if things expand and contract in different temps how do you determine by how much their size changes?

Question

if a copper rod is 3 m at 15 deg c how long is it at 150 deg c

Answer 1

this is high school physics:
Lt = Lo (1 + α . ΔT)

where:
L0 is the initial length (in this case, length at 3m)
α is the expansion coefficient (in this case 1.650 × 10e-5 /K)
ΔT is the difference between the initial temperature and end temperature (in this case 150°C-15°C = 135°C <=> 135K)

Lt is the end length, so:

Lt = Lo (1 + α . ΔT)
Lt = 3 (1 + 1.650 × 10e-5 /K * 135)
Lt = 3 (1 + 0.022275)
Lt = 3 (1.022275)
Lt = 3.066825 m

I hope this is not a homework, I won't do your homework for you.

Answer 2

you have to know the expansion coeficient

this is mostly an empirical number that was measured by heating the material and measuring expansion

this site gives coefficients of linear expansion for several materials including copper at 16.5 m/m-K *10^-6

http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html

if I remember how to use the coefficient correctly, that means that each inch of copper will expand .0000165 m for every meter of material, for every degree K (same as C for differential)

so, that would mean that a 3 meter rod would increase 3*135*.0000165 meters when the temperature rises 135 C

or, if i arithmeticed right, .0067 meters
or 6.7 mm

check my work there but the the concept and coefficient are correct

Answer 3

Compare it to a room temp rod. (about 20deg c)

Idk how long the rod would be, but if i had a lab, a rod, a bunsen burner, and instructions, id tell you.

Answer 4

Depends on the coefficient of expansion.