By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

03 May 2015

Can one save energy by heating a large quantity of bathing water only slightly instead of heating a small amount to a high temperature and then cooling it?  To get the answer, we must ask another question. Which has more energy: one a litre of water and two litres at the same temperature? It’s not a trick like the one of a kilo of iron and a kilo of wool!

To find out, we ask yet another question: how much effort is required to bring the water to a certain temperature? Suppose the two containers are at 20 degrees celcius and we want to heat them separately to 50 degrees. Is it reasonable to expect that the one with 2L will take twice as long at the one with 1L? Yes!

If so, we can conclude that we pumped in twice as much energy into the 2L of water as we did into the 1L. That is, at 50 degrees, 2L of water has more energy than 1L. But does it have twice as much? To find out that we have to do a different experiment.

Suppose we have a heater that can heat 1L of water to 50 degrees in five minutes. To what temperature would it warm 2L in the same duration? Is it reasonable to say 25 degrees (a half of 50)? You might think so but you would be wrong because you are missing one very important piece of information: the starting temperature.

If we are starting from normal room temperature (about 20 degrees celcius) and our heater can heat the 1L of water to 50 degrees, then it is adding 30 degrees in five minutes. Therefore, it would add half of 30 degrees - that is, 15 – to the 2L. That is, the final temperature of the 2L should be 35 degrees.

In summary; adding the energy from our heater for five minutes to 1L of water takes it 50 degrees, but doing the same to 2L only reaches 35 degrees. What would happen if we now added cold water (at 20 degrees) to these two containers to make it 4L in each?

For the container with 2L at 35 degrees, we would add another 2L to make 4L. Half of the excess energy in the hotter water will go to colder one and so the temperature of the mix will be exactly half-way between 20 and 35 degrees. That is, 27.5 degrees.

For the container with 1L at 50 degrees celcius, let’s do things step by step. First we add 1L of cold water. This brings the temperature to middle of 20 and 50, that is, 35 degrees.

Next we add the remaining 2L at 20 degrees and this will drop the temperature to the middle of 20 and 35, that is, 27.5 degrees – exactly the same as the previous case!

Therefore, it doesn’t matter which way you do it; the only important thing is how long you heat the water.