# Finding coefficient of thermal expansion

## Homework Statement

"see attachment" "q1"

## Homework Equations

V=$\frac{-A}{r}+\frac{B}{r^{10}}$
A=5*10^-30
B=8*10^-121

V=potential energy r=interatomic separation distance

Coefficient of thermal expansion = $\frac{change in L}{L*change in T}$

## The Attempt at a Solution

I have tried making graphs for V vs r however it give me a very weird curve. Furthermore, how do I find the coefficient of thermal expansion from potential energy vs interatomic seperation distance? All I know is that in a V vs r, if the energy well to the right of the absolute zero is larger than that of the left, the CTE is positive and negative for vice versa.

"see graph 1"

I also try to draw this graph on my graphic calculator but it gives me result similar to y= -1/x

#### Attachments

• q1.png
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• graph 1.jpg
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In your plot V(r) you also consider $x\leq0$, which is not correct, because distance r must be r>0. The coefficient of thermal (linear) expansion alpha relates the change in longitude L and the change in temperature T, $\frac{\Delta L}{L}=\alpha \Delta T$, in units K-1. So now you have an input for the variation of T...