if a glass and mercury have the same coefficient of expansion, it is still possible to construct a mercury thermometer? justify your answer

Question

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Answer 1

This is a very good question!  Normally, mercury-in-glass thermometers work because the mercury changes volume much more than the glass does, primarily because it has a larger coefficient of volume expansion.  The glass expansion is often so small as to be considered negligible (though it does change volume with change in temperature, as well).

 

If the mercury and glass have the same coefficient of volume expansion, then the situation changes.  The expression for (fractional) volume expansion is:

 

(ΔV/V_o) = βΔT

 

So, as long as the mercury and the glass experience the same ΔT, they will expand together.  We can assume that they experience the same ΔT if the thermometer is used as a thermometer typically is, where all elements are allowed to come to the same temperature before a reading is taken (otherwise, the possibly different heat capacities of the mercury and glass would mean they experience different ΔT's, which would alter the situation).

 

Think of it as if the glass and the thermometer were one solid cylinder of glass, expanding and contracting the same way with temperature.  If we took that solid cylinder and heated it, it would expand a certain amount in volume.  If we did the same thing, except first we cut out a solid inner piece, leaving that solid piece and a corresponding cylindrical shell which we heated it the same way, both parts would expand just as the whole thing did before.  This means the hole inside the cylindrical shell must expand in the same proportion as the outer radius of the inner solid shell we cut out.

 

Thus, the glass and mercury in this proposed thermometer would expand and contract together.  In effect, then, the glass itself is expanding and contracting with temperature.  What it would look like is the glass would be a hollow cylinder, and we can suppose we have filled it to a certain level with mercury.  As the temperature changes, the glass and the mercury would expand (or contract) together, in unison, so the mercury would always keep the same relative height inside the tube.

 

However, the absolute position of the top of the mercury would still change as the glass expands or contracts.  If this absolute change in position could be calibrated, the top of the mercury could still act as a marker of temperature.  I suspect it would not be nearly as sensitive to changes in temperature as when the mercury expands much more in glass, so I think it would not be as accurate a thermometer anymore, unless you can calibrate the change in glass/mercury volume change with temperature REALLY carefully.  But, theoretically, it could work.

 

I hope this helps!  If you want to talk more about the situation, just let me know.