Print ViewCoefficient of Expansion Conceptual Question

[doggieslover]

A standard mercury thermometer consists of a hollow glass cylinder, the stem, attached to a bulb filled with mercury. As the temperature of the thermometer changes, the mercury expands (or contracts) and the height of the mercury column in the stem changes. Marks are made on the stem to denote the height of the mercury column at different temperatures such as the freezing point (0^ \circ \rm C ) and the boiling point (100^ \circ \rm C ) of water. Other temperature markings are interpolated between these two points.

Due to concerns about the toxic properties of mercury, many thermometers are made with other liquids. Consider draining the mercury from the above thermometer and replacing it with another, such as alcohol. Alcohol has a coefficient of volume expansion 5.6 times greater than that of mercury. The amount of alcohol is adjusted such that when placed in ice water, the thermometer accurately records 0^ \circ \rm C . No other changes are made to the thermometer.

Part C
If you want to design a thermometer with the same spacing between temperature markings as a mercury thermometer, how must the diameter of the inner hollow cylinder of the stem of the alcohol thermometer compare to that of the mercury thermometer? Assume that the bulb has a much larger volume than the stem.


5.6 times wider
\sqrt{5.6} times wider
the same diameter but different bulb size
\sqrt{5.6} times smaller
5.6 times smaller

I don't understand this one.

 

[Chi Meson]

What you want is to find the two different changes in volume (assuming the same initial volume, in the bulb) for the same change in temperature.

Then, using "volume of a cylinder" equation, determine what difference in diameter is necessary to have the two changes in volume have the same change in height.

 

[doggieslover]

I have figured it out, thanks.