in calibrating your thermometer by setting only the freezing and boiling points, what assumptions are you making regarding the internal diameter of the thermometer and the expansion of the thermometer fluid?

Answer 1

You're assuming that the internal diameter of the capillary glass tube is virtually the same for the length of the thermometer and that the fluid used in the thermometer expands evenly from the low point registered on the scale to the high point registered on the scale.