# Expansion in a solid rod

## Homework Statement

the difference in length between an aluminium rod and a copper rof at 0 degreeC is 2cm. If they have the same difference in length at any temperature difference, what are the length of the 2 rods at 0 degreeC.?
Al - expansivity = 20*10^-4 K^-1
Cu- expansivity= 15*10^-6 K^-1

## Homework Equations

alpha inversely proportional to the initial length

## The Attempt at a Solution

i divided the expansivities of the two rods and made it equal to the ratio of theinitial lengths of the rods and got the length of the Al rod as 6 cm and the Cu rod as 8 cm. Which is the answer the school teacher said is correct. I can't understand why it can't be the other way around.

Suraj M
Gold Member
I can't understand why it can't be the other way around.
Think of it like this, if these two rods should have the same difference in lengths then the change in length has to be same, and hence you get
alpha inversely proportional to the initial length
Now which material has the higher alpha? knowing that you can judge which should be shorter and which should be longer.
If not why don't you provide your calculations, it'll be easier to explain it to you or rather you'll figure it out yourself.

Avaron Cooper
Think of it like this, if these two rods should have the same difference in lengths then the change in length has to be same, and hence you get

Now which material has the higher alpha? knowing that you can judge which should be shorter and which should be longer.
If not why don't you provide your calculations, it'll be easier to explain it to you or rather you'll figure it out yourself.
okay.. Now I understand. Since Al has the higher alpha it should have the lower initial length. Thank you very much!!