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I am struggling to find a ground for this question

So I have a mercury thermometer. There's a $0.2\, \mathrm{cm^3}$ void in the glass. The question asks for the new volume of void after a change in temperature.

Below are the known quantities $$\Delta T \\ \beta_{\text{mercury}} \\ \beta_{\text{glass}}$$

Normally, if the initial volume of two materials are given, I can calculate the difference between their volume changes $\Delta V$. However, this question did not provide the initial volume of mercury and glass.

The best I can do for this question, is to express the final answer in some unknown variable $x$

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  • $\begingroup$ Where did you get the (0.2)? $\endgroup$
    – R.W. Bird
    Commented Sep 13, 2021 at 13:35
  • $\begingroup$ @R.W.Bird It's 0.2, I made a mistake and said 0.5 at the beginning, edited my post $\endgroup$
    – Sirou Ewei
    Commented Sep 13, 2021 at 23:30

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A hole in a solid expands at the same rate as the solid. If you know the initial volume of the mercury and the void, then you know the initial volume of the “hole”. But, you are right. For a numeric answer, you need the initial volume of the mercury.

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  • $\begingroup$ By "hole", are you referring to the inner space of the thermometer made of glass? $\endgroup$
    – Sirou Ewei
    Commented Sep 13, 2021 at 23:33
  • $\begingroup$ Yes, the region which contains the mercury. $\endgroup$
    – R.W. Bird
    Commented Sep 14, 2021 at 13:18

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