Newton’s law of cooling

Newton’s law of cooling

When a hot body is placed in a room it emits heat energy because of the combined effect of convection as well as radiation. The amount of the heat energy that it can emit per one second can be calculated using this law.

According to this law the rate of loss of heat energy is directly proportional to temperature difference between the body and the surroundings.

It simply means that when the difference between the body temperature the surroundings temperature is more, the loss of heat energy will be quick and vice versa.

It can be also proved that the rate of loss of heat energy is equal to the rate of change of temperature.

We can also state the law as the rate of loss of temperature is directly proportional to the temperature difference between the body and the surroundings.

This law is valid only when the temperature difference between the body and surrounding is small.

Problem and solution

A body at temperature of hundred degrees centigrade is brought in the room of temperature 20°C. To cool from hundred degrees centigrade and 80°C has taken a time of 10 minutes. How much further time it will take to cool from 80°C to 60°C?

We have to solve this problem basing on the Newton law cooling.

The rate of loss of heat energy or the rate of loss of temperature is directly proportional to temperature difference between the body and surroundings. By applying this rule to the two different cases available we can solve the problem as shown.