Heat Equation

Question

You want your water to be exactly 40.0 celsius. You have prepared 100. kg of water, but it is only heated to 38.5 celsius. You hurry over to a pot of boiling water, figuring that you can add just the right amount of water to get to 40 celsius. How much of the boiling water should you add?

Answer 1

Heat lost by the hot water = heat gained by the cooler water

q_(hot) = q_(cold) and q = mC∆T.  Assuming the hot water is at 100ºC and that C_(hot) = C_(cool)  then...

m_(hot) x C x (100-40)deg = 100 kg x C x (40-38.5) deg and C on each side cancel (you can substitute 4.184 kJ/kg/deg if you wish)

60m = 150

m = 2.50 kg of hot water should be added