Calculating Length Change of Heated Copper Rod

In summary, the copper rod in question has a length of 40.0cm at 22.0 Celsius and is heated to 100.0 Celsius. Using the linear expansion equation for copper, the change in length is calculated to be 0.052 cm. However, the small effect of thermal expansion is mainly significant for larger objects.
  • #1
Dantheman1
2
0

Homework Statement


A copper rod is 40.0cm long at 22.0 Celsius. If the rod is heated to 100.0 Celsius, what is it's increase in length.

Homework Equations


Linear expansion of copper is 16.8*10^-6

The Attempt at a Solution


Change in Length= (length)(change in temp.)(α)
So...
(40.0)(78.0)(16.8*10^-6)
=0.052 cm is the change in length?

Please let me know if/what I did wrong here.
 
Last edited:
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  • #2
What answer are you expecting?
 
  • #3
Hypersphere said:
What answer are you expecting?

Don't know, I acctually may have not got it wrong i just wanted to make sure.
 
  • #4
Dantheman1 said:
Don't know, I acctually may have not got it wrong i just wanted to make sure.

OK. Well, if it makes you feel better, those values (assuming you give α in the usual units) and the linear expansion formula does give me the same answer. Basically, thermal expansion is a small effect, which thus mainly matters for larger things.
 
  • #5


Your solution is correct. The change in length of the copper rod is 0.052 cm. This is due to the linear expansion of copper, which is 16.8*10^-6 per degree Celsius. Since the change in temperature is 78.0 degrees Celsius (100.0-22.0), we multiply the length (40.0 cm) by the change in temperature (78.0) and by the linear expansion coefficient (16.8*10^-6) to get 0.052 cm. This is the expected increase in length of the copper rod when heated from 22.0 Celsius to 100.0 Celsius.
 

Related to Calculating Length Change of Heated Copper Rod

1. How does temperature affect the length of a copper rod?

As temperature increases, the length of a copper rod also increases. This is due to the expansion of the metal atoms, which causes the molecules to vibrate and take up more space.

2. What is the formula for calculating length change of a heated copper rod?

The formula for calculating length change of a heated copper rod is ΔL = L * α * ΔT, where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.

3. How do you determine the coefficient of linear expansion for copper?

The coefficient of linear expansion for copper can be determined by dividing the change in length (ΔL) by the original length (L) and the change in temperature (ΔT). This can be represented by the equation α = ΔL / (L * ΔT). The value of α for copper is 1.7 x 10^-5 /°C.

4. What are some factors that can affect the accuracy of calculating length change of a heated copper rod?

The accuracy of the calculation can be affected by factors such as the precision of the measurements, the uniformity of the rod's material, and the consistency of the temperature change. Other external factors, such as air currents or vibrations, can also have an impact on the results.

5. Can the same formula be used for calculating length change of other materials?

No, the formula for calculating length change of a heated copper rod is specific to copper and may vary for other materials. Each material has its own coefficient of linear expansion, which must be taken into account when calculating length change due to temperature.

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