Hey gang, here’s one I’ve been curious about. Why does it seem like coffee is barely tepid halfway done, but the last cautious sip of tea is still mouth-scaldingly hot? Different starting temperatures? Some effect of adding milk? Crazy delusion?
To find out if there’s any basis to this at all, we’ll need a standard of comparison. It seems reasonable to think that the liquid’s cooling rate is proportional to the difference between its temperature and room temperature. In math terms, we might say:
Where T = temp of the liquid, E = room temp (assuming it’s constant), k = a proportionality constant, and t= time.
Solving the equation for T gives: T=E-(E-Ti)e^(-kt)
And linearizing for k gives: ln(T-E)=kt+ln(Ti+E)
This tells us that the rate that the liquid temperature approaches room temperature is dependent on the size of k, and if we plot ln(T-E) against time as the liquid cools, k should show up as the slope of a straight line through the data points!
Perhaps the exclamation point betrays too much excitement over differential equations and slowly cooling water. Please don’t read into it.
To attain the experimental data, we monitored the temperature of a cup of liquid as it cooled to room temperature. The same measuring cup at the same temperature were used during all 3 trials, so its affect on the outcome should be minimized.
Not bad for a kitchen thermometer. After forcing the intercept to the predicted ln(Ti-E), the linear equation gives a k value of 0.0303 ±0.0015 /min.
Here’s the results of the same experiment run on a cup of coffee (brewed using 56g of fine grind coffee in 1L of hot water for 4 minutes). Besides producing a full-bodied blend with citrus notes, it also gave us a k value for coffee of 0.0312 ±0.0015/min.
According to these results, coffee seems to cool faster than water, but only enough to be 0.73°C cooler after 30 minutes. Not exactly the night and day I had in mind. Well, maybe tea cools a whole lot slower than water?
Well, a little. Which I must say is surprising. I had thought water would cool the slowest overall, but tea’s (1 bag of Tetley orange pecoe steeped 3 min in 300mL boiling water) k value of 0.0290 ±0.0015 /min shows it stays warmer longer than the rest.
So, after 300 minutes of carefully watching hot beverages gradually cool to room temperature, what have we learned?
1. Considering the bounds of experimental uncertainty, coffee likely cools faster than tea, but even assuming perfect accuracy it would be warmer by only 1.8°C after 30 minutes.
2. Science isn’t here to prove our ideas, but to improve them! Go science!