The simplest method is to measure the temperature of the mixture of water with any suitable thermometer. Suppose, starting to fill a bathtub or other container, you have put too hot water. Then, discovering his mistake, you immediately turned off the faucet of hot water and added a certain amount of cold. How to determine the final temperature? Thoroughly mix the water and use any suitable thermometer (e.g., medical).
You can also calculate the final temperature of the mixture in advance. Suppose you have a volume V1 of hot water with a temperature of t1. To it is added a quantity of cold water with the volume V2 and temperature t2. Want to calculate what the final temperature t will have a mixture. The heat loss to the environment can be neglected.
And heat capacity, and density of water at different temperatures the same. Therefore, the final temperature will depend on the volume ratio. It is easy to understand that in any case the final temperature t will be between t1 and t2, but less than the value of V2 compared to V1, the closer is t to t1, and Vice versa.
The final temperature t is calculated according to the following formula: t = (t1V1 + t2V2) / (V1 + V2). Substituting in this formula the values of temperatures and volumes, and performing calculations, you determine the desired temperature of the mix water.
Of course, your task would be solved in precisely the same manner, if instead of the volume you would have known mass of water, m1 and m2.
It is easy to understand that in the same way is the temperature of the mixture of any of the same liquids, not just water. If we are talking about the temperature of the mixture of different liquids, then the calculations must take into account their specific heat capacity, and that the simplified formula can not be applied.