Calculating Linear Expansion of Iron Rod for 2.51cm Ring Diameter

In summary, linear expansion is the increase in length of an object due to a change in temperature. This is important to calculate because it can impact the functionality and accuracy of devices or structures that involve precise measurements. To calculate the linear expansion of an iron rod, you will need to know the original length, change in temperature, and coefficient of linear expansion for iron. The coefficient of linear expansion for iron is 11.8 x 10^-6 m/m °C. It can be accurately predicted using the coefficient and change in temperature, but variations in iron quality may affect the accuracy. The diameter of a ring does not directly affect linear expansion, but if the rod is formed into a ring shape, the expansion will occur in both length and
  • #1
furielrage
1
0
An iron rod has a diameter of 2.50cm at 20.0°. To what temperature must it be heated to fit into a ring with an inside diameter of 2.51cm. I'm given: alpha=1.0x10^-5

I'm not sure how to apply it to the △L=(alpha)(object length)△T
 
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  • #2
Since the diameter is one dimensional quantity, L=2.50cm.
It seems a little bit strange but the diameter will expand just like a iron rod.
 
  • #3
equation

Based on the given information, we can use the formula for linear expansion: ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length of the object, and ΔT is the change in temperature.

In this case, we know that the initial diameter of the iron rod is 2.50cm and it needs to fit into a ring with an inside diameter of 2.51cm. Since diameter is twice the length, we can calculate the original length of the rod to be 1.25cm.

Next, we can plug in the values into the formula: ΔL = (1.0x10^-5)(1.25)(ΔT)

To find the change in temperature (ΔT) needed for the rod to fit into the ring, we can rearrange the formula to: ΔT = ΔL/(αL)

Substituting the values, we get: ΔT = (2.51-2.50)/(1.0x10^-5)(1.25) = 8°C

Therefore, the iron rod must be heated to 20.0°C + 8°C = 28.0°C to fit into the ring with an inside diameter of 2.51cm.
 

Related to Calculating Linear Expansion of Iron Rod for 2.51cm Ring Diameter

1. What is linear expansion and why is it important to calculate?

Linear expansion is the increase in length of an object due to a change in temperature. It is important to calculate because it can affect the functionality and accuracy of devices or structures that involve precise measurements, such as thermometers or bridges.

2. How do you calculate the linear expansion of an iron rod?

To calculate the linear expansion of an iron rod, you will need to know the original length of the rod, the change in temperature, and the coefficient of linear expansion for iron. The formula is: ΔL = (α x L x ΔT), where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

3. What is the coefficient of linear expansion for iron?

The coefficient of linear expansion for iron is 11.8 x 10^-6 m/m °C. This means that for every 1°C increase in temperature, an iron rod will expand by 11.8 x 10^-6 meters for every meter of its original length.

4. Can the linear expansion of iron be accurately predicted?

Yes, the linear expansion of iron can be accurately predicted using the coefficient of linear expansion and the change in temperature. However, variations in the composition and quality of the iron may affect the accuracy of the prediction.

5. How does the diameter of a ring affect the linear expansion of an iron rod?

The diameter of a ring does not directly affect the linear expansion of an iron rod. However, if the rod is formed into a ring shape, the expansion will occur in both the length and diameter of the ring. The change in diameter will be greater than the change in length due to the ring's circumference being larger than its diameter.

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