What is the Temperature at which the Gap Between Two Bars will be Closed?

[BOAS]

Homework Statement

A brass bar and an aluminium bar are each attached opposite each other to immovable walls. (There is a diagram, but I think the idea is clear enough). There is a gap between the two bars of 1.3x10^-3m at 28°C.

At what temperature will the gap be closed?

coefficient of linear expansion of brass = 19x10^-6 (C°)^-1
aluminium = 23x10^-6 (C°)^-1

Length of brass bar = 2.0m
Length of aluminium bar = 1.0m

Homework Equations

ΔL = $\alpha$L_oΔT

The Attempt at a Solution

I'm not sure where to begin really. Obviously part of the problem is that the two rods are not going to meet in the middle as they expand.

I have 2 unknowns for both rods in the equation for linear expansion, so it's not really helpful to rearrange for ΔT and set them equal to each other.

If you could get me started that would be great,

thanks!

 

[Doc Al]

What must the sum of the ΔL's equal?

 

[BOAS]

1.3 x 10^-3 m

Can I say:

ΔL + ΔL = $\alpha$L_oΔT + $\alpha$L_oΔT

1.3x10^-3 = (3.8x10^-5 + 23x10^-6)ΔT

ΔT = 21.3 degrees C

28 + 21.3 = Temp when bars will touch

 

[Doc Al]

1.3 x 10^-3 m

Can I say:

ΔL + ΔL = $\alpha$L_oΔT + $\alpha$L_oΔT

1.3x10^-3 = (3.8x10^-5 + 23x10^-6)ΔT

ΔT = 21.3 degrees C

28 + 21.3 = Temp when bars will touch

I didn't check your arithmetic, but that is definitely the way to solve it.

 

[BOAS]

I'll check and double check.

Thanks a lot!