Understanding Linear Expansivity: Tips for Finding L2 with Ease

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In summary, the conversation discusses the formula for finding expansivity, specifically L2, which is not straightforward. The formula involves adding 1 to L1 and multiplying it with the linear expansivity and the temperature difference, then adding it to the original length L1. There is confusion about the correct method of solving for L2, and the speaker suggests brushing up on algebra skills.
  • #1
Eke
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ever since i was taught this along with the other expansivities its been giving me trouble. the formula is for looking for the expansivity and then you'd be seeing questions telling u to look for L2.. and L2 is quite hard to find because the formula is not straight forward...

please anyone,, how can i find L2 without all this stress
 
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  • #2
Exactly which formula are you referring to?
 
  • #3
l2-l1<divided by> l1(temperature2 - temperature1)= e divided by l1*final temperature... try writing it with a pen for better understanding
 
  • #4
Eke said:
l2-l1<divided by> l1(temperature2 - temperature1)= e divided by l1*final temperature... try writing it with a pen for better understanding

You mean
[tex]\frac{l_2-l_1}{l_1(T_2-T_1)}=\alpha[/tex]

What is the question? "How to solve for l2" ?
 
  • #5
yeah yeah.. how to solve for l2... my textbook gave me this formula..
l2=l1(1+linearexpansivity<T2-T1>)
let me write it in text...
l2=l1(1+linearexpansivity...times <T2-T1>)
and the formula is not as straight forward as it seems
 
  • #6
Actually this second form is the most common one.
[tex]l_2=l_1[1+\alpha(T_2-T_1)][/tex]
It follows from the first one from simple algebraic manipulation.
I still don't see what your problem is.
Do you want to plug in and find l2?
 
  • #7
yes.. that's the formula...
first i plus l1 with 1 because multiplying it wouldn't make much sense..
then i add the linear expansivity as told in the formula...
then multiply all that with my final temperature...
but still my answer is diff. from my textbook...
am i doing it wrong
 
  • #8
Eke said:
yes.. that's the formula...
first i plus l1 with 1 because multiplying it wouldn't make much sense..
No, actualy what you say here does not make sense.
You cannot add (in a meaningful way) a length with a pure number.
I am afraid you need to brush up your algebra a bit. About precedence of operations and brackets.

But here is how it may be done here (it's not the only way):
Open the bracket and you will have
[tex]l_2=l_1+l_1\alpha(T_2-T_1)[/tex]
So find the temperature difference ΔT=(T2-T1) and them multiply this ΔT by α and l1.
This will be by how much the length have changed.
Finally add this to the original length, l1. And you will have l2.
 

1. What is linear expansivity?

Linear expansivity is a measure of how much a material expands or contracts when exposed to changes in temperature. It is represented by the symbol L2 and is typically measured in units of length per degree Celsius or Kelvin.

2. How is linear expansivity calculated?

Linear expansivity can be calculated by dividing the change in length of a material by the original length, multiplied by the change in temperature. This can be expressed mathematically as L2 = (ΔL/L) * ΔT, where L2 is the linear expansivity, ΔL is the change in length, L is the original length, and ΔT is the change in temperature.

3. What are some tips for finding L2 with ease?

One tip for finding L2 with ease is to use a material's coefficient of linear expansion, which is a constant value that relates the change in length to the change in temperature. Another tip is to use the linear expansivity formula and plug in known values for ΔL and ΔT to solve for L2. Additionally, using standardized units for length and temperature can make the calculation easier.

4. Why is understanding linear expansivity important?

Understanding linear expansivity is important for various applications, such as engineering and construction, where changes in temperature can affect the dimensions and stability of structures. It is also important in scientific research and experiments, as it can help predict and explain the behavior of materials under different temperature conditions.

5. How does linear expansivity differ from volumetric expansivity?

Linear expansivity measures the change in length of a material, while volumetric expansivity measures the change in volume. The two are related, but linear expansivity is typically used for 1-dimensional materials such as rods or wires, while volumetric expansivity is used for 3-dimensional materials such as solids or liquids.

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