Mechanical Principles, question on linear expansion of aluminium.

[RingwoodPye]

Homework Statement

Question: If the linear expansivity of aluminium is 24 x 10^-6 K^-1, how much does the aluminium expand during the heating?

Homework Equations

As far as additional information on the question goes;
An aluminium rod is heated from 15 degrees Celsius to 120 degrees Celsius. The dimensions of the aluminium rod are 12mm (diameter) x 1.2m long. The density of aluminium is 2700 kg per meters cubed.

The Attempt at a Solution

So far I'm completely stumped, we may have covered it but I literally cannot work it out.

 

[Mapes]

Hi RingwoodPye, welcome to PF.

The linear thermal expansion coefficient is the proportional increase in every (unconstrained) distance per degree temperature increase. That is, a value of 0 K^-1 would mean no expansion, and a value of 1 K^-1 would mean a 100% expansion per degree. Knowing this, can you calculate the new diameter and the new length?

 

[Mene]

I would approach this question by first understanding the concept of linear expansion and its relationship to temperature. Linear expansion is the increase in length of a material when it is heated. This is due to the atoms in the material vibrating faster and taking up more space, causing the material to expand.

To solve this problem, we can use the equation: ΔL = αLΔT, where ΔL is the change in length, α is the linear expansivity, L is the original length, and ΔT is the change in temperature.

In this case, we are given the linear expansivity of aluminium (α = 24 x 10^-6 K^-1), the original length (L = 1.2m), and the change in temperature (ΔT = 120°C - 15°C = 105°C).

Plugging in these values into the equation, we get:

ΔL = (24 x 10^-6 K^-1)(1.2m)(105°C) = 0.03024m

Therefore, the aluminium rod will expand by 0.03024m (or 30.24mm) during the heating process.

It is important to note that the density of the material does not affect the calculation of linear expansion. The linear expansivity is a material property that is independent of its density.

I hope this explanation helps you understand the concept of linear expansion and how to solve problems related to it. If you have any further questions or need clarification, please do not hesitate to ask.