Is the mass of Liquid N2 and its rate of mass loss related?

[Dazzabaijan]

Homework Statement

So I'm doing an experiment at uni which I have to find out the specific heat capacity of given small solid cylinder. We are given an insulated canister(a dewar flask) standing on a scale where we have to pour Liquid Nitrogen(hereafter will be referred as LN2) in. A cork with a hole in the middle is provided to prevent any more energy loss to the surrounding. After a few minutes of measuring the background boil-off of the LN2 we lower in the cylindrical shape material through the hole of the cork and letting it rest at the bottom of the flask and then keeps measuring the mass loss. The readings were done using a datalogger. Essentially we were finding out the relationship between the rate of mass loss of LN2 against the time (t). For most part of the experiment we obtain a graph that looks like this.

As you can see for the first 125s we were letting the LN2 to boil-off to get the background reading and the spike happens when we lower the cylindrical solid into the flask.

Homework Equations

My question is that why is there a small(but significant) discrepancy between the two linear gradient in the beginning and the end. When we lowered the solid we made sure to leave it in there for quite a long time to make sure that the whole system (i.e. the flask and the solids) reaches thermal equilibrium. It seems like a there exists a systematic perturbation/error that is causing the discrepancy of the 2 gradients. If the whole system reaches thermal equilibrium, shouldn't the gradient of those 2 linear lines be the same? The vicinity of the work space was pretty much isolated and we made sure that the solids weren't hanging in the middle of the LN2 to get rid of the buoyancy force or small oscillations/vibrations that might occur otherwise.

The Attempt at a Solution

Everything else is pretty much the same and nothing's changed in the system except the mass of the whole system before and after the solid was lowered, so I can't think of any systematic error that's causing this. So now I'm wondering if the rate of mass loss of LN2 is affected by its whole mass? If so how would one instigate an experiment to investigate the relationship between the mass and the rate of mass loss of LN2? I have not yet found any literature that explains this.

 

[Merlin3189]

First I don't think there's any "mass" effect as such, but I can see a possible reason for the change in slope.
You just have to ask yourself, what has changed? And consider how these changes could affect the rate of evaporation.
The total mass has changed, but how could that affect rate of evaporation?

Or start from the other end and ask why/how the N2 evaporates and what factors affect that. Then see if any of them have changed.

 

[Merlin3189]

...The total mass has changed since the beginning until after the solid was dropped and nothing else has change and that was the exact question that I was asking which was I don't understand how the change of total mass could affect rate of evaporation.
Since there are no external factors such as wind or sunlight that might produce any extra energy nor was there a change of humidity in the system. The only thing that I could think of now is that after the boil-off and decrease of the total mass temperature of the system has increased slightly(or not, since it should be boiling at its boiling point which should be a constant temperature) and that somehow affects the rate of evaporation? Or it could be that due to the loss of mass the surface area of the N2 as a whole has decreased, and that in turn decreases the rate of evaporation(which would probably be more likely since I know that the surface area of the substances affects its evaporation rate). On a second thought the area that will be exposed to air will still be the same though since the loss of mass would just cause the high of the N2 decrease in the flask unless we are talking about the surface area that is in contact with the flask AND the air above it?

Is there a way to instigate an experiment for this particular case to find out if the loss of mass(which causes the loss of surface area) is slowing down the rate of evaporation? Thanks in advance in hindsight your comments made me think some more.

Sorry you feel my comments are unhelpful. They probably were! I'm just trying to follow the PF guidelines and ask questions rather than give answers..

"The total mass has changed since the beginning until after the solid was dropped and nothing else has change..."
I disagree with this. I agree we should ignore "... external factors such as wind or sunlight .. change of humidity" and consider only changes in the vessel itself. But if the mass has changed, there is at least the possibility that something else has changed. (*But see below)

"...the surface area of the N2 as a whole has decreased,..." This could be true (or the opposite could be true) IF the flask were not a uniform cylinder inside. I am assuming it is a uniform cylinder, but this should be checked.
You might ask yourself, why does surface area affect the rate of evaporation? Is this reason applicable in this situation?

