PHAS0008 “Practical Skills 1P”

Experiment T8: Specific Latent Heat of Liquid Nitrogen

(4 Sessions)

Experimental Objectives

To determine the specific latent heat of vaporisation of liquid nitrogen. This quantity is also known as the specific enthalpy change on vaporisation.

To determine the specific latent heat of melting of water and/or heavy water ice.

Relevant Lecture Course

•   Thermal Physics and the Properties of Matter (PHAS0006)

Potential Hazard: Latent Heat of Liquid Nitrogen

•    Nitrogen is non-flammable and weighs approximately the same as air. Inhalation of a Nitrogen enriched atmosphere (ie: loss of oxygen) may cause dizziness, drowsiness, nausea, vomiting, excess salivation, diminished mental alertness, loss of

consciousness, and ultimately: death.

•    Freeze burns from spilled liquid nitrogen that leaves the dewar or the equipment, for example when retrieving samples.

Existing Control Measures

•    Prevent unauthorized people having access to areas used for delivering, storing, dispensing and using liquid nitrogen.

•    Avoid direct skin contact with items which recently been in proximity of liquid nitrogen, by using insulated gloves or tongs.

•   Oxygen depletion monitors are situated around the laboratories, and will detect the amount of Liquid Nitrogen build up in the laboratories.

•    Latent Heat of Liquid Nitrogen. Technician or qualified demonstrator for the use of liquid nitrogen, distributes the Liquid Nitrogen.

•    Users are required to wear Safety Glasses at all time when using the nitrogen.

•   Only persons fully trained in the use of cryogenic liquids may use the LN2

•    The container of the Liquid Nitrogen is covered once the nitrogen has been applied.

•    The wiring of the circuit for experiments involving the use of Liquid Nitrogen is  checked by the Technician and Demonstrator before being allowed to continue.

•   Supervision from Technician and Demonstrators regarding Health and Safety.

•   Safety guidelines are adhered to at all times.

•    No Lone working permitted at any time.

Risk Level with existing controls

Low/Tolerable

Safety Note: Use of Liquid Nitrogen

Please read this Safety Services policy:

• https://www.ucl.ac.uk/safety-services/policies/2022/dec/liquid-nitrogen

This experiment uses a small amount of liquid nitrogen. There is no reason for you come into contact with the liquid nitrogen, however if you do there is a possibility that the

extreme low temperature of the liquid may cold burn you. To avoid accidents you should take the following precautions.

•    Use the safety spectacles provided while performing the experiment.

•    Remove rings. If liquid nitrogen falls on your hands it could be trapped behind a ring and this could result in burning.

•   On finishing the experiment, ask the technician to return the unused liquid to the storage vessel.

Should you come into contact with the liquid, please note that small splashes of liquid nitrogen on your skin will not harm you. However, exposure to the liquid for more than 3 or 4 seconds may cause cold burns. If this should happen for any reason, call the lab    technician for help and take steps to get the liquid away from your skin. If possible run  cold water over the affected region.

Please note that on evaporation, one litre of liquid nitrogen will produce around 700 litres of gas.

1. Introduction

The term “latent heat” was first used by Joseph Black in a posthumous work, Lectures on the Elements of Chemistry, published in 1803, but describing experiments done 40 years  earlier [1, 2]. The term was first applied to the heat required to vaporise a liquid, but a similar effect is encountered when going from solid to liquid. The modern definition of the specific latent heat of vaporisation, as given, for example, in Chambers’ Dictionary of Science and Technology [3], is “The heat required to change the state of unit mass of a substance from solid to liquid, or from liquid to gas, without change of temperature.

Most substances have a latent heat of fusion and latent heat of vaporization. The specific latent heat is the difference in enthalpies of the substance in its two states. Unit J kg-1”.  In Black’s day, the latent heat was quantified by comparing the time taken to boil a vessel of water dry, with the time taken to bring it to boiling point, assuming a constant rate of heat flow. Nowadays we have more accurate ways of measuring the heat input.

Latent heat is a key quantity in many natural and industrial processes, for example in temperature regulation and engine performance. It also plays a central role in atmospheric, oceanic and climate stability and modelling. [4-6]

2. Background and Theory

Nitrogen and other inert gases, such as helium and propane (C3 H8), can be liquefied by    compression/expansion cycles at around 30 bar and exploitation of the Joule-Thompson effect [see PHAS0006 and 7]. The boiling points of He, H2, N2  and C3 H8 at atmospheric pressure are 4.21, 20.27, 77.35 and 231.1 K respectively.

Liquefied gases used in experiments are kept in dewars (named after their inventor Sir James Dewar, the first person to liquefy hydrogen). These are flasks with a double wall of glass, separated by a vacuum, which are used to thermally insulate materials so as to keep them either hot or cold. Dewars insulate the liquid from nearly all sources of ambient heat in the laboratory, but are not 100% efficient. A quantity of liquid nitrogen in a dewar, assumed to be at 77K (the boiling point of N2) [8], will slowly boil away due  to background heat.

