# Homework Help: Deriving expressions for Linear Expansivity and Young's Modulus

1. Oct 15, 2012

### Jappey101

1. The problem statement, all variables and given/known data
The equation of state of a system consisting of a cylinder of a certain perfectly elastic material, subjected to an axial load F, is

F= CT(L-Li)^2

where Li is the unstretched length, L is the length under a load F when the temperature is T on a selected empirical scale and C is a constant.

DERIVE EXPRESSIONS FOR THE LINEAR EXPANSIVITY AND YOUNG'S MODULUS OF THE MATERIAL.
2. Relevant equations

dW=FdL

dL=(∂L/∂θ)- F held constant+(∂L/∂F)-θ held constant

linear expansivity=1/L(∂L/∂θ)- F held constant

young's modulus= (L/A)(∂F/∂L)-θ held constant

3. The attempt at a solution

I am lost. I tried integrating the formula, i tried expanding the equation of state, but all my attempts left me nowhere. I just need the first step because I am lost. Thank you!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution