Newton's Law of Cooling is a fundamental principle that describes how objects lose heat to their surroundings. When a hot object is placed in a cooler environment, it will cool down over time. The key insight is that hotter objects cool faster when there's a larger temperature difference between the object and its environment.
The mathematical formula for Newton's Law of Cooling is expressed as a differential equation: dT over dt equals negative k times the quantity T minus T environment. Here, dT over dt represents the rate of temperature change, T is the object's temperature, T environment is the constant environmental temperature, and k is a positive cooling constant. The negative sign indicates that temperature decreases when the object is hotter than its surroundings. This creates an exponential cooling curve as shown in the graph.