Thermal expansion of brass and iron rings

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SUMMARY

The discussion focuses on the thermal expansion of brass and iron rings, specifically determining the common temperature required for a brass plug with a diameter of 8.731 cm to fit into an iron ring with an inside diameter of 8.719 cm at 10°C. The formula for thermal expansion, Δl = α * l0 * ΔT, is highlighted, emphasizing that the differing thermal expansion coefficients for brass and iron must be considered. The conclusion is that simply equating the thermal expansions of both materials is insufficient for achieving a proper fit.

PREREQUISITES
  • Understanding of thermal expansion coefficients for materials
  • Familiarity with the formula Δl = α * l0 * ΔT
  • Basic knowledge of temperature conversion and measurement
  • Concept of material properties, specifically for brass and iron
NEXT STEPS
  • Research the thermal expansion coefficients for brass and iron
  • Explore calculations involving thermal expansion in engineering applications
  • Learn about the effects of temperature on material properties
  • Investigate practical applications of thermal expansion in manufacturing and assembly
USEFUL FOR

Engineers, materials scientists, and students studying thermodynamics or material properties will benefit from this discussion, particularly those involved in applications requiring precise fitting of components under varying temperatures.

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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