Thermal expansion of brass and iron rings

In summary, in order for the brass plug to fit into the iron ring, both must be brought to the same temperature. However, even if they both increase in diameter by the same amount, the plug will still not fit because the thermal expansion coefficients for brass and iron are different. Therefore, simply equating the change in length for both materials will not work.
  • #1
emc92
33
0
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 = [itex]\alpha[/itex] * l0 * ΔT

do i just equal Δl for brass and iron?
 
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  • #2
No, if each increases in diameter by the same amount, the plug will still not fit.
 
  • #3
Hint:

The thermal expansion coefficients for brass and iron are different.
 

1. What is thermal expansion and how does it affect brass and iron rings?

Thermal expansion is the tendency of materials to expand or contract in response to changes in temperature. Brass and iron rings are both metallic materials that exhibit thermal expansion, meaning they will expand when heated and contract when cooled.

2. How does the thermal expansion of brass and iron rings differ?

Brass and iron have different coefficients of thermal expansion, meaning they expand at different rates when exposed to the same change in temperature. Brass has a higher coefficient of thermal expansion than iron, meaning it will expand more for the same change in temperature.

3. What factors can affect the thermal expansion of brass and iron rings?

The thermal expansion of brass and iron rings can be affected by factors such as the initial temperature of the material, the magnitude of the temperature change, and the composition and structure of the material.

4. How is the thermal expansion of brass and iron rings measured?

The thermal expansion of brass and iron rings can be measured using a device called a dilatometer, which measures the change in length or volume of a material in response to a change in temperature.

5. How does the thermal expansion of brass and iron rings impact their use in practical applications?

The thermal expansion of brass and iron rings can impact their use in practical applications, as it can cause changes in size and shape that may affect the functionality of the rings. This is why it is important for engineers and designers to take into account the thermal expansion properties of these materials when creating products.

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