The temperature to which it must be heated in order to fit the shaft is 73.33 ⁰C.
Linear expansivity
The temperature to which it must be heated in order to fit the shaft is calculated as follows;
[tex]\frac{\Delta L}{L} = \alpha \Delta T\\\\\Delta T = \frac{\Delta L}{\alpha L}[/tex]
where;
- ΔT is change in temperature
- ΔL is change in length = 50.04 mm - 50 mm = 0.04 mm
- α is coefficient of linear expansion
- L is original length
ΔT = (0.04)/(50 x 15 x 10⁻⁶)
ΔT = 53.3 ⁰C
Final temperature
T₂ - T₁ = ΔT
T₂ = ΔT + T₁
where;
- T₂ is final temperature
- T₁ is initial temperature
T₂ = 53.3 + 20
T₂ = 73.33 ⁰C
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