## Thermal expansion

at 20C a rod is exactly 20.05cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270C, where the rod now measures 20.11cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

2. Relevant equations
$$\Delta$$L=L$$\alpha$$$$\Delta$$T
L(i)rod=20.05cm
L(f)rod=20.11
L(i)steel=20.05 ??
$$\Delta$$T=250C
$$\alpha$$steel=11 x 10^-6

3. The attempt at a solution
Ls=20.05cm(11x10^-6)(250C)
L=.055cm

I don't know what to do now-

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 The change in length for the rod is 20.11cm-20.05cm plus the expansion of the steel ruler at its 20.11cm mark: ∆L = La∆T = (20.11 cm)(11 x 10-6 /C˚)(270˚C-20˚C)-- u should assume it = 0.055 cm ∆L = (20.11cm-20.05cm) + 0.055 cm = 0.115 cm The coefficient of thermal expansion of the material the rod is made of is: a = ∆L/L∆T=23 x 10-6 /C˚