Non-Linear Evaporation: Explained for Beginners

[Zuchi]

Hello to you all,
Can someone please explain non-linear evaporation to me. I have not studied physics and it was a very long time ago that I learned chemistry and maths at school. So please explain it to someone with no prior knowledge of physics.
A small glass tube is filled with the liquid methyl benzoat. The radius along the glass tube appears constant. The glass tube is housed in a plastic case with metal backing, and fixed to a radiator. When turned on the radiator has hot water flowing through it so as to warm up a room in winter. The idea is that the extent of evaporation in the glass tube shows the heat consumption and so used to apportion heating costs to individual users. The hot water feeding the radiator comes from a communal central heating system.
Below is a photo of the glass tube, or google Minotherm II:
https://www.google.de/search?q=Minotherm+II&client=ubuntu&hs=N6v&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiMqKKm85zgAhWCjCwKHfKkDh8Q_AUIDigB&biw=1859&bih=942#imgrc=hzA_s3oxM_XwRM:It is said that evaporation is non-linear, and differs depending on the liquid level in the glass tube.
Q1. What is here meant by non-linear?

Q2. What role does the height of the liquid play in the evaporation rate?On the left of the glass tube is a normal millimetre ruler, 7mm above zero, below zero 0-60mm, placed there for comparison.
To measure the amount of methyl benzoat that has evaporated in a year, they used a scale that has a unique layout ( the „unique scale“). This is the scale on the right of the glass tube. This unique scale has 7 units above 0, marked by 901, 903, 905 and 907. These equate to 7mm.
Below 0 the unique scale diverges from a normal millimetre ruler. The spacing is different and for every 10 units down the glass tube, the bands become increasingly narrower. After 30, each 10 units (30-40, 40-50, 50-60, 60-70, 70-80) are shown by only 5 dashes which seem to be due to limited place for marking. Still, the bands continue to be increasingly narrower from 30 to 80. The unique scale runs up to 80 units whereas the millimetre ruler runs up to 60 mm.
The effect of the unique scale is that lower down the glass tube, a smaller amount of liquid evaporated will reach the next dash / the next unit / the next consumed unit used for calculating heating costs.Q3. Is the unique scale an adjustment to neutralize non-linear evaporation?
Phrased differently - When the same amount of heat flows through the radiator, leading to units of methyl benzoat in the glass tube being evaporated (the consumed units), is the unique scale used to counter non-linear evaporation? Is it used to neutralize possible influence from the height of the liquid in the glass tube (be it at 4, 34 or 44) in the evaporation?
Q4. If not, what is the use of such unique scale?I am grateful for your clarifications. Thank you in advance.
Zuchi

 

[jrmichler]

The rate of evaporation is proportional to the vapor pressure gradient of the liquid immediately above the free surface. The liquid has a vapor pressure, the atmosphere in the room has a vapor pressure (actually partial pressure). The partial pressure in the room will be effectively zero. The tube between the liquid free surface and the room has a methyl benzoat (benzoate?) vapor pressure gradient between the liquid free surface and the room. The longer the distance, the lower the vapor pressure gradient, and the lower the evaporation rate.

If you put some methyl benzoate in an open pan, it will evaporate much faster.

 

[Zuchi]

Thank you jrmichler for answering.
Yes in English there is an “e” at the end of methyl benzoate, I am talking about C8H8O2.

Your sentence “The longer the distance, the lower the vapour pressure gradient, and the lower the evaporation rate.”
Is my following understanding correct? – When a certain amount of methyl benzoate has already been evaporated and the liquid level now lower down the glass tube (say half way down), because further evaporated vapour has a longer distance to travel upwards to escape, the evaporation rate is lower.
Presumably that was why they designed that unique scale?
Does condensation play a role? When traveling a longer way up the glass tube, would some vapour convert back into liquid?

 

[jrmichler]

It's diffusion. The vapor partial pressure will be highest at the surface of the liquid, then drops continuously toward the free opening. Since the vapor pressure away from the liquid surface is always lower than at the liquid surface, and since the entire apparatus is at constant temperature, the vapor partial pressure in the air is always lower than the liquid vapor pressure. So no condensation. Try search terms diffusion, diffusion in gases, and Fick's law to learn more.