What happens to the temperature when you mix hot and cold water together?

Answer 1

This can be confusing at first but after you do the calculations there is really nothing to it.

NOTE: adding temperatures DOES NOT work for this eg

if you have 53 degrees C of water and you add 32 degrees C of water, despite how much I wish that it worked like that and so that our energy bills wouldn't cost a thing, the final temperature is NOT 85 degrees C nor vice versa

The easiest method of calculating the change of temperature is to know the heat energy of the system. Whereby

Q = mcT

m = mass of water in this case

c = heat capacity of water

T = Temperature in Kelvin I believe

so take 33 mL of water at 45 degrees C and add that to 750 mL of water at 87 degree C

Calculate the respective energies and add them together:

we have c = 4.1855 [J/(g·K)] (15 °C, 101.325 kPa)

m1 = 33g

T1 = 45 + 273 = 318 degrees K

Q1 = 43.922 Joules

m2 = 750g

T2 = 87 + 273 = 360 degrees K

Q2 = 1130.085 Joules

Now Qfinal = mfinal * c * T final

so Qfinal = Q1 + Q2 = 1174.007 Joules

mfinal = 33 + 750 = 783g

therefore the final temp of the system must be (given that I've got the correct values so far :P ) :

Tfinal = Qfinal /mfinal *c

Tfinal = 358 degree K or 85.23 degrees C, which makes sense if you think about it, as most of the water was hotter, and you only added a small amount of cold, meaning that the temp. shouldn't, if you think about it, drop too substantially.

Hope this helps.

Cheers.