why does it take faster for hot water to cool down than for cold water to warm up?


Just realized that everytime I have a cup of hot water out it cools down fairly quickly, but a cold cup of water does not necessarily warn up

In: Chemistry

The water in the cup will want to have the same temperature as it’s surrounding. The bigger the temperature difference the quicker the water will change its temperature to get closer to the temperature of the surrounding air. Since the difference between hot water (90-100C) and the air (~20) is usually much greater than between cold water (0-10C) and air the hot water will change its temperature much faster.

It doesn’t, thermodynamics doesn’t care which direction it goes. If you think about how heat transfer works this makes sense, because “cooling” and “heating” are not really different. If there is a temperature difference, then heat goes from the hot object to the colder object. So when you have cold water on a warm day it means the heat from the hair goes to the water. If you have hot water on a cold day it means heat goes from the water to the air.

As you can see, in both cases it is heat from the highest temperature that goes to the lowest temperature. This is important, because it means there are fundamentally no difference. The terms “cooling” and “heating” are basically just used to refer to which way the heat transfer goes – from the water or to the water.

Okay, so that don’t completely explain your question – because you clearly have noticed a difference. Well, if you have room temperature of 20 degrees celsius and then have two glasses of water, one being 10 degrees and the other being 30 degrees then they will reach room temperature of 20 degrees at the same time.

Now, take two new glasses of water, but now they are 10 degrees and 40 degrees. The hot one will *not* take double the time as cold one, despite having double the temperature difference. This is because heat transfer goes *faster* with a higher temperature difference. At the start it goes fast, then gradually it goes slower and slower. So the time from 40 to 30 degrees might take a minute, then the 30 to 20 takes 2 minutes (totally random numbers, but you get the idea).

A more common example from your normal day is a cup of coffee. When you make it with boiling water it is 100 degrees, that is extremely hot and burns your tongue. Yet, in a few minutes it cools down to where it is perfectly drinkable, but takes quite a long time to get down to room temperature. This shows how the heat transfer kind of “decelerate”.