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A brass plate has a circular hole whose diameter is

Chapter 16, Problem 14P

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QUESTION:

Problem 14P

A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. If the ball and the plate are always kept at the same temperature, (a) should the temperature of the system be increased or decreased in order for the ball to fit through the hole? (b) Choose the best explanation from among the following:

I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperature should be decreased.

II. Changing the temperature won't change the fact that the ball is larger than the hole.

III. Heating the brass plate makes its hole larger, and that will allow the ball to pass through.

Questions & Answers

QUESTION:

Problem 14P

A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. If the ball and the plate are always kept at the same temperature, (a) should the temperature of the system be increased or decreased in order for the ball to fit through the hole? (b) Choose the best explanation from among the following:

I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperature should be decreased.

II. Changing the temperature won't change the fact that the ball is larger than the hole.

III. Heating the brass plate makes its hole larger, and that will allow the ball to pass through.

ANSWER:

Step 1 of 3

To get the ball through the hole depends upon the relative coefficients of thermal expansion. If the hole expands faster than the ball, the system should be heated. If the ball contracts faster than the hole, the system should be cooled.

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