# Cooling things down and the method of mixtures

A hot cup of black coffee can be cooled by putting some milk in it.
If your bath is too hot you can cool it down by running in some cold water.
A car engine is cooled by water flowing round it.
Sane nuclear reactors are cooled by liquid sodium.
Fire walkers can walk on red hot cinders without damaging their feet.

These things can all be explained by thinking about the "sharing out" of heat energy. Lets think about the coffee and the milk.

When you add the cold milk to the coffee the coffee gives some of its heat energy to the milk. The coffee cools down and the milk warms up. They will both end at the same temperature of course.

So if we mix together something that is hot and something that is cold and as long as no heat is lost to the outside:

HEAT ENERGY LOST BY HOT OBJECT = HEAT ENERGY GAINED BY COLD OBJECT

Water is a very good liquid for cooling things down, for one thing there is plenty of it and it has also got a high specific heat capacity. This means that it can absorb a large amount of heat energy without getting too hot.

Fire walkers can walk on the red hot embers because the embers are light and have a low specific heat capacity. Your feet and body are heavy and so can absorb the heat energy without the temperature of your skin getting too hot.

THIS IS A DANGEROUS PRACTICE – DO NOT ATTEMPT TO TRY WALKING ON ANY HOT MATERIALS.

Example problem– a difficult one. Almost advanced level!
A 2 kg lump of cast iron at 90oC in put into a plastic bucket containing 10 kg of water at 20oC. What is the final temperature of the water and iron (you can ignore the heat energy absorbed by the bucket and assume that no heat energy is lost to the surroundings.)

Specific heat capacity of water = 4200 J/(kg K).
Specific heat capacity of cast iron = 500 J/(kg K)

Let the final temperature of the mixture be θ.
Heat energy lost by the iron = 2x500x(90 - θ) = heat energy gained by the water = 10x4200x(θ-20)

Therefore 1000(90 - θ) = 42000(θ -20)     90000 – 1000θ = 42000q – 840000
930000 = 41000<θ    and so θ = 930000/41000 = 22.7oC

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB

© Keith Gibbs 2020