(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

When you take a bath, how many kilograms of hot water (49°C) must you mix with cold water (12°C) so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 191 kg. Ignore any heat flow between the water and its external surroundings.

Temperature of the Cold Water: 12 C

Temperature of the Hot Water: 49 C

Temperature of the Total Water: 36 C

Mass of the Cold Water: y, 191-x

Mass of the Hotwater: x, 191-y

Mass of the Total Water: 191 kg

2. Relevant equations

Q =mcΔT

Where Q is Joules of Energy, m is Mass of the substance (kg), c is the specific heat coefficient, ΔT is change in Temperature (in Celsius)

3. The attempt at a solution

Total Q = 191 kg * 4186 J/kgC * 36 C

Total Q = 28782936 J

Hot Q = X kg * 4186 J/kgC * 13 C

Cold Q = (191 - X) kg * 4186 J/kgC * 24 C

28782936 J = Hot Q + Cold Q

28782936 J = (X kg * 4186 J/kgC * 13 C) + ((191 - X) kg * 4186 J/kgC * 24 C)

28782936 J = (X kg * 54418 J/kg) + ((191 - X) kg * 100464 J/kg)

28782936 J = 54418X J + 19188624 J - 100464X J

28782936 J = 19188624 J - 46046X J

9594312 J = 46046X J

208.36 kg = X (Answer only needs to be to 2 decimal places)

^This does not make sense, because the mass of the hot water is larger than the mass of the total water. Assistance?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Heat and Internal Energy and Heat and Temperature Change: Specific Heat Capacity

**Physics Forums | Science Articles, Homework Help, Discussion**