Volume Expansion: Answers to Homework Questions

[negation]

Homework Statement

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∘C) and the boiling point (100∘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∘C. No other changes are made to the thermometer.

1) When the alcohol thermometer is placed in 20∘Cwater, what temperature will the thermometer record?

2)
When the alcohol thermometer is placed in a −10∘C substance, what temperature will the thermometer record?3)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.(solved)

The Attempt at a Solution

ΔV_A = V_AiαΔT

The cylinder has a volume: πr²h

Change in volume of alcohol in a cylinder: ΔV_A = πr²h(5.6α)ΔT

Change of volume of mercury in a cylinder: ΔV_M = πr²h.α.ΔT

I am experiencing a confusion here. Question states that the thermometer is placed into a water of 20°C. However, nothing was said about the initial temperature. Without this piece of information I cannot utilize ΔT.

 

[BvU]

You know the reading at 0 degrees C. So 20^∘ would be a good ΔT. You also know that the corresponding ΔV_M makes the mercury rise to the 20[sup∘[/sup]C mark.

 

[negation]

You know the reading at 0 degrees C. So 20^∘ would be a good ΔT. You also know that the corresponding ΔV_M makes the mercury rise to the 20[sup∘[/sup]C mark.

I don't...
what is the height of the thermometer at 0 and 20 degree celsius?

 

[BvU]

Give it a name: "0". The makers of the device make a mark and write a zero at that height. Then the Hg is drained and the C₂H₅OH is filled up to that height on the scale.

[edit] as for the 20 one: that's the real exercise for you to do. It has to be calculated from the difference in ΔV.