What Stress Is Needed to Maintain an Aluminum Bar's Length from 15°C to 35°C?

[pupatel]

An aluminum bar has the precisely desired length when at 15°C. How much stress is required to keep it at this length if the temperature increases to
35°C?

How do I do this? can anyone help me please...

 

[Doc Al]

If no stress were applied, how much would the bar expand? (You'll need to understand the coefficient of thermal expansion.)

Then consider how much pressure needs to be applied to compress the bar back to its original length. (You'll need to understand Young's modulus.)

 

[M98Ranger]

To calculate the stress required to keep the aluminum bar at its desired length when the temperature increases from 15°C to 35°C, we can use the principles of temperature and kinetic theory. According to this theory, as the temperature of a material increases, the average kinetic energy of its particles also increases, causing them to vibrate and move more rapidly.

In the case of the aluminum bar, as the temperature increases from 15°C to 35°C, the kinetic energy of its particles will also increase, causing them to expand and increase in length. This expansion will cause the bar to exert a force on its surroundings, known as thermal stress.

To calculate the thermal stress, we can use the formula:

Stress = Young's modulus x Coefficient of thermal expansion x Change in temperature

Young's modulus is a measure of a material's stiffness, and the coefficient of thermal expansion is a measure of how much a material expands when its temperature increases. Both of these values can be found in reference tables for aluminum.

Substituting the values for Young's modulus and the coefficient of thermal expansion for aluminum, we get:

Stress = (70 GPa) x (23.6 x 10^-6 m/m°C) x (35°C - 15°C)

= 16.52 GPa

This means that in order to keep the aluminum bar at its desired length when the temperature increases from 15°C to 35°C, a stress of 16.52 GPa will be required. This stress will counteract the expansion of the aluminum bar and keep it at its desired length.

In conclusion, by understanding the principles of temperature and kinetic theory, we can calculate the stress required to keep the aluminum bar at its desired length when the temperature changes.