Temperature don’t add up; they average out
The Sunday Nation
Nairobi,
11 August 2013
Some times you make an innocent comment and it turns out to be a very
serious matter. On September 27 1905, Albert Einstein wrote a short
(700-word) letter to the scientific journal
Annalen der Physik in which he
posed a simple question: “does the inertia of
a body depend upon its energy-content?” In it he showed the derivation
of the now famous equation “E=Mc2” which has helped in the
development of nuclear energy and atomic bombs.
Another not very well know scientist, Louis de
Broglie, posed an equally innocent question in his PhD thesis: “Is the
momentum of a particle a wave phenomenon?” That formed the basis for the
principles of quantum mechanics.
In that spirit, when Kibet Kipkeu sent in a
question which says is a joke, I decided to take him seriously. Here it
is: “Why is it that when two people stay close together the temperature
does not go up to 74 degrees centigrade (assuming that average temp for
each person is 37 degrees)?”
This question sounds like another one that was
asked a few years ago by a different reader: “What temperature is twice
as cold as zero degrees?”
Perhaps it may help to understand why that
doesn’t happen when we consider a slightly different scenario. If you
have a litre of water at 50 degrees and you added another litre at the
same temperature, would the resulting mixture now be at 100 degrees?
Such a suggestion sounds totally irrational!
Of course we know that the final temperature will be just 50 degrees.
Temperatures don’t add up, they average out. Thus if the second litre
was at 30 degrees (50 + 30 = 80; 80/2 = 40), the mixture would settle at
40 degrees.
Therefore; when two people at 37 degrees sit
together, their new average temperature is: 37 + 37 = 74; 74/2 = 37.
They don’t get hotter. But why do they feel warmer? Indeed, in this cold
season, why does a crowded room feel a lot warmer than an empty one?
The reason for the warming is the heat
radiated by the human body. Two bodies at the same temperature radiate
twice as much heat as one.
I do recall calculating the heat radiated by a
human body in a previous article published in August 2004. The answer
came to about 200W when a person is standing naked on a normal day when
the temperature is around 20 degrees.
But when all dressed up, we may estimate that
the rate of heat loss drops by three-quarters to just 50W. Thus when two
people are sitting close together, the total radiation goes up to 100W.
But, just like in the case of mixing water, their temperatures do not
add up!
The two people will obviously raise the temperature of their surrounding, but estimating the magnitude of that rise is a very difficult exercise. There are two many variables at play so the rise in one room is totally different from that of another.
Nevertheless, Kibet may want to answer this one: if it takes one hour to dry one shirt in the sun, how long would it take to two identical ones?
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