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What does it mean to find a formula as a function of temperature

  1. Feb 23, 2004 #1
    What does it mean to find a formula as a function of temperatue? Could I have an example so that I can find a formula for the following question as a function of temperature?

    Question: Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50K) can be fit to the formula Cv=aT +bT^3, where Cv is the heat capacity of one mole of aluminum and the constants a and b are approximately a =0.00135 J/K^2 and b=2.48 x 10^-5 J/K^4. From this data, find a formula for the entropy of mole of aluminum as a function of temperture.
  2. jcsd
  3. Feb 23, 2004 #2
    Will someone please help me?

    Will someone help me with the question I asked? It's due tomorrow.
  4. Feb 23, 2004 #3
    Finding a formula as a function of temperature means that you will have an equation of the form:

    [tex]E = f(T)[/tex]

    Where E (in the case of the question you were asked) would be the dependent variable, the "output," you could say, and f(T) is some function where T is the independent variable, the "input," you could say. Also, since you're finding E as a function of only T, then all other parts of f(T) must be either constant or also a function of T.

    For instance, [itex]E = \sigma T^4[/itex] is a function of only T if [itex]\sigma[/itex] is a constant (note: this is not the equation you're looking for), whereas [itex]z = x^2 + y^2[/itex] is a function of x and y, but not T and not only x or only y.

    Last edited: Feb 24, 2004
  5. Feb 24, 2004 #4


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    Actually, to "a function as a function of temperature" doesn't mean anything and your problem doesn't say that. You are asked to find the entropy as a function of temperature. That simply means to write down a formula in which the variable is temperature and the result of the formula is entropy.

    Since you are given "Cv=aT +bT^3", which is "heat capacity", and you are given a and b for this particular experiment. Do you know any formula that connects entropy and heat capacity? If you do, replace Cv in that formula with aT+ bT^3.
  6. Feb 24, 2004 #5
    Sorry. Poor wording. I was trying to mimic jlmac2001's and I ended up throwing one too many "function"s and one too few "formula"s.

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