What efforts has mankind made to approach the low temperature limit?

Every summer, people living in hot environments always try various ways to cool down. As ordinary people, we use fans, air conditioners, cold drinks and other tools to bring ourselves coolness in the summer.

For humans, 26 degrees Celsius is already a very comfortable temperature, but this is not the case for scientists. Scientists have been trying to explore how to approach the low temperature limit. So, how low can humans create the lowest temperature, and how can it be achieved?

Heat conduction cooling

When it comes to cooling down, the most direct way we can think of is to get some ice . Yes, this is also the most common way in our lives, such as a glass of iced Americano or ice compress.

Image source network

So why can ice cubes cool things down? This involves the concept of heat conduction that we learned in middle school.

There are three ways of heat transfer: heat conduction, heat convection and heat radiation.

Three ways of heat transfer | Image source network

Heat conduction means that when two objects with different temperatures come into contact, heat will flow from the high-temperature object to the low-temperature object. It mainly comes from the vibration of molecular atoms in solids. For example, we use ice cubes to cool down and use hot packs to keep warm.

Convection is the main way of heat transfer in gas or liquid, which can be divided into natural convection and forced convection . Natural convection is the spontaneous convection process, such as the mixing of hot and cold water; forced convection is the convection caused by external forces, such as when we use a hair dryer.

Thermal radiation is the transfer of heat in the form of electromagnetic waves. For example, when we bask in the sun, the sun's energy is transferred to us in the form of thermal radiation.

So the question is, where does the ice come from in such a hot day?

The simplest way is to freeze it in the refrigerator . The refrigeration principles of the refrigeration equipment commonly used in our lives, refrigerators and air conditioners, are similar, both of which are thermodynamic cycle processes.

Thermodynamic cycle refrigeration

The definition of a cyclic process in thermodynamics is " the entire process of a system starting from a certain equilibrium state, going through an arbitrary series of processes and returning to the original equilibrium state is called a cyclic process ."

On the pV diagram, the cycle process in the clockwise direction is a positive cycle . The heat engine performs a positive cycle, that is, the working substance absorbs heat from the high-temperature heat source, part of the increased internal energy is used to do work, and part is transferred to the outside through the low-temperature heat source.

The process that proceeds in the counterclockwise direction is called a reverse cycle . The refrigerator performs a reverse cycle process, that is, the outside world does work on the system, causing the working substance to absorb heat from the low-temperature heat source, thereby lowering the temperature of the low-temperature heat source to a lower level and achieving the purpose of refrigeration.

With these basic understandings, let's look at the working principle of the refrigerator:

Schematic diagram of the working principle of a refrigerator. | Source: Reference [1]

After being compressed by the compressor , the working substance (usually high-temperature and high-pressure gas) releases heat at the condenser and becomes a high-pressure liquid. The high-pressure liquid passes through the throttling expansion valve and its pressure is reduced, becoming a low-pressure liquid. It enters the evaporator, absorbs heat from the freezer compartment to lower the temperature of the freezer compartment , and heats up itself to become a gas and enter the next cycle, thereby achieving the refrigeration effect of the freezer compartment.

The refrigeration principle of air conditioners is similar. The difference is that there is an electromagnetic reversing valve inside the air conditioner, which can change the flow direction of the working substance, so that cooling can be achieved in summer and heating in winter.

Schematic diagram of the air conditioner principle. | Source: Reference [1]

However, these refrigeration methods can only meet our actual life needs. The temperature required in the laboratory is much lower than these temperatures. The extreme temperature pursued by the laboratory is absolute zero . Although the third law of thermodynamics tells us that absolute zero is impossible to achieve , scientists are also approaching it step by step.

Evaporative cooling

The most common refrigeration methods in laboratories are liquid nitrogen and liquid helium.

In high school physics, we learned about phase diagrams, in which we can see that under high pressure and low temperature, gas can be compressed into liquid. Therefore, liquid helium and liquid nitrogen can provide a low temperature environment.

Phase diagram | Image source network

In 1900, the International Temperature Scale stipulated that the thermodynamic temperature scale is the basic temperature scale. Thermodynamic temperature is represented by T, the unit is Kelvin, and the symbol is K. Celsius temperature is represented by the symbol t, the unit is Celsius, and the symbol is ℃. The relationship between Celsius temperature and thermodynamic temperature is:

t=T-273.15

Nitrogen was first liquefied by Polish physicists Zygmunt Wróblewski and Karol Olszewski in 1883. Helium was liquefied by Dutch physicist Onnes in 1908, and it was also the last gas to be liquefied. The emergence of liquid helium prepared the conditions for the discovery of superconductivity.

The boiling point of liquid nitrogen is about -196℃, which is 77K, and the boiling point of liquid helium is 4.2K.

Since liquid nitrogen and liquid helium have very low temperatures and are extremely volatile at room temperature, it is necessary to minimize the heat exchange between them and the air when storing them, which requires them to be stored in special containers.

The container for storing liquid nitrogen and liquid helium in the laboratory is a Dewar , which was invented by Dewar in 1892 and has a good thermal insulation effect. There is a vacuum interlayer between the two walls of the Dewar flask. The existence of the vacuum interlayer reduces the molecular thermal motion, thereby effectively preventing heat loss.

