Linear Thermal Expansion

  • Thread starter BOAS
  • Start date
  • #1
555
19

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 = [itex]\alpha[/itex]LoΔT

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!
 

Answers and Replies

  • #2
Doc Al
Mentor
45,071
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What must the sum of the ΔL's equal?
 
  • #3
555
19
1.3 x 10^-3 m

Can I say:

ΔL + ΔL = [itex]\alpha[/itex]LoΔT + [itex]\alpha[/itex]LoΔT

1.3x10^-3 = (3.8x10^-5 + 23x10^-6)ΔT

ΔT = 21.3 degrees C

28 + 21.3 = Temp when bars will touch
 
Last edited:
  • #4
Doc Al
Mentor
45,071
1,380
1.3 x 10^-3 m

Can I say:

ΔL + ΔL = [itex]\alpha[/itex]LoΔT + [itex]\alpha[/itex]LoΔT

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.
 
  • #5
555
19
I'll check and double check.

Thanks a lot!
 

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