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