Understanding Linear Expansivity: Tips for Finding L2 with Ease

[Eke]

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

 

[jtbell]

Exactly which formula are you referring to?

 

[Eke]

l2-l1<divided by> l1(temperature2 - temperature1)= e divided by l1*final temperature... try writing it with a pen for better understanding

 

[nasu]

l2-l1<divided by> l1(temperature2 - temperature1)= e divided by l1*final temperature... try writing it with a pen for better understanding

You mean
\frac{l_2-l_1}{l_1(T_2-T_1)}=\alpha

What is the question? "How to solve for l2" ?

 

[Eke]

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

 

[nasu]

Actually this second form is the most common one.
l_2=l_1[1+\alpha(T_2-T_1)]
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?

 

[Eke]

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

 

[nasu]

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
l_2=l_1+l_1\alpha(T_2-T_1)
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.