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

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Finding a formula as a function of temperature involves expressing a dependent variable, such as entropy, in terms of temperature as the independent variable. In this case, the heat capacity of aluminum is given by Cv = aT + bT^3, where constants a and b are specified. To find the entropy, one needs to use the relationship between heat capacity and entropy, substituting Cv into the appropriate formula. The discussion clarifies that the goal is to derive an equation where temperature is the sole variable influencing the outcome. Understanding this relationship is crucial for solving the problem effectively.
jlmac2001
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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.
 
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Will someone please help me?

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

E = f(T)

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

cookiemonster
 
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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.
 
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.

cookiemonster
 

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