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.

Desired temperature (Celsius)

Hot water weight (grams)

Hot Water temperature (Celsius)

Cold Water temperature (Celsius)

### 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.

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.