(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An experiment was conducted on a liquid at varying temperatures and the volume obtained at the differing temperatures are as follows:

Assume that [tex] V = 1 + B\theta + D\theta^2[/tex] , where B and D are constants.Code (Text):V/cm3 θ/oC

1.032 10

1.063 20

1.094 29.5

1.125 39.5

1.156 50

1.186 60.5

1.215 69.5

1.244 79.5

1.273 90

1.3 99

Question: Linearize the above equation and plot the corresponding curve.

2. Relevant equations

Microsoft Excel LINEST function, Least squares method statistical equations (too many to post)

3. The attempt at a solution

Here's what I understand about linear least squares fitting. I attended a lab session where I was taught how to apply the least squares method in Excel to linearize a given equation and then use mbest and cbest to calculate the other unknown constants in the equation. My understanding is that firstly one takes the equation, and tries to express it, in any mathematical way possible in the form y=mx + c, where y is the dependent variable and x the independent variable. Hence while the y does not have to be the same independent variable as measured directly in the experimental setup, x has to be the same. Hence the resulting linearized equation cannot use expressions of x which are functions of x expressed in ways apart from simply x. eg. x^2 is not allowed, ln x is not allowed.

Is this understanding correct? If so, then how is it possible for me to linearise the above given equation? I only got as far as:

[tex]\theta + \frac{B}{2D} = \sqrt{ \frac{V-1}{D} + (\frac{B}{2D})^2 [/tex]

which should suggest (or at least it does to me) that mbest in Excel using the LINEST function should be 1, since the coefficient of θ is 1. But instead I get 0.003004423, which means I have somehow linearized the equation wrongly. How else could it have been linearized?

EDIT: I didn't quite get what it means by "plot the corresponding curve". I assume this involves using Excel, but apart from using as source data the values of V and theta from the table, what else could it mean?

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# Method of Least Squares Linear Fitting

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