# Newton's law of cooling

Newton's law of cooling states that the rate of cooling of an object is approximately proportional to the temperature difference between the object and its surroundings.

Let ΔT be the difference in temperature between the object and its surroundings.

Then,

Rate of cooling ~ ΔT

~ means closely equal.

Now, what do we mean by rate of cooling and temperature difference?

What usually happens when the temperature of an object is not the same as the temperature of its surrounding?

We know for a fact that the object will try to reach a temperature that is as close as possible to the temperature of the surroundings.

If this was not true, then you could never cool down a pizza or your house will never get cold during the winter season.

The rate of cooling is referring to how fast an object will cool down or lose its heat.

Suppose you just baked a pizza and you removed it from the oven.

At that instant the pizza is removed from the oven, its temperature could be as high as 150 degrees Fahrenheit.

A temperature of 50 degrees Fahrenheit in your kitchen will cool down the pizza faster than a temperature of 80 degrees Fahrenheit.

You can see that the temperature difference between the pizza and the room temperature of 50 degrees is 100 degrees Fahrenheit.

Similarly, a temperature of -5 degrees Fahrenheit outside will make your house lose heat faster than a temperature of 50 degrees Fahrenheit.

That is why it is more expensive to keep your house warm during the winter season.

### Newton's law of cooling or heating

If an object is cooler than its surrounding, its rate of warming up is also proportional to the temperature difference between the object and its surroundings.

A frozen chicken will warm up faster in a warm kitchen than a cold kitchen.

We can use Newton's law of cooling to find the temperature of an object after a certain amount of time has elapsed.

However, this will require the use of differential equations to find an appropriate equation. This is beyond what we are trying to accomplish at the moment.

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