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.
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
∴ new length (assuming rule is 1m still) is ΔL + L(original)
change in length for rule (steel)
ΔL = (11*10^-6) * 41.6 * 1
∴new length = 1.0004576
so new length of rod (after both expanded) in my mind should be;
= 1.0004576 * 0.52641575
= 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.