What determins the range of a mercury thermometer.?

Question

If you say both the stem and bulb? Then why? doesn't the stem decide sensitivity and not range?

Answer 1

The stem has to be long enough to hold all the expansion of the mercury to the high end of the range. The bulb has to be big enough to supply mercury for the whole range and hold the contracted amount.
Mercury has an expansion coefficient of (25 °C) 60.4  µm·m−1·K−1 for a uniform area which is the same as volume change 0.000604 % per degree K (or C) or 0.06 % for 100 degrees
Imagine a thermometer with a bulb of 100 ml (huge) and a stem with a volume of 1 ml. The mercury in the bulb would want to expand 6 ml for a 100 degree change and the stem would not allow it. So change the stem volume to 10 ml. The same expansion would go about 60% of the way up the tube, leaving 40% unused. until you go to a higher temp. Cutting the area by a third (times 66%) would make the same expansion go all the way to the end, decreasing the range, but increasing the sensitivity.
Now imagine the bulb and original stem are filled with 101 ml of mercury at 0C. That means the stem is 1/6th full to start. The range has been extended down because the mercury can contract and lower the amount in the stem yet the upper limit has been lowered because less length is available for expansion from the base state.
Actually, of course, the bulb volume is more like 0.01 ml and the stem a fraction of that.