constant:

\[ k = \frac{\ln\left(\frac{80 - 20}{40 - 20}\right)}{30} = \frac{\ln(3)}{30} \approx 0.0366 \text{ 1/minutes} \]

Example 2:

Initial Temperature (Ti): 100°C
Final Temperature (Tf): 50°C
Ambient Temperature (Ta): 25°C
Time (t): 45 minutes

Step 1: Calculate the cooling constant:

\[ k = \frac{\ln\left(\frac{100 - 25}{50 - 25}\right)}{45} = \frac{\ln(3)}{45} \approx 0.0244 \text{ 1/minutes} \]