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Homework Help: Calculate the power temperature

  1. Jan 19, 2010 #1
    Edit: Topic title should read power and temperature

    1. The problem statement, all variables and given/known data

    Humans convert most of a 2000 kcal typical daily diet into heat. Calculate the power. What is the increase of temperature in a room with a volume of 15000 m^3 filled with 250 people over a 60 minute period?

    Note: Power is defined as energy/time.
    1kcal = 4.186kJ.
    density of air = 1.29kg/m^3
    molar mass of air = 29g
    Treat air as a diatomic gas

    2. Relevant equations

    C = change in internal energy/ number of moles * change in temperature = f/2*R

    3. The attempt at a solution

    60 * 60 = 3600

    2000 * 4.186 = 8372kJ/3600s = 2.3kJ/s = 2.3W

    Specific Heat Capacity = 5/2 * R = 5/2 * 8.31 = 20.8 kJ/moleK

    I'm really struggling with where to take it from there. I'd guess you would either use change in internal energy/ number of moles * change in temperature or use average kinetic energy = 5/2kT = 1/2mv^2rms but I'm not sure how to calculate the relevant data for either plus that doesn't use all the information given.
    Last edited: Jan 19, 2010
  2. jcsd
  3. Jan 19, 2010 #2
    I have not played with attempting the find the specific heat of air before so I'll let someone else help you there. I can tell you that the power involved is not 2.3 W because there are not 3600 seconds in a day. Note that the problem said "daily." And a watt is not equal to kJ/s but J/s. Due to those two errors, your power is small by an order of magnitude.
  4. Jan 19, 2010 #3
    Thank you for the help.
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