Have you ever wondered how accurate the measurement of your temperature
And I don't mean the accuracy of your thermometer; most of the thermometers
you can buy nowadays are accurate to less than 0.1 degree celsius.
Imagine that you just had a nice cool drink from your mother but a few minutes
later she wants to take your temperature AGAIN.
You stick the thing into your mouth and patiently wait for the beep. ...
BEEP! Ok, lets see. Well, this looks rather good. Much less than this morning! Good boy (or girl)!
Keep at it!
Later that evening, after having a nice chicken broth for dinner, it's time for a last
BEEP! This time your mother gives it a wide-eyed stare and reaches for the phone...
Well, it COULD be that the things you've devoured right before the measurement might have
an influence to the local temperature in your mouth. Why not? After all we all know that
things can be heated up and then will cool down following a negative exponential curve.
'Right', one might say, 'but the human body is not a 'thing'. It's living tissue that controls
its own temperature quite successfully. At least we do not FEEL that our mouth is
colder than usual after a cool drink, do we?'
To clarify this lets do a little experiment. The following graph shows my temperature take in intervals
after having a piece of hot apple pie (red) and after half a glas of icewater (blue). The dotted
horizontal line represents my average temperature taken four times right before the experiments.
As you can see the temperature sharply jumps +0.7 (red) and -2.0 (blue) degrees right after
the intake of warm and cold substances respectively.
After that it takes a rather long delay (about 1000sec)
until the temperature returns to the average value.
Lets call this effect the STE effect (Schiel Temperature Error) for now.
Now, if STE is indeed a negative exponential decrement (at least that's what it looks like),
T(t) = T_aver + T_0 * exp[ -t/tau ]
with: T_aver = average temperature
T_0 = temperature deviation at time 0
tau = time constant
then there are two things to learn:
- the time constant
tau seems to be independend from the initial deviation
(since both curves return to the average at about the same time).
- the time constant
tau for both curves is about about 200sec (when the temperature
So, what can we learn from these premises:
If we want to achieve reliable measurements, it follows that deviations caused by prior
intake of food or beverages should not influence the measurement more than the assumed accuracy
of the thermometer itself. Most manufacturers claim that their thermometers are exact to less than
0.05 degrees celsius (not taking into account all the errors that may be caused by inproper
So, lets say the maximum error we allow due to the STE effect should be +/- 0.05 degrees celsius.
Unfortunately this means that the minimum time period
that we have to wait after the food/beverage intake
depends on the temperature deviation at time zero
t_min = - tau * ln[ 0.05/T_0 ]
This is rather impractical because we don't know what
T_0 is without an extra
measurement. Therefore lets simplify by using the worst-case-scenario of
T_0 = 3 degrees
(I doubt that we can actually achieve that; at least not on the warm side!).
t_min can be directly determined as:
t_min = - 200 * ln[ 0.05 / 3.0 ] = 818sec
From the observed SET effect it follows deductively that Moms should always allow a time
period of at least 818 seconds after any food or beverage intake before taking the temperature.