After helium is liquefied, using the evaporation of helium for refrigeration is the main means to achieve low temperatures.

Helium has two isotopes: ³He and ⁴He. The main component of helium on Earth is ⁴He, and the ³He content in the atmosphere is only one millionth of the ⁴He content.

According to the relationship between saturated vapor pressure and temperature, evaporative cooling can be achieved. ⁴He evaporative cooling can achieve a low temperature of 1K , but because ⁴He has a superfluidity phenomenon at extremely low temperatures, that is, at extremely low temperatures, ⁴He will form a layer of liquid film that climbs up along the container wall, which will cause evaporation and heat leakage , limiting the lowest temperature that ⁴He evaporative cooling can reach.

However, ³He does not have this problem. In addition, under the same saturated vapor pressure, the temperature of ³He is lower than that of ⁴He. Therefore, using ³He evaporation cooling can achieve lower temperatures. The lowest temperature can reach 200-300mK.

Conventionally, people refer to environments below 1K or below 300mK as ultra-low temperatures . In other words, an ultra-low temperature environment is an environment that cannot be simply achieved by evaporating helium-4 for refrigeration. Therefore, in order to obtain ultra-low temperature experimental conditions, other cryogenic technologies and methods are required.

Dilution Refrigeration

What should we do if we want to obtain temperatures in the mK range? In 1965-1966, a ³He dilution refrigeration technology was developed, which is a refrigeration technology with strong refrigeration capacity and long continuous working time. The concept of dilution refrigeration was proposed in 1951 and realized in 1965. Mature commercial dilution refrigerators did not appear until the 1970s.

³He-⁴He solution phase diagram. | Source: Reference [3]

What is the principle of dilution refrigeration? It is simple.

Experiments have found that He-He has phase separation at extremely low temperatures, which can also be seen from the He-He solution phase diagram. In the phase separation region, the solution is divided into a concentrated He phase and a dilute He phase. Since He atoms are lighter, the concentrated He phase is distributed on the top, and there is a clear interface between the two phases. However, it can also be seen from the phase diagram that even at absolute zero, there is still a certain amount of He in the dilute phase, which is also the key to dilution refrigeration.

The understanding of the principle of dilution refrigeration can be compared to evaporative refrigeration.

In the dilute phase, the superfluid He is completely ordered, and the movement of He in it is completely unimpeded. Therefore, for He atoms, the He solution can be regarded as a **"vacuum" state**, and the penetration of He from the dense phase to the dilute phase can be regarded as the "evaporation" of He liquid. The "evaporation" process absorbs heat , so the temperature of the He dense phase can be lowered even further .

Using the He dilution refrigeration method, the temperature can be reduced to a few mK, greatly improving the ability to obtain low temperatures.

But what should we do if we want to lower the temperature further to below 1mK?

Nuclear adiabatic demagnetization refrigeration

In 1934, Gorter and in 1935, Kurti independently proposed adiabatic demagnetization refrigeration methods based on nuclear spin .

Nuclear adiabatic demagnetization refrigeration uses the fact that the entropy of a magnetic moment system can be controlled by both temperature and external magnetic field . Its principle is also very simple.

Schematic diagram of the principle of nuclear adiabatic demagnetization refrigeration. | Source: Reference [2]

In the initial state , when the external magnetic field is zero, the magnetic moment arrangement of the refrigerant is disordered . Keeping the temperature unchanged and increasing the magnetic field can make the arrangement of the magnetic moments tend to be consistent (this is a simple phase change process, which can be compared to the process of water freezing into ice at low temperature, from disorder to order). This is a process of entropy reduction and the temperature of the system decreases .

Next, the magnetic field is reduced under adiabatic conditions , and the refrigerant absorbs heat from the surrounding environment and becomes disordered again , thereby further reducing the ambient temperature , thus achieving the purpose of nuclear adiabatic demagnetization refrigeration. Using this method, the temperature can be reduced to the order of tens of μK.

The liquefaction of helium can reduce the temperature from 300K at room temperature to 4.2K ;

By using evaporative cooling of He, a low temperature of 1K can be achieved;

By using evaporative cooling of ³He, a low temperature of 300mK can be achieved;

Using a ³He dilution refrigerator, a low temperature of 2mK can be achieved;

Nuclear adiabatic demagnetization refrigeration can reduce the temperature of macroscopic objects to the order of 10μK ;

From room temperature to nuclear adiabatic demagnetization refrigeration , the temperature has leaped by 7 orders of magnitude , reaching the macroscopic refrigeration limit of human beings.

Every leap forward in low-temperature physics promotes the development of basic disciplines and the progress of human society. In the process of moving towards lower temperatures, we have already broken through the boundaries set by nature.

References

[1] Huang Shuqing, Thermodynamics Course (Second Edition), Higher Education Press

[2] Lin Xi, “Nuclear Adiabatic Demagnetization Refrigeration”, Physics, Vol. 52 (2023), No. 8

[3] Yan Shousheng, “Dilution Refrigeration: A New Method for Achieving Extremely Low Temperatures”, Physics, 1975, 4(2)

Planning and production

Source: Institute of Physics, Chinese Academy of Sciences (ID: cas-iop)

Author: Abai

Editor: He Tong

Proofread by Xu Lailinlin