Suppose that you had a mercury-in-glass thermometer and calibrated to measure temperatures from -10 degrees C to 110 degrees C and you wished to measure a temperature of approximately 115 degrees C accurately. How might you use your thermometer to do it?

There may be an easier way to do it but here are a couple of ideas that you can build on.

a. Add a measured amount of cool solvent (say at about 50C) to a measured amount of the sample, stir, and measure the temperature accurately. It should be less than 115 at that point and well withing the calibrated range.
b. same process with ice or dry ice.
There isn't much to go on here. No mention of the size of the sample, the ease of handling, the kind of solvent, etc but perhaps this will get you started.

If your mercury-in-glass thermometer is calibrated to measure temperatures from -10 degrees C to 110 degrees C, it would not be suitable for directly measuring a temperature of approximately 115 degrees C accurately. However, there are a few ways you can try to estimate the temperature using the existing thermometer:

1. Extrapolation: If you have temperature measurements beyond the calibrated range, you can try to extrapolate based on the known values. For example, plot a graph of temperature against expansion of the mercury and extend the line to estimate the reading for 115 degrees C. However, this method introduces some level of uncertainty and may not provide an accurate result.

2. Interpolation: If the thermometer is not accurate near its extreme calibrated values, you can interpolate between known readings to estimate the temperature. This method assumes a linear relationship between the expansion of the mercury and temperature. For example, if you know the expansion for 100 degrees C and 110 degrees C, you can estimate the expansion for 115 degrees C and convert it into a temperature reading.

3. Calibration adjustment: It might also be possible to recalibrate the thermometer in order to extend its range. This can be a complex process that involves comparing it against a reference thermometer at various temperatures, adjusting the scale accordingly, and possibly replacing the mercury if necessary. However, this method requires expertise and special equipment.

If accuracy is crucial for measuring a temperature of approximately 115 degrees C, it would be recommended to use a thermometer specifically designed and calibrated for that temperature range.