The formula to calculate the cooling constant is:
\[ k = \frac{\ln\left(\frac{T_i - T_a}{T_f - T_a}\right)}{t} \]
Where:
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 1:
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:
Step 1: Calculate the cooling constant:
\[ k = \frac{\ln\left(\frac{100 - 25}{50 - 25}\right)}{45} = \frac{\ln(3)}{45} \approx 0.0244 \text{ 1/minutes} \]
