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To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter in a metal at 24 ∘C.To what temperature must the rivet be cooled if it is to fit in the hole?

Respuesta :

jorgezarate

Answer:

[tex]T_{o}=-65.2C[/tex]

Explanation:

The steel rivet is going to retract due to temperature change:

[tex]D_{f}= D_{o}(1+\alpha(T_{f}-T_{o}))[/tex]

D are the diameter

[tex]\alpha[/tex] : thermal coefficient of expansion, for steel =12*10^(-6)/°C

We know the diameters and the final temperature equal 24°C

so:

[tex]T_{o}=T_{f}-(D_{f}/D_{o}-1)/\alpha=24-(1871/1869-1)/(12*10^{-6})=-65.2C[/tex]

Answer:

-65 degC

Explanation:

ΔD=[tex]D_{0}[/tex]αΔT

1.869-1.871=1.871(1.2E-5)ΔT

ΔT≈-89 degC

24-89=-65 degC