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The molar mass of helium and the superfluidity phenomenon

The molar mass of helium : fundamental chemical conceptions and physical properties

Let us use the periodic table, which indicates the relative atomic masses of chemical elements. Hence, the relative atomic mass of hydrogen (Mr) is 1, whereas for helium Mr = 4. Helium is an inert monatomic gas, so M (He) = 10-3*Mr (He) kg/mol = 10-3*4 kg/mol = 0,004 kg/mol. Where do we begin when we are to speak about helium? Right, with the molar mass of helium. It is a well-known fact that this inert gas is the most stubborn of all gases. Its atoms in no circumstances do not want to engage with one another or with atoms of other elements. Exactly the obstinate unwillingness of helium atoms to interact explains why this gas was the last, which yielded to chemists’ efforts and succumbed to liquefaction (helium has the known lowest critical temperature T = 5.25 K). But the gas keeps its stubbornness even in the liquid state, thus becoming the only substance that does not solidify at absolute zero (scientists managed to get solid helium only at a pressure of 25 atmospheres). It is this transcendent state with the temperature below 2.17 K that allows helium to acquire amazing properties and become superfluid – in other words, it loses viscosity and is able to flow even through the thinnest capillaries with virtually no friction.

The fruitfulness of the classical model of electric current makes it quite useful in the present time – doing a PowerPoint presentation related to this topic might be a very good idea. It is this model that so efficiently reveals the relationship between the phenomena of superconductivity and superfluidity as well as peculiarities of their nature. However, scientists usually talk about electron gas in the conductor, while superfluid helium is considered to be liquid. With all this going on, it is possible to dispute the latter statement. Practically all evidence indicate that superfluid helium is an actual gas, so here the analogy with electron gas is complete and holistic. Let us begin with the fact that in all gases viscosity decreases with the temperature from the law η ~ T ½, as opposed to liquids. That is why many scientists used to associate temperature increase with the resistance of metals: naturally, the viscosity of electron gas grows as temperature increases. It is easy to see that this theory also predicted the complete disappearance of the resistance point near absolute zero, T = 0 K. Therefore, it is adequate to assume that when helium is cooled below 2.17 K this critical temperature makes molecules shift to the superfluid state at the expense of becoming a gas, which has almost zero viscosity η under such conditions.

The molar mass of helium and the phenomenon of superfluidity: the modern state of the problem

Physicists are used to repeating that the transition of helium to the superfluid state fundamentally differs from ordinary phase transitions, such as liquid – gas (boiling), liquid – solid body (crystallization), etc., which are accompanied by the release or absorption of certain amounts of heat. Such processes are called phase transitions of the first kind (you can easily find a load of courseworks describing the phenomenon of phase transitions). A shift from He (I) to He (II) that does not produce heat is called a phase transition of the second kind. But here we are confronted by a mistake: the transition of helium to the superfluid state requires a withdrawal of a certain standard amount of heat and the same amount of heat is necessary for returning of helium back to normal. Physics missed the fact of this truly hidden heat of transition, mostly because they were accustomed to deal with phase transitions where the heat is transferred at a constant temperature (also, one should remember about the molar mass of helium ). Thus, the temperature of ice in a melting state will not make a move from the point of 0 ºC until it does not finish absorption of all the heat of fusion. And if we were to draw a curve of the heat capacity of water, we would portray a very sharp peak (a so-called delta-function) at the melting point of ice apart from a specific heat jump. Such a peak would correspond to an infinite heat capacity because the input of heat in the melting point does not increase temperature per se.

As we may well expect, the heat capacity of helium at the transition point also tends to infinity creating the usual phase transitions peak. This peak is slightly blurred, which indicates the extendedness of the phase transition; however, it is clearly transition of the first kind followed by the transfer of heat. The amount of heat (q) equals the area (S) within a narrow temperature band at the transition point. These “fuzzy” phase transitions actually exist, especially in the complex two-phase systems. Thus, previously we have considered an anomalous behavior of water density near the melting point, which is also presumably associated with the melting of ice crystals suspended in water. The same, obviously, serves as a reason for another anomaly of water. Its heat capacity does not grow as the temperature increases, which is characteristic of all liquids, but falls until it reaches a minimum at 40 ºC, and only after reaching this point it begins to grow (it is believed that exactly this behavior of water, which has nothing to do with the molar mass of helium, sets the standard body temperature of warm-blooded animals). Abnormally high heat capacity of water and its decline in the range from 0 to 40 ºC can be attributed to the melting of heavy ice crystals, which need a supply of additional heat (80 cal/g). And it is this excessive amount of heat (0.14 cal/g), which is represented by a segment of the area under the left branch of the heat capacity curve, that exactly equals to the melting heat of heavy-isotope ice contained in the water. 0.0018 g of heavy-isotope ice H218O contained in 1 g of water is capable of absorbing exactly this amount of heat: 0.14 cal = (80 cal/g) × (0,0018 g). It turns out that water without isotopes would have normal appearance of both the curve of density and the curve of heat capacity.

