When two quantities of water are mixed at different temperatures, a heat transfer occurs during the process. In this case the mass of colder water, absorbs a quantity of heat equal to that released by the hot water.

The equation of the amount of heat absorbed or released by a substance, for a variation in temperature is:

Q = m Ce (Tf – Ti), where:

Q: is the amount of heat absorbed or released

Ce: is the specific heat of the substance

m: is the mass of the substance

Ti: is the initial temperature T

Tf: is the final temperature T

Then we can write for each portion of water, the following equations:

For hot water:

- Qh = mh Ce (Tf – Th); the negative sign represents that heat is released.

For cold water:

Qc = mc Ce (Tf – Tc)

Equating the above equations:

- Qh = Qc

- (mh Ce (Tf – Th)) = mc Ce (Tf – Tc)

Now we solve this equation for the value of the final temperature Tf

- ((200 g) Ce (Tf – 90°)) = (20 g) Ce (Tf – 0°)

- 200 Tf + 18000 = 20 Tf

Tf = 81.8°C

**So that, the final temperature of the mixture is 81.8 °C**