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The ends of the two rods shown in the figure are separated by 5.0 mm at 25 °C. The left-ha...

The ends of the two rods shown in the figure are separated by 5.0 mm at 25 °C. The left-hand rod is brass and 1.0 m long; the right-hand rod is steel and 1 m long. Assuming that the outside ends of both rods rest firmly against rigid supports, at what temperature will the ends of the rods that face each other just touch?

Step-by-Step Solution

Solution 1
Step #1 of 6

THINK:

The coefficient of linear expansion depends on the temperature and initial length.

Linear expansion coefficient for brass is

Linear expansion coefficient for aluminum is

Step #2 of 6

RESEARCH:

The change of length with change in temperature is given by

…… (1)

Here is the linear expansion coefficient, is initial length.

Step #3 of 6

CALCULATE:

Given,

The length of the brass rod is

Length of the steel rod is

Separation between two rods is

Initial temperature is

Let the final temperature is

Change in temperature is

Step #4 of 6

The change in the length of brass rod is

The change in the length of steel rod is

Step #5 of 6

To fill the gap the total linear expansion of given two cubes is must equal to the gap between them.

Step #6 of 6

Therefore the required temperature will the ends of the rods that face each other just touch is

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Solutions For Problems in Chapter 17
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