# Linear expantion and elastic modulus- brass vs. glass

In summary, the question asks at what temperature change will a glass thread break when attached to a thick brass rod with a temperature coefficient of linear expansion of 20 x 10^-6 K^-1 for brass and 7 x 10^-6 K^-1 for glass, and a Young's modulus of 7 x 10^10 N/m² and shear modulus of 7 x 10^7 N/m² for glass. Using the modulus for glass, we calculate the strain at which the glass would break. Then, using the relative expansion of brass and glass, we determine that the glass will break at a temperature change of approximately 140 K.

## Homework Statement

Onto a thick brass rod we attach equally long glass thread. At what temperature change will the glass thread break if the temperature coefficient of linear expansion for brass is
α1= 20 x 10 ^-6 K^-1, and for glass is α2= 7 x 10^-6 K^-1? Young’s (elastic) modulus for glass is E1= 7 x 10^10 N/m², and shear modulus for glass is σ1= 7 x 10^7 N/m².

## Homework Equations

Linear thermal expansion: α(L)= ΔL/ L(0)ΔT
Young’s (elastic) modulus: E= FL(0)/ AΔL

## The Attempt at a Solution

And from here I have no clue how to build a relationship between linear thermal expansion and elastic modulus and how to incorporate all the terms given to find the result.
Can someone please give me some hint?

Thank you for helping!

You don't need a relation between them as such.
You use the modulus for glass to work out at what strain the glass would break.

Then you use the relative expansion of brass and glass to work out at what temperature the glass would have been stretched that amount.

hint. remember the glass is also expanding as the brass does

OK, I think I understood right:

Strain: ε= ΔL/ L
Stress: σ= F/A

E= FL(0)/ AΔL → E= stress/strain= σ/ ε → ε= σ/ E

ε = 7 x 10^7 N/m²/ 7 x 10^10 N/m²
ε= 0.001

α(L-glass)= [ΔL/ L(0)]/ ΔT= ε/ ΔT → ΔT= ε/ α(L-glass)
ΔT= 0.001/ 7 x 10^-6 K^-1
ΔT=0.14 x 10^3 K= 140 K

Is this correct (big doubt?!, too low temperature)?
Thank you for helping!

Last edited:

## 1. What is linear expansion?

Linear expansion is the increase in length of a material when it is subjected to a change in temperature. It occurs due to the increase in the average distance between the atoms or molecules in the material.

## 2. What is the elastic modulus of a material?

The elastic modulus, also known as Young's modulus, is a measure of a material's stiffness or ability to resist deformation when a force is applied. It is the ratio of stress to strain within the material.

## 3. How does brass compare to glass in terms of linear expansion?

Brass and glass have very different linear expansion properties. Brass has a higher coefficient of linear expansion, meaning it expands more when heated, compared to glass. This is due to the difference in the atomic structure and bonding of the two materials.

## 4. What is the practical application of understanding linear expansion and elastic modulus?

Understanding linear expansion and elastic modulus is important in designing structures and materials that can withstand temperature changes without breaking or deforming. It also has applications in fields such as engineering, construction, and materials science.

## 5. Can the linear expansion and elastic modulus of a material be changed?

The linear expansion and elastic modulus of a material are intrinsic properties that cannot be changed. However, they can be affected by external factors such as temperature, stress, and composition of the material.

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