# Question #48b2b

##### 1 Answer

Final temperature:

#### Explanation:

The idea of this problem is that the water with the *higher* temperature will lose heat and that the water with the *lower* temperature will gain **the same amount** of heat.

Mathematically, this is expressed as

**lost** by the warmer sample;

**gained** by the cooler sample.

Heat *lost* by a system is **negative**, while heat *gained* by a system is **positive**, hence the minus sign used in the above equation.

The equation that establishes a relationship between heat gained or lost and change in temperature looks like this

So, you mix the two samples together and a thermal equilibrium is reached, meaining that the final temperature will be the same for both samples.

This means that you can write

which is equivalent to

Finally,