Question

Consider a fever thermometer that contains 0.01 cm³ of mercury, Find the diameter of the capillary if a 1 C° change corresponds to a level change of 0.5 cm . Assume the glass does noe expand.

Answer 1

$h=h_0(1+\alpha T),$

$\Delta h=\alpha Th_0,$

$h_0=\frac{\Delta h}{\alpha T}=3.6~cm;$

$V=\frac{\pi d^2}4h_0,$

$d=\sqrt{\frac{4V}{\pi h_0}}=0.6~mm.$