The rate at which the liquid loses mass is proportional to the rate of influx of background heat:

(1)

where L is the specific latent heat of vaporisation and Q  = mL [9]. If we supply additional heat, the rate of mass loss will increase:

(2)

Hence, even if we don’t know the background rate of heat fIow, as Iong as we do know the additional rate we can calculate L from the difference between the two rates of mass loss - in other words, by subtracting equation 1 from equation 2:

(3)

and hence;

(4)

Make sure you understand what is meant by the latent heat of vaporisation and latent heat of fusion of a substance, and how they differ from heat capacity.

3.  The Experiment

In this experiment the additional heat will be supplied by a resistor in which a current is flowing. According to electrical theory, a resistor, across which there is a potential

difference V, and in which a current I is flowing, dissipates power (energy per unit time) according to the formula;

P = VI.                                                                      (5)

So, if all this power is absorbed by the liquid nitrogen as latent heat, equation 4 is then;

(6)

We therefore need to measure V, I, and the rates of mass loss with and without the current flowing.

Q3.1: Why might V and I fluctuate? Can this be controlled?

3.1 Equipment

The experimental set up (see Figure 1) is very simple: a dewar with a loose fitting polystyrene lid through which two wires lead to the resistor is placed on a weighing scale. The mass of the dewar and contents will decrease with time as the liquid nitrogen evaporates.

Q3.2: Why is the polystyrene lid loose?

Q3.3: What methods of heat transfer are relevant?

The diagram in figure 1 is useful, but whenever an electrical circuit is built as part of an experiment a circuit diagram should also be included.

The electrical circuit should supply about 10W of electrical power to the resistor.

Q3.4: What is the value of resistance of the resistor?

Q3.5: What I-V combination(s) will you use? Is there a reason for your choice?

3.2 Safety Note

Ask a member of technical staff to fill the dewar nearly to the brim with liquid nitrogen. It should weigh around 200 ± 20 g.

DO NOT TURN ON THE ELECTRIC POWER SUPPLY UNTIL THE RESISTOR IS IMMERSED IN NITROGEN – the resistor becomes very hot and needs to be in the liquid nitrogen before the power is turned on to prevent it from burning. It should remain in the same position  at all times, completely surrounded by liquid nitrogen (in both “background” and

“power-on” runs) and not in contact with the dewar.

Q3.6: How will you ensure that the resistor stays where you want it to be?

3.3 Experimental Procedure

In this experiment you will evaluate the rate of mass loss of the liquid nitrogen under two sets of circumstances: [1] with the power on (you can use more than one power

setting: is there an advantage in doing this?), and [2] with the power off (the

background rate). During these two data runs, you should control all other factors that might influence the mass loss rate. Think carefully about the following questions:

Q3.7: As the liquid boils off due to background heat alone, is the rate of mass loss likely to be constant?

Q3.8: Is there anything in the design of the equipment that might cause this rate to vary?

Q3.9: If you are not sure, can you find out experimentally?

Q3.10: If you think there will be variation, how can you limit the effect of such variation on the result of your experiment?

It is recommended that your first data run is done under background conditions only, and lasts long enough for you to observe any changes that occur as the liquid boils away.

N.B. Under normal background conditions, the liquid boils away quite slowly; it takes more than an hour for a full dewar to lose half its contents.

Devise an initial plan for your method, write it in your lab book and discuss with a demonstrator before proceeding.

Remember that when taking data you must also estimate the associated uncertainties at the same time - not as an afterthought.

After your initial background run, you should assess your data and decide whether your plan needs modification. The best way to do this is by drawing a graph of mass against   time immediately after finishing the run. What do you deduce from the graph?

Remember that the formula we are using to calculate L, namely (6), was based on combining together equations (1) and (2), which correspond to the “background” and “power-on” runs respectively.

Q3.11: There is an assumption underlying this; what is it?

In order to use (6), therefore, you must ensure that your values for the rate of mass loss under “background” and “power-on” conditions are consistent with this assumption.

When you draw up your experimental plan, you should also consider whether there is an advantage in measuring for more than one power input – please see equation 6.

4. Data Analysis

Plot a graph of the mass of liquid nitrogen versus time; determine dm/dt, together with its uncertainty, with power(s) on and off. When fitting the data to obtain the gradient (and intercept), you should also determine and comment on (reduced) X 2.

Using Equation 6, draw up an estimate for L and compare your answer with that found in the literature. [8]

At the end of your first set of measurements you should have:

•   Graphs of mass versus time;

•    Estimates of dm/dt with power on and off;

•   Values of V and I;

•   An estimate of L with an uncertainty estimate.

Q4.1:   How does your estimate for L compare with the published value in terms of its uncertainty?

If you conduct multiple runs at identical power, you may wish to consider whether it is appropriate to find an average value. Remember that we can only justify taking an average of two or more values if they were obtained under the same conditions. If you suspect that one of your values is more reliable than the others, you may choose this one as your final result as long as you can justify the choice. You cannot justify picking out a result simply because it is the nearest one to the accepted value!

