Thermal Elongation of Alumina: 0.00036

In summary, The pendulum of a clock, made of alumina, has a coefficient of thermal elongation of 24E-6^0 celsius. When cooled from 750 fahrenheit to 450, the relative elongation is 0.00036, which means it shortens by 0.0004. This coefficient is also given as 22.2x10^(-6) in the book and refers to aluminum, not alumina.
  • #1
Karol
1,380
22

Homework Statement


The pendulum of a clock is made of alumina. what is the relative elongation when cooled from 750 fahrenheit to 450?

Homework 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

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
 
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  • #2
It should be 0.00036
Is there a negative sign for its "elongation" when cooled?
 
  • #3
In the book there isn't a negative sign, but i think it's clear that it shortens in the amount 1-0.00036
 
  • #5
It is given in the book and it's aluminium
 

1. What is thermal elongation?

Thermal elongation is the increase in length or size of a material when it is exposed to heat. This phenomenon occurs due to the expansion of the material's atomic structure as the temperature increases.

2. How is the thermal elongation of alumina measured?

The thermal elongation of alumina is typically measured using a dilatometer, which is a device that can accurately measure the dimensional changes of a material as it is heated or cooled.

3. What is the thermal elongation coefficient of alumina?

The thermal elongation coefficient, also known as the thermal expansion coefficient, of alumina is 0.00036 (in/in)/°F. This means that for every degree Fahrenheit increase in temperature, alumina will expand by 0.00036 inches per inch of its original length.

4. How does thermal elongation affect the properties of alumina?

Thermal elongation can affect the properties of alumina by causing dimensional changes, which can lead to stress and cracking in the material. It can also affect the accuracy and stability of components made from alumina.

5. What are the applications of understanding the thermal elongation of alumina?

Understanding the thermal elongation of alumina is important in various industries, such as aerospace, where precise and stable components are required. It is also useful in the design and development of high-temperature materials and in predicting the behavior of alumina in different thermal environments.

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