Time it takes to reach equilibrium

  1. Pengwuino

    Pengwuino 7,119
    Gold Member

    Ok lets say i have a metal ball at 50 C and 2 thermal reservoirs at 300 C and 500 C.

    Will the metal ball reach 200C faster in the 300C or 500C reservoir? (Sorry the title name is misleading). Basically, the question is there a relation between temperature and the time it takes to transfer energy or is the tim relationship only dependant on the type of material being used?
  2. jcsd
  3. Peng,

    Hint: What if one reservoir were at 200 degrees. How long would it take for the ball to get to 200 degrees?
  4. Pengwuino

    Pengwuino 7,119
    Gold Member

    Thats what i want to know and i want to know the relationship to the temperature. Will the ball reach 200 faster in a 300C reservoir or a 500C reservoir? Or is the time it takes only dependant on the materials used.
  5. Q_Goest

    Q_Goest 2,949
    Science Advisor
    Homework Helper
    Gold Member

    Heat transfer is always a function of the difference in temperature, so given a ball at 50 C, if the only difference is environment temperature, it will warm faster in the hotter environment.
  6. HallsofIvy

    HallsofIvy 40,225
    Staff Emeritus
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    Newton's law of cooling (or heating): Heat moves from the hotter environment to the cooler at a rate proportional to the difference in temperatures. In this case, the heat moves from the reservoir to the metal ball at a rate proportional to the difference in temperatures: heat moves faster from the higher temperature environment and so the ball heats faster.
  7. Pengwuino

    Pengwuino 7,119
    Gold Member

    Whats the formula for this?
  8. FredGarvin

    FredGarvin 5,087
    Science Advisor

    [tex]q = h*a \Delta T[/tex] where:

    q = rate of heat transfer (watts usually)
    h = heat transfer coefficient (in w/m^2*K)
    a = effective area (m^2)
    Delta T = temperature difference (K)

    You may also see it in the form of:
    [tex]q'' = h \Delta T[/tex] where:

    q'' = heat density in W/m^2
    Last edited: Apr 4, 2005
  9. Gokul43201

    Gokul43201 11,141
    Staff Emeritus
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    You missed the point of jdavel's hint. If the reservoir itself is at exactly 200C, it will take an infinitely long time to reach 200C. So, is that not indicative of what your answer should be ?

    The shape of the heating/cooling curve is an exponential growth/decay. The driving force is the temperature gradient.
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