# Homework Help: Thermal elongation

1. Sep 14, 2014

### Karol

1. The problem statement, all variables and given/known data
The pendulum of a clock is made of alumina. what is the relative elongation when cooled from 750 fahrenheit to 450?

2. Relevant equations
$$L=L_0(1-\alpha \Delta t)$$
From Fahrenheit to Celsius:
$$t_f=\frac{9}{5}t_c+32^0$$
Coefficient of thermal elongation of alumina: 24E-6^0 celsius

3. The attempt at a solution
300 fahrenheit are: $\Delta t_c=\Delta t_f \frac{5}{9} \Rightarrow \Delta t_c=16.67^0$
$$\frac{L}{L_0}=\frac{L_0(1-\alpha \Delta t)}{L_0}$$
$$24E-6^0 \cdot 16.67=0.0004$$
Exactly, and it It should be 0.00036

2. Sep 14, 2014

### Staff: Mentor

Is there a negative sign for its "elongation" when cooled?

3. Sep 14, 2014

### Karol

In the book there isn't a negative sign, but i think it's clear that it shortens in the amount 1-0.00036

4. Sep 14, 2014

### nasu

5. Sep 14, 2014

### Karol

It is given in the book and it's aluminium