Does the expansion of air affect the overall volume increase of a glass stopper?

[zorro]

Suppose there is a glass stopper with a hollow in it. If the ambient temperature rises the volume of the hollow(say 1cm³ initially) also rises. To find out the increase in volume, do we have to take into account the expansion of air along with the expansion of glass?

 

[Mapes]

Unconstrained thermal expansion is stress-free. So you can imagine that a glass piece fits into the hollow and expands stress-free; therefore, the hollow expands as if it were filled with glass, not air. Does this help?

 

[zorro]

So you can imagine that a glass piece fits into the hollow and expands stress-free

The question does not say about the glass fitting in a hollow. There is a hollow in the glass stopper.

 

[Mapes]

Read my answer again: imagine that the hollow part is filled with glass. It would expand the same amount.

 

[zorro]

Okay, I get you now.
But is that not loss of generality? If we consider some amount of air to be present in the hollow, both of them will expand which can lead to a different final volume (greater) compared to your case.