It is interesting that water and superfluid helium have in common this very rare quality to reduce the volume when heated. Note the molar mass of helium and that natural helium also contains the isotope – 3He being in an amount from about 10-4 to 10-8% – however, 3He is light, as opposed to heavy 18O in water. Hence, the transition of helium to the superfluid state may well be a simple phase transition with the heat taken away. Probably, monohydric helium forms two and polyatomic molecules He2 and Hen at a low temperature. And at this temperature below 2.17 K, it is energetically more favorable for He to form the polyatomic gas than the monatomic liquid. Therefore, changing from liquid to gas, helium does not absorb but release heat, which must be taken. And, indeed, sole helium still forms diatomic molecules sometimes. Thus, it was possible to identify ions He2+ in discharges. Moreover, the transition of 3He to the superfluid state is said to be possible only if its atoms confluence into pairs like electrons in a superconductor. But, most likely, helium atoms do not fuse in pairs but form giant complexes with thousands and tens of thousands of atoms. It is, in fact, no longer a molecule; now we can deem them microcrystals that do not have a fixed number of atoms and move like Brownian particles, the team of which behave like a gas of high molecular weight. The size of these crystals should be around ten widths of an atom of helium – that is, about 10 nm, or 1 Å. So, as far as we can conclude, helium still goes into the solid state (and this is what the heat output is associated with), but behaves like a gas at the same time, since thermal motion and weak links between inert helium atoms prevent a buildup of crystals and their agglomerations. The result is a cross between a gas and a crystal: “ice gas” or spray of crystals, something like powdery snow or ice vapor. That is the main and most important reason for the similarity of properties of helium and water that contains micro-crystals of ice. Students should try writing an argumentative essay built on similar methods of adducing evidence.

Molar mass of helium : the historical background and relevancy of unique characteristics

But how could physics have confused a gas and a liquid? It is quite possible with helium. Usually, one just rarely observes gases in an environment where a gas really should resemble a liquid. Due to its low temperature, the molecules will have speed so negligible that it would be insufficient even for overcoming the force of gravity and departing from the container. Such a gas will not have a major feature of all gases – it would not be able to fill the entire volume, accumulating instead, like a liquid, on the bottom of the vessel. That is why He (II) looks like a liquid near absolute zero: it can be poured out of a glass into another glass, it flows like a liquid, and even has a noticeable interfacial area due to the visible refractive index (density 146 kg/m3). At the same time, liquid helium He (I) is strongly reminiscent of a gas. The fluid is so clear and light (its density is ten times less than that of water) that you question yourself instantly – should a gas look like this? But superfluid helium He (II) is a cross between a gas and a solid body and it should resemble a liquid.

Let us overlook several specific properties of superfluid He and see how they can be explained from the position of contemporary physics. In addition, students may use the abovementioned phenomena for writing a critical essay :

  • If superfluid helium is a gas, then all its “strangeness” will find a simple and natural explanation. It is well known that if a tube with superfluid helium is immersed in a vessel then difference levels will gradually have been aligned after a short period of time. Typically, this can be explained by the formation of a thin film on the surface of the helium test tube, in which helium flows according to the siphon principle. But even without that helium can easily flow from a test tube into the surrounding liquid and back, since glass tubes are not perfect and always have a lot of defects and micro-cracks, which subtlety serves an insurmountable obstacle for all liquids and gases, except for superfluid helium. Remembering the molar mass of helium it is no wonder that the helium leakage rate depends not on the length of the illusory film, but only on the number of glass defects, that is, cracks and scratches. Similarly, we found that superfluid helium easily passes through the walls of a ceramic vessel, dribbling through its finest pores.
  • Mechano Thermal effect is especially interesting. If two vessels filled with superfluid helium to different heights are connected by a tube coated with emery powder, then leveling the temperature will grow in the vessel from which helium leaves, and will decrease in the one into which it flows. This is usually attributed to the fact that, supposedly, only the superfluid component of helium flows through the tube and it does not carry the heat. In these two cases, theorists contradict themselves because a great thermal conductivity of helium is associated exactly with the superfluid component, which ensures ultra-fast transfer of heat. Such inconsistency is typical for the whole of quantum physics and there is no dissertation methodology that can do without such overlaps.
  • There exists also thermomechanical effect. In case of the latter, the heating of one of the two vessels connected by a filter leads, on the contrary, to an influx of superfluid helium into the heated vessel. This happens because of the molar mass of helium as well as because heated helium that has higher viscosity hardly flows to the filter while helium from the cold vessel can easily pass through the capillaries into the heated vessel due to low viscosity. In case of a strong heating of the vessel, the influx of superfluid helium is so strong that a helium fountain begins spurting from the nozzle.

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