What is Newton’s Law of Cooling?

Newton’s Law of Cooling is a principle in thermodynamics that describes the rate at which an object cools down when exposed to a cooler environment. The law states that the rate of heat loss from a body is directly proportional to the difference in temperature between the body and its surroundings. This principle is widely used in physics, engineering, and even forensic science to predict how quickly objects will cool or warm up under certain conditions.

The mathematical expression of Newton’s Law of Cooling is:

T = T_ambient + (T_initial – T_ambient) * e^(-kt)

Where:

• T is the temperature of the object at time t
• T_ambient is the ambient (surrounding) temperature
• T_initial is the initial temperature of the object
• k is the cooling coefficient (a constant that depends on the object’s properties)
• t is the time elapsed

How to Use the Newton’s Law of Cooling Calculator

Step 1: Enter the Initial Temperature

Input the starting temperature of the object in degrees Celsius. This is the temperature at which the object begins cooling.

Step 2: Input the Ambient Temperature

Enter the temperature of the surrounding environment in degrees Celsius. This is the temperature that the object will eventually reach if given enough time.

Step 3: Specify the Cooling Coefficient

Input the cooling coefficient, which is a measure of how quickly the object loses heat. This value is typically determined experimentally and is specific to the object and its environment. The unit for this coefficient is s⁻¹ (per second).

Step 4: Set the Time

Enter the duration for which you want to calculate the cooling, measured in seconds.

Step 5: Calculate and Interpret Results

Click the “Calculate” button to obtain the final temperature. The calculator will display the result along with an explanation of how it was derived using Newton’s Law of Cooling.

By following these steps, you can easily predict the temperature of an object after a certain period of cooling. This tool is invaluable for various applications, from determining how long it takes for a hot beverage to cool to a drinkable temperature, to more complex scenarios in industrial processes or scientific experiments.