# Linear expansivity

1. Apr 29, 2013

### 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

2. Apr 29, 2013

### Staff: Mentor

Exactly which formula are you referring to?

3. Apr 29, 2013

### Eke

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

4. Apr 29, 2013

### nasu

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

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

5. Apr 29, 2013

### Eke

yeah yeah.. how to solve for l2... my text book 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. Apr 29, 2013

### 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?

7. Apr 29, 2013

### Eke

yes.. thats the formula...
first i plus l1 with 1 because multiplying it wouldnt 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 text book...
am i doing it wrong

8. Apr 29, 2013

### nasu

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.