Thermal expansion across a copper rod

In summary, the task is to determine the shape of a copper bar in contact with a furnace and ice bank, with a diameter of 2.54 cm and length of 0.5 meters. The thermal conductivity of copper is 380 J/(smC). The equation to be used is ΔQ = kA(Thot-Tcold)/ΔtL. However, the individual attempting the solution is unsure of how to proceed and is seeking assistance.
  • #1
dabess
2
0

Homework Statement



Determine the actual shape of a copper bar in contact with a furnace at a constant 200 C at one end and a constant ice bank at 0 C at the other end.

Diameter of the rod is 2.54 cm. Length is .5 meters. Thermal conductivity of copper is 380 J /
(smC)

Homework Equations




Q = k A (Thot – Tcold)
t L

The Attempt at a Solution



Honestly, I have no idea how to do this. I know that I must find the temperature distribution across the rod in order to find the linear and volumetric expansion at each point. But I don't know how to do this.
 
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  • #2
bump. someone please help.
 

FAQ: Thermal expansion across a copper rod

What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature. This can occur in various materials, including metals like copper.

How does thermal expansion occur in a copper rod?

Thermal expansion in a copper rod is caused by the increase in kinetic energy of its atoms as the temperature rises. This increase in energy causes the atoms to vibrate more and take up more space, resulting in an expansion of the material.

What factors affect the amount of thermal expansion in a copper rod?

The amount of thermal expansion in a copper rod is influenced by several factors, including the material's coefficient of thermal expansion, the change in temperature, and the length and cross-sectional area of the rod.

What are the practical applications of understanding thermal expansion in copper rods?

Understanding thermal expansion in copper rods is important in engineering and construction, as it allows for the design of structures that can withstand changes in temperature without causing damage or structural failure. It is also useful in the creation of precision instruments, such as thermometers and thermostats.

How is thermal expansion in copper rods measured and calculated?

The change in length of a copper rod due to thermal expansion can be measured using a micrometer or caliper. The coefficient of thermal expansion for copper is 16.5 x 10^-6 m/mK, so the change in length can be calculated by multiplying the original length of the rod by this coefficient and the change in temperature in Kelvin.

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