This is a question in a physics lab and my algebra skills are alittle rusty so I

Question

This is a question in a physics lab and my algebra skills are alittle rusty so I thought maybe somebody here could give me someidea of what to do.

Here is the question:

Suppose that physical considerations lead you to expect thatmeasurements on a certain thermodynamic system will lead to thefollowing relationship between the pressure 'p' and the temperature'T':

p = 2/3(kT2)

where 'k' is a constant. Pressure measurements are taken onthe system as the temperature is varied and you would like toperform a curve fit on this data in order to measure the constant'k'. As you can see, the equation is non-linear so thetechniques of linear least squares curve fitting do not immediatelyapply. Fortunately, however, if you make a correctsubstitution, you can transform this equation into a linear one andthen the techniques you learned in this lab do apply.

1. Make a simple mathematical substitution thattransforms the equation from quadratic to linear form. Then, show the equation in its new form.

2. What maximum number of points is required to fit some data to a quadratic function?

3. Suppose someone wanted to fit a set of 10 data points to the exponential equation y(x)=Ae^kx where A and K are the fit parameters. What is the number of degrees of freedom in this fit? Explain your answer.

Explanation / Answer

the equation is

p = 2/3(kT^2) ----------(1)

we know that

pV = nRT

or T = pV/nR ---------(2)

from (1) and (2) we get

p = 2/3(k x p^2V^2/n^2R^2)

or p^3V^2 = (2/3k/n^2R^2)

the term on right side is a constant therefore

p^3V^2 = constant

or p1^3V1^2 = p1^3V2^2

the number of degrees of freedom are 3

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