Thermal expansion of brass and iron rings

AI Thread Summary
To fit a brass plug into an iron ring, both must be heated to a common temperature that accounts for their differing thermal expansion coefficients. The initial diameters are 8.731 cm for the brass plug and 8.719 cm for the iron ring at 10°C. The formula for thermal expansion, Δl = α * l0 * ΔT, indicates that the increase in diameter will differ for each material due to their unique coefficients. If the plug were made of iron and the ring of brass, the same principles apply, but the calculations would yield a different common temperature for fitting. Understanding the distinct thermal expansion rates is crucial for determining the necessary temperature adjustments.
emc92
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A brass plug is to be placed in a ring made of iron. At 10°C, the diameter of the plug is 8.731 cm and that of the inside of the ring is 8.719 cm.

a) They must both be brought to what common temperature in order to fit?

b) What if the plug were iron and the ring brass?


formula for thermal expansion: Δl = \alpha * l0 * ΔT

do i just equal Δl for brass and iron?
 
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No, if each increases in diameter by the same amount, the plug will still not fit.
 
Hint:

The thermal expansion coefficients for brass and iron are different.
 
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