A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100°C, and that of the far end of the aluminum rod is held at 0°C. If the copper rod is 0.30 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50°C?

College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100°C, and that of the far end of the aluminum rod is held at 0°C. If the copper rod is 0.30 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50°C?

Expert Solution
Step 1

In conduction mode of heat transfer, heat is transferred from a hot temperature region to a cold temperature region.It will occur as long as there is a difference in temperature between the two regions. Once the two locations have reached the same temperature, thermal equilibrium is established and the heat transfer stops. 

Other important factors that affect the rate of heat transfer are the materials involved, their area and length. The mathematical expression to calculate the rate of heat transfer, connecting the above variables is given as

Rate of heat transfer  =kATL

where k is the thermal conductivity, A is the area of cross-section,Tis the difference in temperature and L is the distance or length.

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