If you add cooler water to hotter water is the end temperature the average between the two?

Question

E.g. If you have some water at boiling point, 100 C, and add the same volume of water again which is at half way to boiling point, 50 C, does the resulting water end up at 75C?

Answer 1

If you add equal volumes and assume there is no heat loss during pouring and mixing, then yes it will be the average.

If you add unequal amounts, you will have to weight the average by the amounts.

Answer 2

It depends on how accurate you want to get. For most purposes, saying its 75 degrees would be close enough, but its not completely accurate.

To be more accurate, you would need to add equal masses of water together, not volumes (since the density of water changes with the temperature).

Even then, it's still incorrect because the heat capacity (amount of heat energy it takes to raise its temperature) also varies by temperature. Generally, the higher the temperature, the higher its heat capacity. Or, for example, it actually takes slightly more energy to raise water from 86 C to 87 C than it did to raise it from 85 C to 86 C.

What this ultimately means is that mixing 1kg of 100 C water and 1kg of 50 C water will end up with 2kg of slightly above 75 C water; eyeballing it off of a chart puts it at about 75.15 C. Unfortunately I don't have the equation for the heat capacity of water in front of me to give you an exact answer.

Answer 3

So moist and so delicious, I was asked to bring this to work every time they had a bake sale for the employees. Apple Cake 4 cups diced peeled apples 2 cups sugar 1 cup raisins 2 tsp salt, divided ================= 3/4 cup oil 2 eggs, beaten 1 cup walnuts ================= 2 cups flour 2 ½ cups apple juice 2 t baking soda 2 t cinnamon • Mix apples, sugar, raisins, 1 tsp salt. Let stand 1 hour • Add oil, eggs and walnuts. • Sift in flour, juice, baking soda, cinnamon and 1 tsp salt. • Pour into greased 13” x 9” baking dish, 350 degrees for 1 hr and 15 minutes. • Let cool 15 minutes before serving.

Answer 4

As long as it's the same volume of pure water, then yes.