# Homework Help: Work done by rod when heated

1. Aug 30, 2015

### gracy

1. The problem statement, all variables and given/known data
a metal rod of length "L",cross sectional area "A",young modulus "Y" and coefficient of linear expansion "α " is heated to "t" degree celsius .The work that can be performed by the rod when heated is
2. Relevant equations
work done by rod when heated=1/2 force exerted by rod(when heated) multiplied by extension
I know force exerted by rod(when heated)=Y α ∆t multiplied by A
(here ∆t is increase in temperature by due to heating)and extension would be final length -initial length let L' be final length.So extension would be L' - L
As L'=L(1 +α ∆t )
So L' - L=Lα ∆t

3. The attempt at a solution
with the help of equations above we can see
work done by rod when heated=1/2 Y α ∆t A multiplied by Lα ∆t
=1/2 YAL(α ∆t )^2
right?but in my book answer is given 1/2 YAL(αt)^2
which one is right?

2. Aug 30, 2015

### BvU

It looks like the reference for the exercise writer is zero degrees celsius. You take a more general approach where the environment temperature can be 0 or 20 or whatever.

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Last edited: Aug 30, 2015
3. Aug 30, 2015

### gracy

if that's the case then
but as we can see nothing such is mentioned in the question