Calorimetry

Let be the mass of water at , and be the mass of water at .

We are given that g, , g, and . Let be the final temperature of the mixture.

We can use the principle of calorimetry, which states that the heat lost by the hotter water is equal to the heat gained by the colder water.

Let be the specific heat of water.

Heat gained by the colder water is

Heat lost by the hotter water is

According to the principle of calorimetry, , so

Since is a common factor, we can divide both sides by :

So the final temperature of the mixture is .