Answer to Question #23995 in Molecular Physics | Thermodynamics for Maria

Question

When you take a bath, how many kilograms of hot water (49 degrees Celsius) must you mix with cold water (13 degrees Celsius) so the temperature of the bath is 36 degrees Celsius? The total mass of water (hot and cold) is 191 kg. Ignore any heat flow between water and it's external surroundings.

Answer 1

Total mass is 191:

m1+m2=191
mix of 49C and 13C water must five 36C water.
Hence

m1*(49-36)=m2(36-13)
13m1=23m2
m1=m*23/13
m2(1+23/13)=191
m2=69
m1=191-69=122

So, there must be 122 kg 49C of water and 69 kg of 13 Cwater