"Is there a way to instigate an experiment for this particular case to find out if the loss of mass(which causes the loss of surface area) is slowing down the rate of evaporation? " Well, if you started with 1360g of N2 and allowed it to evaporate down to 1341g you could compare the slope at the beginnig with the slope at the end. If there is a "mass effect" then thie graph should gradually change slope.

* Note - I started this calculation to try to confirm my idea above that something else had changed. But it leads me to think I was wrong!
In your first 120 sec only about 2g of N2 was lost. You appear to have added about 16g with your cylinder, then rapidly boiled off about 9g more of N2. You now have 11g less N2 than you started with, but have added 16g of some other material - probably a copper rod. I could check what it was made of, by calculating the energy required to boil off the extra N2 and comparing it with the energy required to cool the rod from room temp to the BP of N2 for different metals.
I was hoping this would show me another change, but in fact it shows a change, but in the opposite direction to what I expected! So I may be wrong..

Ultimately, what is it that is making the N2 boil?

 

[Chestermiller]

The hard part is understanding how the slope is less than the initial slope.

 

[kuruman]

The hard part is understanding how the slope is less than the initial slope.

One explanation is because the level of the liquid has dropped because of the evaporation. I would guess that the major source of heat loss is through conduction along the walls from the top of the container at room temperature to the surface at 77 K. When the level drops, the temperature gradient is less steep meaning less heat transfer per unit time.

 

[Dazzabaijan]

Sorry you feel my comments are unhelpful. They probably were! I'm just trying to follow the PF guidelines and ask questions rather than give answers..

"The total mass has changed since the beginning until after the solid was dropped and nothing else has change..."
I disagree with this. I agree we should ignore "... external factors such as wind or sunlight .. change of humidity" and consider only changes in the vessel itself. But if the mass has changed, there is at least the possibility that something else has changed. (*But see below)

"...the surface area of the N2 as a whole has decreased,..." This could be true (or the opposite could be true) IF the flask were not a uniform cylinder inside. I am assuming it is a uniform cylinder, but this should be checked.
You might ask yourself, why does surface area affect the rate of evaporation? Is this reason applicable in this situation?

"Is there a way to instigate an experiment for this particular case to find out if the loss of mass(which causes the loss of surface area) is slowing down the rate of evaporation? " Well, if you started with 1360g of N2 and allowed it to evaporate down to 1341g you could compare the slope at the beginnig with the slope at the end. If there is a "mass effect" then thie graph should gradually change slope.

* Note - I started this calculation to try to confirm my idea above that something else had changed. But it leads me to think I was wrong!
In your first 120 sec only about 2g of N2 was lost. You appear to have added about 16g with your cylinder, then rapidly boiled off about 9g more of N2. You now have 11g less N2 than you started with, but have added 16g of some other material - probably a copper rod. I could check what it was made of, by calculating the energy required to boil off the extra N2 and comparing it with the energy required to cool the rod from room temp to the BP of N2 for different metals.
I was hoping this would show me another change, but in fact it shows a change, but in the opposite direction to what I expected! So I may be wrong..

Ultimately, what is it that is making the N2 boil?

Hi first of all thank you for being so patient with me and I understand the POV you're coming from.

"But if the mass has changed, there is at least the possibility that something else has changed."
From this statement I can only assume that you mean that evidently the volume has increased too?Unless you mean that the density of the system as a whole has increased?I understood that denser liquid has a slower evaporation rate, but I'm not sure if you could put a solid(aluminium in this case) in N2 and treat it as a denser liquid as a whole whereby the evaporation rate is then decreased.

"This could be true (or the opposite could be true) IF the flask were not a uniform cylinder inside. I am assuming it is a uniform cylinder, but this should be checked. You might ask yourself, why does surface area affect the rate of evaporation? Is this reason applicable in this situation?"
The flask was a uniform cylinder and the inside sure looked cylindrical to me!(need to confirm that). I don't think the surface area loss of surface area argument would be applicable in this situation since the increase of surface area means more area is exposed to air, allowing liquid nitrogen to acquire more heat energy from the surroundings and thus increase the rate of evaporation since there's more rapid movement of the nitrogen molecules which helps them overcome the force of attraction and hence evaporates. However, assuming the inside of the flask is a uniform cylinder of $V = \pi r^2 h$; since only the top side of the circular area is exposed to air i.e. it leads to the opening, and a decrease of mass would just be reducing the height $h$ of the N2 inside the flask and not necessarily decreasing the surface area for which it is exposed to the air! Am I right in saying this which means the surface area of the N2 doesn't play a role here?

