[net.physics] Last of the tea discussion?

lew (01/09/83)

Jeff Halle stated:

"Adding the cream will reduce the temperature of the tea by the same
amount whenever it is added. That is, the temperature will drop by
x degrees, not by x%."

The error of this assertion is obvious if one considers the limiting
case when the tea is nearly at room temperature. I'm sure most readers
know that the final temperature is the weighted average of the initial
temperatures, the weights being the heat capacities. This is just energy
conservation:

	Ca*Ta + Cb*Tb = (Ca + Cb)*Ta+b

Lew Mammel, Jr. ihuxr!lew

halle1 (01/10/83)

Lew is incorrect in his statements.  The final temperature is a weighting
of the heat CONTENTS of the fluids.  The equation he states is far too
simple on the left and incorrect on the right (although that may be due
to typos).  The correct eqn. is:
m(tea)c(tea)(T[i]-T[f])+m(milk)c(milk)(T[i]-T[f])=0, where c is the
specific heat or heat capacity, and the T's are the obvious ones.
	Lew is correct that my statement is wrong if the two liquids are 
too close in temperature.  If the temperature change when the milk is added
immediately is greater than the difference in temperature when the milk is
added later, then the temp. cannot drop the same amount.  However, this
is a case that would not occur (why heat it if you're going to drink it
at room temperature).  I did not state the assumption that the temperatures
were far enough above room temperature, which by the way does not have to be
too far if only a moderate amount of milk is used, because I felt it was
obvious and my discussion was too long as it was.  I will be more careful
in the future.  
	Please address further discussion through mail to clear the net
for new and/or more interesting topics.
					Jeff Halle
					houxz!halle1