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Temperature vs Heat

  1. Jun 1, 2012 #1
    In terms of Kelvins, if the temperature of a sample doubles, does the energy content from heat double as well?

    Also, if you are passing a current through a sample, what should be the temperature vs current relation be theoretically? i.e. what is f(I) in T = f(I).

  2. jcsd
  3. Jun 1, 2012 #2

    Ken G

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    Gold Member

    Usually, though not always. It's not a fundamental feature of the connection between energy and temperature, but it is a common connection.
    Generally one talks about the heating rate generated by a current, according to P = I2/R. So given I and R, you can find the heating rate. What that does to T depends on the cooling rate. Sometimes the cooling rate is proportional to T, so in equilibrium T would be proportional to I2, but there are many other ways that the cooling could depend on T.
  4. Jun 2, 2012 #3

    Andrew Mason

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    Just to add to what Ken G has said, temperature is a measure of the translational kinetic energy of the molecules in the sample. But the internal energy of a sample is not just the translational kinetic energy. It can include potential energy as well. A good example is water. It takes a lot of energy to turn ice at 0C into water at 0C. This is the energy required just to break enough of the inter-molecular bonds between water molecules to turn the substance from a solid to a liquid. The liquid water molecules at 0C have much more potential energy than ice - 334 J per gram more energy - but temperature has not increased at all.

    Use the first law of thermodynamics: Q = ΔU + W.

    Lets assume you pass a current I through a resistance R for one second and no mechanical work (such as turning a motor to lift something) is done (W = 0). In that case, Q = ΔU. The electrical energy flow is heat flow: Q = I2RΔt = I2R (since Δt = 1) The units would be in Joules.

    In general if no mechancal work is done, in time t: Q = ΔU = I2Rt.

    Assuming a constant heat capacity for the sample over the temperature change that this energy causes, then Q = mCvΔT where m is the mass and Cv is the heat capacity at constant volume. So ΔT = I2Rt/mCv.

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