# Thermal Expansion - Both rule and rod

## Homework Statement

A brass rod's length is measured at 20.0 degrees C with a metre steel rule. The length of the rod is determined to be 0.5260 m. The measurement is repeated at 61.6 degrees C. Taking into account the expansion of the rule and rod, what is the new measured length in metres? Coefficients of linear expansion: Brass: 19.0 X 10-6 K-1; Steel: 11.0 X 10-6 K-1. Express answer to five (5) significant figures.

## Homework Equations

ΔL = coefficient of linear expansion * ΔT * L

(rearranged original equation)

## The Attempt at a Solution

change in length for rod (brass)
ΔL = (19*10^-6) * 41.6 * 0.5260
= 0.00041575
∴ new length (assuming rule is 1m still) is ΔL + L(original)
= 0.52641575

change in length for rule (steel)
ΔL = (11*10^-6) * 41.6 * 1
= 0.0004576
∴new length = 1.0004576

so new length of rod (after both expanded) in my mind should be;
= 1.0004576 * 0.52641575
= 0.526656637
= 0.52666 (5 sig figs)

I do not have the answer to this question - it is marked online (either correct or incorrect, not giving the answer if incorrect). This answer is apparently incorrect so i must be doing something wrong.

Any help would be appreciated.

## Answers and Replies

tiny-tim
Homework Helper
welcome to pf!

hinrb93! welcome to pf!
∴ new length (assuming rule is 1m still) is ΔL + L(original)
= 0.52641575

so new length of rod (after both expanded) in my mind should be;
… = 0.52666 (5 sig figs)

if the ruler is expanding, shouldn't the length measured by it be shorter?

hinrb93! welcome to pf!

if the ruler is expanding, shouldn't the length measured by it be shorter?

ah, thanks a lot ;) hehe, for further reference for anyone else; you can simply do the new length of the rod divided by the new length of the ruler (as calculated above) OR instead; can do (1 - (ΔL of the ruler)) * rod.