How to Calculate Rate of Cooling from a Graph

Rate of Cooling Calculator

Calculate the gradient from your Temperature vs. Time graph.

Point 1 (Initial Data)

Point 2 (Final Data)

Settings

Minutes (min) Seconds (s) Hours (h)

Celsius (°C) Fahrenheit (°F) Kelvin (K)

How to Calculate Rate of Cooling from a Graph

Calculating the rate of cooling from a graph is a fundamental skill in physics and chemistry, particularly when studying heat transfer or verifying Newton's Law of Cooling. The graph typically plots Temperature on the vertical axis (y-axis) against Time on the horizontal axis (x-axis).

Understanding the Gradient

The rate of cooling is represented by the gradient (slope) of the temperature-time graph. Since cooling involves a drop in temperature over time, the graph curves downwards, resulting in a negative gradient.

The formula for the average rate of cooling between two points is:

Rate = (T₂ – T₁) / (t₂ – t₁)

Where:

• T₁ and t₁ are the initial temperature and time.
• T₂ and t₂ are the final temperature and time.

Steps to use this Calculator

1. Identify Point 1: Select a starting point on your graph's curve or tangent line. Note the Time ($t_1$) and Temperature ($T_1$).
2. Identify Point 2: Select a second point further along the x-axis. Note the Time ($t_2$) and Temperature ($T_2$).
3. Input Data: Enter these four values into the calculator above.
4. Select Units: Match the units to your graph labels (e.g., Minutes and Celsius).

Average vs. Instantaneous Rate

If you select two points far apart on a curved cooling graph, you are calculating the average rate of cooling over that interval. To find the instantaneous rate of cooling at a specific time, you must draw a tangent line touching the curve at that exact time, pick two points on that straight tangent line, and calculate the gradient using those coordinates.

Why is the result negative?

A negative result confirms that the object is losing heat. For example, a rate of -2.5 °C/min means the object's temperature drops by 2.5 degrees Celsius every minute. In many physics contexts, the "rate of cooling" is often referred to by its magnitude (2.5 °C/min) with the understanding that it represents a loss.