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?


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.



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

Detailed Solution#

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


We can calculate heat transfer quantity using


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




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