Galileo Thermometer!

Classical Mechanics Level 1

The glass bulbs of a Galileo thermometer are sealed such that their densities are constant. The clear liquid in which the bulbs are submerged is ethanol, which changes density depending on the surrounding temperature.

Each bulb is labeled with the temperature at which its density is equal to that of the ethanol. For example, if the ethanol temperature is $20^\circ \text{C},$ then the bulb labeled $20^\circ \text{C}$ would have the same density as the ethanol.

At $25^\circ\text{C}$ ethanol temperature, what do you observe inside the thermometer?

Details and Assumptions:

The density of ethanol decreases with increasing temperature.

All the bulbs labeled smaller than

25^\circ\text{C}

are sunk Only the bulb labeled

25^\circ\text{C}

is sunk All the bulbs labeled greater than

25^\circ\text{C}

are sunk Only the bulb labeled

25^\circ\text{C}

remains floating

4 solutions

Ram Mohith
Jun 4, 2018

Galileo Thermometer works on the principle of Buoyancy.

The basic idea is that as the temperature of the air outside the thermometer changes, so does the temperature of the ethanol surrounding the bubbles. As the temperature of the ethanol changes, it either expands or contracts, thereby changing its density. So, at any given density, some of the bubbles will float and others will sink. The bubble that sinks the most indicates the approximate current temperature.

Ex : If the $35^\circ C$ bulb sinks the most the surrounding temperature is $35^\circ C$ . And if the $50^\circ C$ bulb sinks the most the surrounding temperature is about $50^\circ C$ .

Coming to our question the temperature given is $25^\circ C$ . So the surrounding temperature is $25^\circ C$ .

Therefore, $\color{#20A900}\text{All the bulbs labelled smaller than }25^\circ C\text{ will sink.}$

But haven't all the bulbs labelled <25 already sunk to the bottom before reaching 25 degree? They wouldn't move then because where if they had already sunk to the bottom. I probably missunderstood something, but I would like to understand it properly :)

Alex Waldherr - 2 years, 11 months ago

At temperature around $25 ^\circ C$ all the bulbs marked less than 25 (like 24,23,22, etc) had already been sunk. When the temperature is exact $25 ^\circ C$ the bulbs marked 25 will begin to sink and by the time the temperature reaches $26 ^\circ C$ all bulbs marked 25 had been sunk.

Ram Mohith - 2 years, 11 months ago

Okay, thanks!

Alex Waldherr - 2 years, 11 months ago

This was my reasoning as well, which is why I chose the second option and was called incorrect.

The wording of the question is not clear. It should include information about the start state of the container. The verb 'sink' means 'travelling downwards through the liquid', not 'being at the bottom of the liquid'.

Chris Wylie - 2 years, 11 months ago

Yes, they sink...and they end up at the bottom. Seems to be an unimportant distinction.

Richard Desper - 2 years, 11 months ago

I agree. All the bulbs less than 25 are already on the bottom. They don't sink at 25 degrees. Only the bulb labeled 25 sinks at 25 degrees. The answer is incorrect.

G Silb - 2 years, 11 months ago

What wrong is there in my answer

Ram Mohith - 2 years, 11 months ago

@Ram Mohith – I agree with your answer.

G Silb - 2 years, 11 months ago

Nope. Go to wiki and look it up.

Maddy Feltus - 2 years, 11 months ago

@Maddy Feltus – Staff agreed with my answer and changed the wording of the responses to reflect it.

G Silb - 2 years, 11 months ago

@G Silb – ok..your original answer (uncorrected) was not exact. Glad they changed it, even after I commented. I also tried to put in the Wiki address and a comment about why it works and these columns are still used at the US National labs to get very exact density measurements. The only instrument better is a mercury porousimeter that injects mercury gas at high pressures into a possibly porous object and gets the internal voids filled.....

Maddy Feltus - 2 years, 11 months ago

"The bubble that sinks the most..."

This is misleading language. You need to say either "the bubble with the highest number that sinks" or "the bubble with the lowest number that doesn't sink".

Richard Desper - 2 years, 11 months ago

Sarthak Ram Nimbarmunde
Jun 17, 2018

The density of ethanol decreases with increase in temperature. Each bulb is labeled with the temperature at which its density is equal to that of the ethanol .Density at lower temperature is greater than at higher temperature for ethanol which is indicated the sealed glass bulb labeled at the particular temperature.(The glass bulbs of a Galileo thermometer are sealed such that their densities are constant) Hence all the bulbs labeled smaller than given temperature will sink as they have values of densities at lower temperature.

Noko Rammutla
Jun 19, 2018

If the temperature were increased until the ethanol becomes a gas, all the bulbs would sink/fall to the bottom (The temperature is above all labels), and if the temperature were decreased slowly until the ethanol freezes, all the bulbs would float to the top (The temperature is below all labels). Each bulb would be in the middle of the mixture when it's density is the same as the ethanol. This occurs when the temperature is the same as it's label. So at any given temperature the bulbs with a lower number rise and the bulbs with a number higher than the temperature sink.

The question only concerns itself with ethanol in a liquid state.

The density of the ethanol is decreasing as the temperature increases.

Thus as the temperature increases, more and more of the indicator bubbles are going to drop. So the only way this scale works as a thermometer is if the bubbles with the densest fluids have the lowest numbers. Because they will drop first.

Richard Desper - 2 years, 11 months ago

Mj Kim
Jun 23, 2018

It said in the problem "Ethanol density decreases with increasing heat" so the opposite is also true. Ethanol increases density with decreasing heat. Usually, more dense objects tend to sink more than less dense objects. So the colder the temperature gets, the more dense the glass balls become. All the balls below 25 C are "colder" than the 25 C ethanol, which makes the balls more dense. This makes the balls sink.

Galileo Thermometer!

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