"Note - I started this calculation to try to confirm my idea above that something else had changed. But it leads me to think I was wrong!
In your first 120 sec only about 2g of N2 was lost. You appear to have added about 16g with your cylinder, then rapidly boiled off about 9g more of N2. You now have 11g less N2 than you started with, but have added 16g of some other material - probably a copper rod. I could check what it was made of, by calculating the energy required to boil off the extra N2 and comparing it with the energy required to cool the rod from room temp to the BP of N2 for different metals."
To give you some specific numbers the mass starts of with 1342.99g, when the Aluminium cylindrical solid with a mass of 17.78g was added the mass first peaked to 1358.65g, and it finishes at 1348.76g at 362.88s. I did the same experiment on Copper, Lead, Graphite and Rock Salt and also repeated all of them at the temperature of dry-ice(cooling them with dry ice).

"Ultimately, what is it that is making the N2 boil?"
Heat energy given by air molecules that are exposed to the N2 so the N2 molecules have enough energy to escape?

 

[Dazzabaijan]

The hard part is understanding how the slope is less than the initial slope.

Hopefully you can offer some insight from the discussion above. Thanks in advance!

 

[Chestermiller]

One explanation is because the level of the liquid has dropped because of the evaporation. I would guess that the major source of heat loss is through conduction along the walls from the top of the container at room temperature to the surface at 77 K. When the level drops, the temperature gradient is less steep meaning less heat transfer per unit time.

I think you are onto something here with regard to the liquid level. However, in my judgment, the heat flow from outside into the liquid is more likely radially through the wall than axially along the wall to the top. Even though the heat flux (per unit surface area) will be unchanged below the liquid surface, the available heat transfer area is reduced when the liquid level is lower. So the overall heat flow to the liquid will be lower.

A way to check this experimentally is to fill the container to different levels (without dropping the metal object in), and measure the rate of weight loss as a function of the liquid level.

 

[kuruman]

A way to check this experimentally is to fill the container to different levels (without dropping the metal object in), and measure the rate of weight loss as a function of the liquid level.

OP mentions a dewar flask. The space between the inner and outer walls are evacuated, possibly super-insulated and silvered to minimize convective and radiative losses. But you're right about checking this experimentally by measuring boiling rate as a function of level. As an aside I was amused to see the change to an almost infinite slope at about 160 s just before the liquid settles down to the equilibrium boiling rate. Anyone who has dumped an object at room temperature in LN2 cannot help but notice that the liquid suddenly starts boiling very rapidly just before settling down. This effect in more noticeable when the object has relatively good thermal conductivity (piece of copper as opposed to a banana). I think it has to do with how the heat gets out of the metal as a function of time, but I have not really tried to model it mathematically.

 

[Merlin3189]

Since people have now just told OP an answer, I'll admit that I wanted him to realize that not just the mass changed, but the volume and hence the level in the flask changed. And also that the key to evaporation is how much heat gets to the liquid.

Interestingly the level does not change in the way I first imagined - the level rising due to the added object. It appears that the heat added by the metal boils off a greater volume of N2 than its own volume. From some rough calculations, lead boils off about 130% of its volume, iron about 360%, with both gold and aluminium being (surprisingly) about the same at 250%. This based on their starting at about 20^oC. You could of course reduce these values by pre-cooling the cylinder.
The calculation for the specific heat of the cylinder came to 460 J/kgK so I revise my guess at copper and say it was iron, about 2cm3.

FWIW I favour kuruman's conduction down the glass wall rather than Chester's conduction & radiation through the near vacuum. I'm not sure the simple experiment measuring loss from full to near empty will distinguish, as , I think, heat flow varies linearly with depth in both cases.

Maybe the Dewar could be held inside another bigger flask of N2 to keep the lower part of the outside wall at the same temperature as the inner and remove Chester's route? It would also change kurumans route, but still might allow that to vary with depth.

 

[Dazzabaijan]

I just want to thank you all for the help and it made me think a lot about my experiment.