A warm can of soda is placed in a cold refrigerator. Sketch...

A warm can of soda is placed in a cold refrigerator. Sketch
the graph of the temperature of the soda as a function of time.
Is the initial rate of change of temperature greater or less than
the rate of change after an hour?

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Key Concepts

Newton's Law of Cooling

This concept explains how the rate of temperature change of an object is proportional to the difference between its own temperature and that of the surrounding environment. It provides the mathematical framework, using a differential equation, to model the cooling (or heating) process, illustrating that a larger temperature difference results in a more rapid change initially, and as the difference decreases, the rate slows down.

Exponential Decay

The temperature of an object cooling in a constant environment typically follows an exponential decay curve. This means that the rate of temperature change is fastest at the beginning and asymptotically approaches the ambient temperature, resulting in a curve that is steep at first and then levels off as the object reaches thermal equilibrium.

Thermal Equilibrium

This is the state that the object eventually reaches where its temperature becomes equal to the ambient temperature. At thermal equilibrium, the net heat transfer ceases, and the temperature of the object remains constant. In the cooling process, the changing rates of temperature adjustment in the graph approach zero as equilibrium is reached.

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