Linear Expansion - Finding temperature

In summary, the three equations are correct, but you need to post an equation that expresses the desired result in terms of the given variables.
  • #1
JoeyBob
256
29
Homework Statement
See attached
Relevant Equations
change length= a*original length * change in temp
So if I am understanding the question correctly, I need to find the change in temperature that causes one rights outer radii to be the same as another rings inner radii.

Now what I tried is two equations

change length_1= a_1*original length_inner * change in temp

change length_2= a_2*original length_outer * change in temp

But the problem is that there is one too many unknowns here - i don't know the temp, change in L_1 or change in L-2. Either there's another equation I am missing or I am using the wrong approach.
 

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  • #2
Okay I think I found the equation I was missing.

L_1+change in L_2 = L_2 + change in L_2

The answer I got was only a bit off from the right answer, probably from rounding or something.
 
  • #3
JoeyBob said:
Okay I think I found the equation I was missing.

L_1+change in L_2 = L_2 + change in L_2

The answer I got was only a bit off from the right answer, probably from rounding or something.
That equation makes no sense since you have "change in L_2" on both sides. What did you mean, in terms of the given variables ri etc? Use α1, α2 for the coefficients.
Please post your answer and working so that we can check whether it is just rounding error.
 
  • #4
haruspex said:
That equation makes no sense since you have "change in L_2" on both sides. What did you mean, in terms of the given variables ri etc? Use α1, α2 for the coefficients.
Please post your answer and working so that we can check whether it is just rounding error.
It looks like a typo.
 
  • #5
haruspex said:
That equation makes no sense since you have "change in L_2" on both sides. What did you mean, in terms of the given variables ri etc? Use α1, α2 for the coefficients.
Please post your answer and working so that we can check whether it is just rounding error.
Its a typo. change in L_1.

The 3 equations are correct?
 
  • #6
JoeyBob said:
The 3 equations are correct?
Impossible to say without definitions of the variables.
This is certainly correct:
find the change in temperature that causes one ring's outer radius to be the same as the other ring's inner radius.
But you have not posted an equation that expresses that in terms of r1, r2, α1, α2 and Δθ.
 

Related to Linear Expansion - Finding temperature

1. What is linear expansion?

Linear expansion is the increase in length of a material when it is heated. This phenomenon occurs due to the increase in kinetic energy of the particles, causing them to vibrate and take up more space.

2. How is temperature related to linear expansion?

The change in temperature is directly proportional to the change in length of a material. As temperature increases, the material expands and as temperature decreases, the material contracts.

3. What is the formula for calculating linear expansion?

The formula for linear expansion is ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length of the material, and ΔT is the change in temperature.

4. How is the coefficient of linear expansion determined?

The coefficient of linear expansion is determined experimentally by measuring the change in length of a material for a given change in temperature. It is a unique property of each material and can vary depending on factors such as composition and structure.

5. What are some real-life applications of linear expansion?

Linear expansion is used in various everyday objects, such as thermometers, bimetallic strips in thermostats, and expansion joints in bridges and buildings. It is also utilized in the construction of railway tracks to prevent buckling due to temperature changes.

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