Will the Gap Between (B) and (C) Change When Heated?

[barcat]

The question is- In the metal object below, will the gap between the
ends of (B) and (C) become narrower, wider, or remain unchanged if heated?

                    ____________
                    |          |
                    |          | (B)
                    |          |
                    |
                 (A)|
                    |
                    |          |
                    |          | (C)
                    |          |
                    ------------

This question has been on our class discussion board for
two weeks. The class is split 50/50.

My answer was-

"My thinking is this. Being that the total continuous
length of the metal of side (A) is longer than the sum
of sides (B+C), and we know that longer objects of the
same material (with the same expansion coefficient)expand
more, this would mean that the gap between (B) and (C)
would get wider because the total expansion of (B + C)
would never be equal to or longer than (A)."

Am I off base here?

 

[Doc Al]

You are exactly right. The expansion affects every linear dimension--including the gap--in the same way.

 

[mathman]

Practical application: When you try to get a metal lid off a jar (that has not been opened), it can be extremely tight. Put it under hot water and it will be easier to get off, since the size of the interior gap of the lid has expanded.

 

[barcat]

mathman;
I never thought to apply that example to this situation. It was even shown in the book as an example for something else. I had to prove it mathematically by applying what ever type metal I chose, then doing the calculations. I guess the gap in the ring was throwing me off.

THANKS-barry.

 

[barcat]

Originally posted by Doc Al
You are exactly right. The expansion affects every linear dimension--including the gap--in the same way.

Thanks also to Doc Al. Confermation goes a long way here!