I needed hot water at around 80-85 Celsius to use with AeroPress. At the time, I didn't have a thermometer that goes higher than 50C. I know the room temperature and the temperature of near-boiling water (close to 100C ). The result: a calculator, for a cool (pun intended), practical use of thermodynamics.

### The Question#

How many grams of ~20C water are needed to lower the temperature of 500g of ~100C water to ~85C?

### Calculator#

Here is a calculator to do that for us. Go ahead and change the values for desired temperature and room/ambient temperature to get your answer.

### Answer#

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(Note: desired temperature should be between Cold and Hot water temperatures)

### Detailed Solution#

Via convection, heat transfers from the hotter liquid to the colder.

$$QLostFromHot=QGainedFromCold$$

We can calculate heat transfer quantity using

$$Q=mC(ΔT)$$

Putting those two together we get

$$Q1 + Q2 = 0$$

$$M1•C•(T - T1) + M2•C•(T- T2) = 0$$

$$500•C•(85 - 100) + M2•C•(85 - 20) = 0$$

$$500•C•(-15) + M2•C•(65) = 0$$

$$M2•C•(65) = 500•C•(15)$$

And, solving for M2, we get

$$M2=\frac{500•(15)}{65}$$

$$M2=\frac{500•(15)}{65}$$

$$M2=\frac{7500}{65}=115.3g$$

I need to add 115.3g of room-temperature water.