Chapter 10, Problem 15P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, (a) to what temperature must the combination be cooled to separate the two metals? Is that temperature attainable? (b) What if the aluminum rod were 10.02 cm in diameter?

(a)

To determine
The temperature of cooling (T).

Explanation

Given Info: The diameter of brass at T0=20Î¿C . ( d0b ) is 10.00 cm. The diameter of aluminum at 20Î¿C . ( d0a ) is 10.01 cm. Co-efficient of expansion of brass ( Î±b ) is 19Ã—10âˆ’6/Î¿C . Co-efficient of expansion of aluminum ( Î±a ) is 24Ã—10âˆ’6/Î¿C .

For the ring to be removed from the rod,

db=da Â Â Â Â Â Â  (I)

• db and da are the diameters of brass and aluminum at the final temperature.

The formula for the diameter of brass,

db=dob[1+Î±b(Tâˆ’T0)] Â Â Â Â Â Â  (II)

The formula for the diameter of aluminum,

da=dob[1+Î±a(Tâˆ’T0)] Â Â Â Â Â Â  (III)

Substitute Equation (II) and (III) in (I)

(b)

To determine
The temperature change.

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