Thermometer

The following is copy from email message sent to me by a physics teacher from Republic of Maldives.

Quote

Sir
Can u construct and send a java or EJS applet on liquid-in-glass-thermometer to teach the sensitivity and range the thermometer as its bulb size, diameter and thickness of glass changes.

Details:
1. The applet should contain two liquid in glass thermometer (alcohol thermometer or mercury thermometer) both should always show same temperature. The color of thread should be red.
2. The length, diameter, size of the bulb can be changed by user.
3. As we change (increase) its length the range shown by it should change (increase).
4. As user changes (reduces) the diameter of the bore of the thernometer, its sensitivity should increase and range should decrease.
5. As user changes (reduces) the size of the bulb of the thermometer, its sensitivity should decrease and range should increase.
6. There should be provision for changing the temperature, so that the thermometer displays the reading, as user increases or decreases.
Thanking you,

Here is a simple model for a thermometer:
Assume at temperature T=0 , it consists of two cylinder: bulb (raduis R , length H) and expandable parts (radius r,length h)
The volume of the filled liquid V(T=0)=πR²*H+πr²*h
The volume of the filled liquid at temperature T>0 V(T)=V(T=0)*(1+βT) where β is coefficient of volumetric thermal expansion.
β: Mercury=182*10^-6 K^-1, Ethanol=750*10^-6K^-1 , Glass=25.5*10^-6K^-1.

If we ignore the thermal expansion of glass, the volume increased is equal to V(T=0)*βT=πr²*Δh
where Δh is the change of the display part (indicator for sensitivity).
If V₀ is kept as a constant, then Δh=V(T=0)*βT/(πr²)
which means that the sensitivity is depends on r (however, it is not depends on R).
-*-

Alcohol, which is used as a thermometric liquid, has the following characteristic properties :
1. Alcohol has a very low freezing point of about −112^oC and hence is suitable in thermometers to record very low temperatures.
2. Alcohol has a low boiling point of about 78^oC and therefore cannot be used to measure high temperatures.
3. Alcohol can be colored brightly (by adding a dye, generally red) and then it is clearly visible through glass.
4. Alcohol expands more than mercury.
5. Alcohol is fairly inexpensive.
6. Alcohol wets glass.
7. Alcohol is not a good conductor of heat.

Mercury, which is used as a thermometric liquid, has the following characteristic properties :
1. Mercury has a high boiling point of about 357^oC and therefore can be used to measure temperatures as high as 357oC.
2. Mercury has a freezing point of about −39^oC and hence is suitable in thermometers to record low temperatures (although not very low temperatures).
3. Mercury is opaque and has a shining silvery color of its own, making it clearly visible in the capillary tube of a thermometer.
4. Mercury needs very little heat to expand and so it can easily measure the temperature of a body without causing a decrease in the body's temperature.
5. Mercury does not stick to the side of the glass capillary tube of a thermometer. Therefore, it allows accurate temperature measurement.
6. Mercury is a good conductor of heat.
7. Mercury is relatively expensive.

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