Thermal Expansion Problem Involving a Brass Ring

[BrainMan]

Homework Statement

Homework Equations

ΔL = LαΔT

The Attempt at a Solution

What I did was to set the diameter of the inside of the brass ring + the change in diameter of the brass ring equal to the diameter of the steel rod + change in the diameter of the steel rod. So,

L_brass + ΔL_brass = L_steel + ΔL_steel

Where L is the diameter

Then I used ΔL = LαΔT to solve both ΔL's

L_brass + L_brassα_brassΔT = L_steel + L_steelα_steelΔT

Then I solved for ΔT and got

(L_brass - L_steel) / (L_steelα_steel - L_brassα_brass) = ΔT

Then since it states that the hole is 50 μM too small I did

(50 μm) / (L_steelα_steel - L_brassα_brass) = ΔT

I get a very small answer for ΔT but the answer says ΔT should be about 313 °C

 

[haruspex]

I get a very small answer for ΔT

I get about 370 from your equation (what coefficients are you using?). Please post your detailed calculation.

 

[BrainMan]

I get about 370 from your equation (what coefficients are you using?). Please post your detailed calculation.

I did

(50 x 10^-9) / ( 0.020 * 1.1 x10^-5 - 0.020*1.9 x10^-5)

 

[haruspex]

50 x 10^-9

μm.

 

[BrainMan]

μm.

I see. Thanks