How Does Copper's Thermal Conductivity Affect Heat Transfer?

In summary, the problem involves a copper bar with a thermal conductivity of 401 W/(m·K) and a length of 0.10 m, with one end at 102°C and the other end at 23°C, and a cross sectional area of 1.0 multiplied by 10-6 m2. The rate of heat conduction along the bar is 0.50125 W, the temperature gradient is 79.25 K/m, and in the series case, the temperature at the junction of the two bars is 62.5°C.
  • #1
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Homework Statement


A copper bar of thermal conductivity 401 W/(m·K) has one end at 102°C and the other end at 23°C. The length of the bar is 0.10 m and the cross sectional area is 1.0 multiplied by 10-6 m2.
(a) What is the rate of heat conduction along the bar?

(b) What is the temperature gradient in the bar?

(c) If two such bars were placed in series (end to end) between the same temperature baths, what would script p be?

(d) If two such bars were placed in parallel (side by side) with the ends in the same temperature baths, what would script p be?

(e) In the series case, what is the temperature at the junction where the bars meet?


Homework Equations


P=KA(deltaT/d)


The Attempt at a Solution


I'm stuck on part (a). I used the above equation and got: (401)(1x10^-6)(102+23/.1)=.50125 which is apparently wrong.
 
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  • #2
Did you plug in the correct value for delta T?Delta T should be the temperature difference.
 
  • #3
opps...yeah that was suppose to be a negative sign. Thanks
 

Related to How Does Copper's Thermal Conductivity Affect Heat Transfer?

What is the rate of heat conduction?

The rate of heat conduction, also known as thermal conductivity, is a measure of how quickly heat energy is transferred through a material. It is typically measured in units of watts per meter per kelvin (W/mK).

How is the rate of heat conduction affected by different materials?

The rate of heat conduction is influenced by the type of material and its physical properties, such as density, thermal conductivity, and specific heat. Materials with high thermal conductivity, such as metals, are better at conducting heat than materials with low thermal conductivity, like insulators.

What factors affect the rate of heat conduction?

The rate of heat conduction is affected by several factors, including the temperature difference between two objects, the distance between the objects, the type of material, and the surface area of contact. Higher temperature differences and shorter distances typically result in faster heat conduction, while insulating materials and smaller surface areas slow down the rate of heat transfer.

How is the rate of heat conduction calculated?

The rate of heat conduction can be calculated using Fourier's law of heat conduction, which states that the rate of heat transfer is proportional to the temperature gradient and the thermal conductivity of the material. This can be expressed as Q = kA (T1-T2)/d, where Q is the heat transfer rate, k is the thermal conductivity, A is the surface area, T1 and T2 are the temperatures of the two objects, and d is the distance between them.

Why is understanding the rate of heat conduction important?

Understanding the rate of heat conduction is crucial in many practical applications, such as designing efficient insulation, assessing the performance of heating and cooling systems, and predicting the behavior of materials in extreme temperatures. It is also essential in fields like thermodynamics, engineering, and material science.

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