   Chapter 11, Problem 63AP

Chapter
Section
Textbook Problem

A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P11.63). One end of the compound bar is maintained at 80.0°C, and the opposite end is at 30.0°C. Find the temperature at the junction when the energy flow reaches a steady state. Figure P11.63

To determine
The temperature at the junction when the energy flow reaches a steady state.

Explanation

Given info: A bar of gold is in thermal contact with a bar of silver of the same length and area, Temperature at one end is 80.0°C , temperature at the opposite end is 30.0°C .

At steady state the rate of energy transfer through conduction by the gold bar PAu is same as the rate of energy transfer through the silver bar PAg that is PAu=PAg .

Expression for the steady state is,

kAuA(TiTf)L=kAgA(TfTi)L

• kAu is the thermal conductivity of gold,
• kAg is the thermal conductivity of silver,
• Ti is the temperate at the end of the gold bar,
• Ti is the temperate at the end of the silver bar,
• Tf is the final temperature at the junction,
• L is the length of the bar,
• A is the area of the bar,

Simplify and rearrange the steady state equation in terms of Tf

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