# Thermal Expansion Problem Involving a Brass Ring

1. Dec 20, 2016

### BrainMan

1. The problem statement, all variables and given/known data

2. Relevant equations
ΔL = LαΔT

3. 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,

Lbrass + ΔLbrass = Lsteel + ΔLsteel

Where L is the diameter

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

Lbrass + LbrassαbrassΔT = Lsteel + LsteelαsteelΔT

Then I solved for ΔT and got

(Lbrass - Lsteel) / (Lsteelαsteel - Lbrassαbrass) = ΔT

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

(50 μm) / (Lsteelαsteel - Lbrassαbrass) = ΔT

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

#### Attached Files:

File size:
117.6 KB
Views:
59
2. Dec 20, 2016

### haruspex

3. Dec 20, 2016

### BrainMan

I did

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

4. Dec 20, 2016

### haruspex

μm.

5. Dec 20, 2016

### BrainMan

I see. Thanks