What happens at Absolute Zero Temperature?

The Zeroth Law of Thermodynamics laid the foundation of the important thermodynamic property, “Temperature“. While absolute zero temperature is the lowest attainable temperature (theoretically) in thermodynamics. Absolute zero temperature is ‘0 K’ on the Kelvin Scale which is the absolute temperature scale.

Earlier in classical physics, scientists believed that all molecular motion ceases at absolute zero. But now quantum mechanics says, the matter at absolute zero temperature is at the ground state where it has the lowest internal energy. The energy of the ground state is called Zero-Point Energy. So there would be minimal particle energy at absolute zero temperature. But we can’t transfer this energy, i.e, nothing could be cooled or heated at that temperature. The reason is that the temperature of both the cooling agent and the substance being cooled gets the same.

We now try to understand this phenomenon by going a bit deeper into the subject. Since we know, the model of an ideal gas doesn’t allow the phase transition. The ideal gas does not change its phase down to 0 K. But the real gases change their phases at higher pressures and low temperatures. This change in phase brings in the enthalpy of vaporization (vapour to liquid) and enthalpy of fusion (liquid to solid) to the substance. Therefore, at absolute zero a real gas exceeds in terms of energy to an ideal gas. This means at absolute zero (which is impossible to achieve thermodynamically as discussed above) a real gas still has some energy. It is the lowest internal energy (ground state energy).

Other Temperature Scales

Besides the Ideal Gas Temperature scale, we have two of the most common temperature scales:

Fahrenheit Scale: America is one of the countries mostly using the Fahrenheit temperature scale. A German instrument maker Daniel Gabriel Fahrenheit made this scale. He actually borrowed the idea of the Romer scale, in which Romer took a reference of 7.5 degrees Romer, as the freezing point of water. The other reference point was 22.5 degrees Romer which he considered the body temperature of a healthy human being. Some modern-day scientists regard it as a bizarre idea to consider two different substances with two different reference points.

However, Daniel Fahrenheit multiplied both these numbers by 4 to get two new reference points as 30 and 90. Then revised these numbers later on to 32 degrees Fahrenheit as the freezing point of water and 96 degrees F as the normal body temperature. However, medical science says that the body temperature of a healthy person is 98.5 °F. That’s how the early age temperature scales worked.

Celsius Scale: Anders Celsius, a Swedish astronomer developed the celsius scale. He considered 0 °C as the freezing point of water and 100 °C as the boiling point. This scale was originally known as the centigrade scale. In Latin centum means 100 and gradus means steps. So the Celsius scale has hundred equally divided parts.

Why the Ideal Gas Thermometer with Absolute Zero Temperature is a better-defined scale?

The two temperature scales discussed above don’t have well-defined reference points. For example, the freezing and boiling points of water are both relative to the pressure. They can change with pressure. Water may have a different boiling point in the Himalayas.

So a well-defined temperature scale is the ideal gas thermometer which also gives us the absolute zero temperature. The ideal gas thermometer uses Boyle’s Law which says that the product of pressure and volume is constant for a constant temperature.

In other words, if we multiply the pressure and molar volume of a gas (PVm) and keep changing the pressure until it approaches zero, i.e, the limit as P→0, the product is always a constant. This constant turns out to be a function of temperature (f(T)). Now we have a property that depends on temperature. Celsius used his reference points 0 °C and 100 °C, which give two points on the f(T) vs T graph as shown. We can connect these two points simply by linear interpolation.

The purpose of using linear interpolation is, it gives an x-intercept on the x-axis which is when f(T)=0. This means the value of PVm = 0. We can’t go beyond this point because it would be PVm < 0. And we know that the negative pressure or negative volume doesn’t make any sense. So the least attainable point is where f(T)=0 which gives us the value of absolute zero. The temperature corresponding to this point is -273 °C.

As we discussed earlier that we must use a well-defined reference point like absolute zero. The above graph showed that absolute zero doesn’t care whatever the pressure is. Therefore, our new reference points were the absolute zero temperature and the triple point of water. The triple point of pure water (273.16 K & 6.11657 mbar) is a unique value of temperature and pressure where all three phases (solid, liquid and vapour) coexist in thermodynamic equilibrium.

Reference: Lec 2 | MIT 5.60 Thermodynamics & Kinetics, Spring 2008 by MIT OpenCourseWare.

Redefining of the reference point

In 2019 redefinition of the SI base units allowed scientists to define kelvin in terms of the Boltzmann constant rather than the triple point of water. They realized that the difference in the isotopic composition of water obtained from different sources can bring about slight variations in its triple point as well. The Boltzmann constant makes kelvin completely independent of the properties of water.

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