Q. 70

Expert-verifiedFound in: Page 546

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A cylindrical copper rod and an iron rod with exactly the same dimensions are welded together end to end. The outside end of the copper rod is held at , and the outside end of the iron rod is held at . What is the temperature at the midpoint where the rods are joined together?

The temperature at the midpoint where the rods are joined together is

Outside end of the copper rod temperature

Outside end of the iron rod temperature

In order to solve this problem, we must recognize that since the welding point is at thermal equilibrium, i.e. its temperature is constant, both the copper and iron rods transmit the same amount of power.

Knowing that the two rods have equal cross-section areas and length we can therefore write,

Simplifying the areas and the lengths, we are left with

We are given in the problem that the copper end is at the highest temperature, let it be denoted by , and the iron end is at the lowest temperature, let it be .

Therefore, letting the temperature of the weld be , the temperature differences will be,

Substituting the expressions for the temperature differences, we have

From this we can express the weld temperature as

Referring to table 19.5 on the book, our thermal conductivities are and

Substituting these and the temperatures, we can find the weld temperature to be,

Hence, the temperature at the midpoint where the rods are joined together is

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