You may wish to consider the average of the data points, include all data points from all  runs on a single graph or simply take the average of your values of L. It will be important to consider your uncertainties and whether the uncertainties affect how much weight should be given to any datum point.

As noted in section 3.3, you should also consider whether repeat runs at different power might help reduce the uncertainty in your measured value of L.

5. Discussion & Conclusions

If the uncertainties are large or your initial estimate for L is inconsistent with the published value, you may wish to consider some of the following:

•    Is your value of VI an accurate estimate of the power dissipated in the resistor?

•   What have you assumed about where this power goes? Is your assumption justified?

•   Are your mass readings accurate estimates of the quantity of liquid in the dewar?

•    Is the procedure you used to convert these mass readings to a rate of loss of mass reliable?

•   What factors govern the background rate of mass loss?

Given what you can and cannot control and measure, you may wish to repeat the experiment with the same procedure or modify the procedure to reduce your uncertainties. Discuss any major modifications with a demonstrator before proceeding since there are limits on what may be possible.

In your conclusions you should discuss whether any modifications you made resulted in an improved result; if you have had any further ideas for modification but do not have either the time or the resources to implement them, describe them in your write-up.

6. Extension Experiment: Specific latent heat of melting for water ice (H2O) and/or heavy water ice (D2O)

After completing the main experiments, you should design and conduct an experiment using your apparatus to measure the specific latent heat of melting of water ice (H2O)   and/or heavy water ice (D2O): would you expect the melting point and specific latent heat to be the same for the two different isotopic compositions?

For this extension experiment, you can use your balance and dewar, and a member of technical staff can provide you with a digital thermometer. On request, Derek Thomas will be able to give you water ice cubes and/or a single heavy water ice cube. You may

also use an IR Thermal Imaging camera which can be borrowed from Derek Thomas. Liquid water can be used as a medium of known heat capacity.

Please note that phase change materials, which release their latent heat on freezing, are currently extremely topical for renewable energy storage. [10, 11]

You will, of course, need to draw up a Risk Assessment for your experimental procedure: this MUST be approved by a member of staff before you conduct any measurements, and should include a description of how you will dispose of any samples once they have been used. The Material Safety Data Sheet (MSDS) for D2O is available on Moodle, and please see: https://www.ucl.ac.uk/safety-services/working-safely-chemicals

Safety Note: You must NOT place the resistor heater in water.

7. References

Notes:

• Please only quote these references if you have actually read and referred to them, and include relevant page numbers.

• The Digital Object Identifier (DOI), is a string of numbers, letters and symbols used to permanently identify an article or document and link to it on the web.

• The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique.

[1] “Joseph Black, carbon dioxide, latent heat, and the beginnings of the discovery of the respiratory gases”, JB West, Am. J. Physiol. Lung Cell Mol. Physiol., 306: L1057–L1063

(2014). DOI: 10.1152/ajplung.00020.2014

[2] “April 23, 1762:  Joseph Black and Latent Heat. Disappearing heat and the dog that did not bark”, R Williams, APS News 21 (2012).

https://www.aps.org/publications/apsnews/201204/physicshistory.cfm(Accessed 12/12/2022)

[3] “Chambers Dictionary of Science and Technology” 2nd editon. JM Lackie General  Editor. Edinburgh: Chambers (2007). ISBN : 9780550104571 (e-book). UCL username and password required for access.

[4] “Latent heat must be visible in climate communications”, T Matthews et al,  WIREs Climate Change, 13, e779 (2022).https://doi.org/10.1002/wcc.779

[5] “Factors of boreal summer latent heat flux variations over the tropical western North Pacific” . Y Wang and R Wu. Clim Dyn 57, 2753–2765 (2021).

https://doi.org/10.1007/s00382-021-05835-4

[6] “Sensible heat has significantly affected the global hydrological cycle over the historical period” . G Myhre, et al. Nat Commun 9, 1922 (2018).

https://doi.org/10.1038/s41467-018-04307-4

[7] “Liquefaction of gases”. WH Isalski, Thermopedia (2011). DOI:

10.1615/AtoZ.l.liquefaction  of  gases

[8] “Tables of Physical and Chemical Constants” 16th edition, originally compiled by G.W.C. Kaye and T.H. Laby; Longman, New York (1995). ISBN-13: 9780582226296.    Available at Kaye and Laby online:http://www.kayelaby.npl.co.uk/toc/

[9] “Physics for Scientists and Engineers” 9th edition, RA Serway and JW Jewett.

Australia: Brooks/Cole Cengage Learning (2014).  ISBN : 9781473711143 (e-book). UCL username and password required for access.

[10] “Phase change materials for thermal energy storage” . K Pielichowska & K Pielichowski, Progress in Materials Science 65, 67-123 (2014).

https://doi.org/10.1016/j.pmatsci.2014.03.005

[11] “Trimodal thermal energy storage material for renewable energy applications” . S Saher, S Johnston, R Esther-Kelvin, et al.  Nature 636, 622–626 (2024).

https://doi.org/10.1038/s41586-024-08214-1