1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
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

  1. Nov 9, 2008 #1
    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?
    Last edited: Nov 9, 2008
  2. jcsd
  3. Nov 9, 2008 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Total Q = 0 .

    So the equation should be [itex]Q_h + Q_c=0[/itex]

  4. Nov 9, 2008 #3
    Thank you very much! I don't know how I missed that.
  5. Feb 12, 2011 #4
    Hey I really need this answered I've been working on it for 3 hours help.
    Question: You want to take a bath with the water temperature at 35.0 degrees C. The water temperature is 38 degrees C from the hot water tap and 11 degrees C from the cold water tap. You fill the tub with a total of 187 kg of water. How many kilograms of water from the hot water tap do you use?
    Please help.
  6. Feb 12, 2011 #5
    Just kidding i'm stupid. i figured it out... sorry for wasting your time.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook