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

1. Feb 23, 2004

### jlmac2001

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. Feb 23, 2004

### jlmac2001

Will someone help me with the question I asked? It's due tomorrow.

3. Feb 23, 2004

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.

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

### HallsofIvy

Staff Emeritus
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.

5. Feb 24, 2004