The spirit-in-glass thermometer, invented in Florence, Italy, around 1654 consists of a tube of liquid (the spirit) containing a number of submerged glass spheres with slightly different masses (Fig. Pl4.73). At sufficiently low temperatures all the spheres float, but as the temperature rises, the spheres sink one after another. The device is a crude but interesting tool for measuring temperature. Suppose that the tube is filled with ethyl alcohol, whose density is at 20.0°C and decreases to at 30.0°C.
(a) Assuming that one of the spheres has a radius of 1.000 cm and is in equilibrium halfway up the tube at 20.0°C, determine its mass.
(b) When the temperature increases to 30.0°C, what mass must be a second sphere of the same radius have to be in equilibrium at the halfway point?
(c) At 30.0°C, the first sphere has fallen to the bottom of the tube. What upward force for the bottom of the tube exerts on this sphere?
