# Range of a thermometer - and bulb size

I have a question.

How does the size of the bulb (mercury) affect the range of the thermometer?

I know that to increase the range, the bore size of the capillary tube should be large.

Would the size of the bulb affect the range?
If bulb is large - then there will be more mercury - so that the range should increase....

but if the bulb is larger - then it takes a longer time for the mercury to be heated up and would that limit its range?

Thanks for the help....

cheers !

sunny Singapore

Matthew

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Matthew,

A simple (though pretty effective) model for thermal expansion of liquids gives the following equation:

$$\triangle V = \beta V \triangle T$$

$$\triangle V = \mbox{change in volume}$$
$$\beta = \mbox{a constant that depends on what liquid you use}$$
$$V = \mbox{volume}$$
$$\triangle T = \mbox{change in temperature}$$

So we can see that having a larger volume of mercury to start with (as would be the case with a bigger bulb) would produce a bigger change in volume. So with a larger bulb, the mercury would expand further up the capillary with the same change in temperature. In this sense, yes, the bigger bulb would make the range increase. But then you have to think about what you mean by 'range'. The liquid will go further up the tube for the same temperature, but this actually means that, if you have a fixed tube-length, you will not be able to record as high of temperatures, because the same temperature will now make the fluid rise higher. For a concrete example, let's say that you have a thermometer that tops out at 100 C. If you now make the bulb bigger while leaving the length the same, 100 C will make the mercury rise higher than the top of your thermometer! It's new maximum might now be, say, 80 C. So, if by 'range', you mean the range of temperatures accessible by a fixed length of tube, then you would want a smaller bulb so that the liquid wouldn't rise as high as fast.
I hope that all makes sense. Let me know if some part doesn't, and I (or someone else), can try and clarify.

Peace,
Jason

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Sensitivity vs Range

Hi! I guess what you have mentioned here is that the range is dependent on how much liquid you have and far you allow that liquid to expand within your thermometer. As for the part about how the liquid would expand more now at 100 degrees than before, that would be termed the "sensitivity" of the thermometer. How much of a small change in temperature is observable by the thermometer....for the same bulb size, a narrower capillary tube would be more sensitive than a broad one.

However, I am facing difficulties trying to explain how the volume of the bulb affects sensitivity! Other than using the formula given in the previous post, is there a "non-formula" method that puts things on a more intuitive level that is easier for students to understand?

mgb_phys
Homework Helper
If the liquid was only in the capilallary then the volume wouldn't make any difference to the sensitivity. Increase the temperature by 1% would increase volume by 1% and the height in the tube by 1%
But suppose there is a large bulb containing 99% of the mercury and the tube only holds 1%. Now a 1% increase in temperature again gives a 1%increase in volume but this doubles the amount in the tube and so gives a change in the height of 100% not 1%.

But wouldn't the temperature change occur only at the bulb? Assuming that the thermometer is used correctly? So the volume changes first in the bulb then gets propagated through the rest of the liquid right?

mgb_phys