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?

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.

When calibrating a thermometer by setting only the freezing and boiling points, we make some assumptions regarding the internal diameter of the thermometer and the expansion of the thermometer fluid. These assumptions include:

1. Uniform internal diameter: We assume that the internal diameter of the thermometer is uniform along its entire length. This means that the bore of the thermometer, through which the temperature-sensitive fluid expands and contracts, has a consistent size.

2. Linear expansion: We assume that the expansion of the thermometer fluid is linear within the calibrated temperature range. In other words, we assume that the volume of the fluid varies linearly with the temperature.

It's important to note that these assumptions simplify the calibration process and allow for a reasonably accurate measurement within the temperature range of interest. However, in reality, the internal diameter of the thermometer may not be perfectly uniform, and the expansion of the fluid may deviate from linearity at extreme temperatures. These factors can introduce some degree of measurement error, especially when measuring temperatures outside the calibration range.