## Making coffee: An interesting little physics problem

Yesterday, I broke my thermometer and thus I can no longer boil water to the exact temperature of 194F(90C) required for optimal taste—by now, it is well-known that the right temperature is nine tenths of the secret to great coffee.

Here’s where my education comes into play. I know that water boils at 100C and that by heating water, I can not make it hotter than 100C. I also know that the water coming out of the faucet is about 20C—okay, I’m just guessing about that one.

What I have is

- The ability to make 100C water.
- The ability to make 20C water.
- The ability to combine them at a certain ratio to make 90C water.

I also know that the heat capacity of water is more or less constant, hence if X denotes the fraction of 100C (373K) water and Y denotes the fraction of 20C (293K) water and we want to end up with 90C (363K) water then

X+Y=1 and 373X+293Y=363(X+Y)=363, so *waves hands* Y=0.125.

Hence, I boil 1.75 cups of water, and I add 0.25 cups from the faucet and this automatically gives me the right temperature.

Physics saved the day. More importantly, it saved me from buying a new thermometer; also this is much more convenient than trying to hit 90C/194F by watching the thermometer while heating the water.

On a side note, this is one of the rare instances, where high school math and physics is actually useful outside the class room. I recall an anecdote where the Danish ministry of education or whatever sponsored a contest for math teachers to come up with one realistic real world example where one would have to solve a quadratic equation to get the answer. They received one entry that qualified. It’s not difficult to come up with examples, but it is quite difficult to come up with examples of problems that are frequently encountered.

Well, at least you have now seen a real world example of using linear algebra to brew coffee.

Of course, I could just have bought a new thermometer.

Much thanks to AW and IP for the donations.

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Originally posted 2010-09-07 11:14:45.