Linear expansion of steel question

In summary, The question is about finding the change in density of a steel cube when its temperature changes. The equation used is \DeltaL = \alphaL\DeltaT, where \alpha is the linear expansion coefficient of steel and \DeltaT is the change in temperature. The attempted solution involved substituting values into the equation, but there was an issue with the equation's dimensions. After assuming a side length of 1m or 2m, the solution was found by substituting 1m into the equation and using density = mass/volume. The final result was the change in density of the steel cube.
  • #1
ilyas415
6
0

Homework Statement



The question i need help on is question 6 part (c). I think I need to use the equation:

2. Equations used:
[tex]\Delta[/tex]L = [tex]\alpha[/tex]L[tex]\Delta[/tex]T

Linear expansion of steel: 12x10 K^-1 ([tex]\alpha[/tex])
Density of steel: 7800

3. My attempted solution:
I tried substituting in the values into the equation but the question did not mention anything about the length of the steel so now i am stuck for a solution. I tried using proportionality with density=mass/volume so density is proportional to 1/L. However I am not sure this if this is the correct way.

Thanks for your help in advance.
 

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  • #2
That equation doesn't make dimensional sense; it has meters on the left but is dimensionless on the right. After that issue's fixed, you could try assuming a side length of 1 m, or 2 m. Does it make a difference?
 
  • #3
ah, I've got it, assume it is a cube with edge length 1m, then I've got to substitute 1m into the equation to find the new length, then i use density = mass/volume, then i get the change in density
 

1. What is linear expansion of steel?

Linear expansion of steel refers to the increase in length of a steel material when it is heated. This is due to the individual atoms in the steel vibrating faster and taking up more space, causing the material to expand.

2. How does linear expansion of steel occur?

Linear expansion of steel occurs due to the thermal energy transferred to the material, causing the atoms to vibrate and take up more space. As the material cools, the atoms slow down and return to their original positions, causing the material to contract back to its original length.

3. Why is linear expansion important to consider?

Linear expansion is important to consider in construction and engineering, as changes in temperature can cause steel structures to expand or contract, potentially causing structural issues. It is also important in manufacturing and machining processes, as precise measurements need to be accounted for when working with steel materials.

4. How is linear expansion of steel measured?

The linear expansion of steel is typically measured using the coefficient of thermal expansion (CTE). This is a value that represents how much a material will expand or contract for every degree change in temperature. The CTE for steel is around 11x10^-6 m/m/°C, meaning that for every 1°C increase in temperature, steel will expand by 11x10^-6 meters per meter of its original length.

5. Can linear expansion of steel be prevented?

While the linear expansion of steel cannot be completely prevented, it can be minimized through the use of expansion joints, which allow the material to expand and contract without causing damage to the structure. Additionally, using materials with a lower CTE, such as stainless steel, can also help reduce the effects of linear expansion.

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