From: gerry@cmu.edu (Gerry Roston)
Newsgroups: sci.skeptic
Subject: Re: Well known scientific facts
Date: 30 Sep 92 17:45:46 GMT
Article-I.D.: onion.GERRY.92Sep30124546
Reply-To: gerry@cmu.edu (Gerry Roston)
Organization: Field Robotics Center, CMU

Let me redo my post from yesterday... it was a long day.

Let's start with a basic equations, developed for an ideal gas:
u2 - u1 = m cv (T2 - T1)         (*1)

where 
u2, u1 are the internal energy of the working fluid (J)
cv is the constant volume specific heat (J / kg K)
m is the mass of the working fluid (kg)
T2, T1 are the final and initial temperatures (K)

From the first law of thermodynamics 
U = W + Q                        (*2)

Where 
Q is the heat applied to the system (J)
W is the work done on the system (J, but zero in the case of a
   thermometer) 

So, equation (*1) reduces to
Q2 - Q1 = m cv (T2 - T1)         (*3)

Now, let take the first time derivative of (*3).
qd = m cv (T2 - T1) / t          (*4)

where
qd is the time rate of change of heat (J/s or W)
t is the time (s) 
Note: This assumes that m and cv are constants, and cv isn't, however,
the change will be negligible under the conditions in a thermometer.
Also, dt is approximated by (T2 - T1) / t.  This approximation is
valid since hte temperature excursion is small.

(*4) can now be solved for t:
t = m cv (T2 - T1) / qd          (*5)

Let us assume for the moment that qd, the rate of heat flow into the
thermometer is constant for a person, regardless of their temperature.
This then means that the only factors affecting the time for the
thermometer to register the temperature are m, cv, dT. 
Falsification 1: All thermometers do not have the same working fluid
mass, thus different thermometers will yield different results.  Thus 
the original claim is shown to be false.
Falsification 2: All thermometers do not use the same working fluid, 
thus different thermometers will yield different results.  Thus 
the original claim is shown to be false.
Falsification 3: Noting that the difference in temperature between a 
fevered patient and a healthy patient will not exceed about 6-7C, we
must look at the initial temperature of the thermometer.  Since this
is never accounted for (have you ever seen a thermometer taken from a
temperature controlled box and have it placed immediately in the
patient?), the variation in initial temperatures can exceed the
difference in patient temperatures by a factor of 2-3. Thus the 
original claim is shown to be false.

Now, let us explore the equation to determine the heat flow:
qd = k A (T2 - T1)            (*5)

where
k is the coefficient of heat conduction (W / m^2 K)
A is the area of contact

Falsification 4: All thermometers do not have the same barrier
material surrounding the working fluid.  Thus, the original claim 
is shown to be false.
Falsificaiton 5: Not all patients mouths are the same size, thus
affecting the area of contact. Thus, the original claim is shown to be
false.

Basically, the original claim is completely, and totally, full of
shit. For it to be true, one would have to believe that:
-The thermometer used is specific to the particular patient
-The thermometer is at some known initial coniditions before being
 used
-All thermometers are manufactured such that the thermal constants and
 mass all cancle each other out so they all appeas thermodynamically
 equivelent. 
-People who measure your temperature closely what the thermometer and
 determine differences in rise times with an accuracy of only several
 seconds. 

And if you believe this, you'll believe anything.

--
Gerry Roston (gerry@cmu.edu)    | The most foolish mistake we could possibly
Field Robotics Center,          | make would be to allow the subjected people
Carnegie Mellon University      | to carry arms, history shows that all
Pittsburgh, PA, 15213           | conquerors who have allowed their subjected
(412) 268-3856                  | peoples to carry arms have prepared their own
                                | fall. Adolph Hitler
The opinions expressed are mine | 
and do not reflect the official | 
position of CMU, FRC, RedZone,  | 
or any other organization.      | 
Newsgroups: sci.skeptic