Adjusting the thermometer

Older thermometers are usually made out of a glass tube of mercury with a spherical mercury container at one end. Since mercury is very sensitive to temperature change, a small increase in our body’s temperature causes the mercury in the container to expand and push the mercury in the tube, which we can read off the thermometer. What is the minimal temperature difference in ^\circC our eye can read off in this way?

Details and assumptions

  • A human eye can distinguish points that are up to 0.05 mm0.05~\mbox{mm} apart
  • Volumetric thermal expansion coefficient of mercury is 0.18×1031K0.18 \times 10^{-3} \frac{1}{K}
  • All expansion happens in the sphere and glass expansion can be neglected
  • Ignore gravity effects
  • Diameter of thermometer is 0.15 mm0.15~\mbox{mm}
  • Volume of mercury container is 0.255 cm30.255~\mbox{cm}^3

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