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Newton's Law of Cooling & Specific Heat Capacity

  1. Jun 21, 2012 #1
    Newton's Law of Cooling basically states (I believe):
    TObj = (TInital-TEnv)ekt + TEnv
    where k is a property of the material.

    In the equation:
    Specific heat capacity, C, is also a material property.

    So here's my question:
    Is there a relation between Newton's Law's k and the specific heat capacity of the material?
    Also, I'm in a debate whether Newton's Law requires a draft to be accurate. Any information either way would be useful.

  2. jcsd
  3. Jun 22, 2012 #2
    Yeah ,


    Yeah , it requires draft to be "more" accurate....

    I would like other members as well to post their views...
  4. Jun 22, 2012 #3
    The general law states that the rate of heat transfer is proportional to the temperature difference and the area of contact.
    Solving for a body cooling in some environment with fixed temperature produces an expression like the one you propose. Only that for cooling the exponent is negative. Your solution correspond to a temperature that increases indefinitely in time, unless you assume k<0.
    Indeed the time constant in the exponent depends on the specific heat capacity of the body (and its mass too).
  5. Jun 22, 2012 #4


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    It's not that it requires a draft, merely that what it's in contact with has effectively a constant temperature. In air, some forced draft, rather than mere convection, will certainly be needed. But in principle it could be encased in a solid with a very high specific heat.
    The concept of a Tobj also suggests the object maintains a uniform temperature, which would imply a very high conductance. In practice, the temperature profile through the object will tend to change over time. It is probably not right to take an average temperature and expect the equation to work exactly, but I could be wrong.
  6. Jun 26, 2012 #5
    Newton's Law of cooling can also be stated as
    ln(TObj-TEnv) = kt+c
    k can therefore be found by finding the gradient of the trend line of the natural logarithm of the difference in temperature between object and the environment as a function of time.
    However, would I be correct in thinking that something similar cannot be done to obtain the specific heat capacity, as your link states k=K/mC, for which the mass can easily be found, but as both K and C are unknown, they cannot be determined to a specific value. I know that there are other ways of determining specific heat capacity, I'm just wondering if it can be done using Newton's Law of Cooling.
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