# Good Example Of Report On Negative Absolute Temperature

Type of paper: Report

Topic: Temperature, Energy, Absolute, System, Absolute Temperature, Atom, Thermodynamics, Equation

Pages: 3

Words: 825

Published: 2020/12/02

The absolute temperature pertains to the temperature scale measured in kelvin where the zero on the Kelvin scale pertains to the theoretically lowest attainable temperature. This particular temperature scale was established after the observations of a phenomenon that at any given pressure, the plot of the temperature and the volume of a gas follows a straight line. Even with different pressures, the plot is always straight; furthermore, all plots seem to be directed towards a similar y-intercept which is -273.15 ˚C, that is, the temperature value when the volume is zero – or close to zero (Chang & Overby 144).

Theoretically, absolute zero is nearly impossible to reach. According to Braun et al. (52), the absolute temperature is usually positive, however, negative values are not impossible. Up to this day, the idea that the negative absolute temperature exists is highly debated. The macroscopic development of the second law of thermodynamics argues that negative absolute temperatures should be impossible to exist, however, statistical thermodynamics and mechanics state otherwise. What then is a negative absolute temperature depends on the definition of temperature, more specifically, the absolute temperature (Manzano).

In this light, this paper will provide brief discussions of two concepts of temperature fundamental to understanding what the negative absolute temperature means.

## Thermodynamics: Temperature and Entropy

Temperature usually pertains to how cold or how warm an object is. However, its definition is more complicated than that, and to simplify matter, there is a need to introduce another concept in thermodynamics that would help in widening our knowledge about the negative absolute temperature: entropy.

According to Chang and Overby (630-5), entropy (S) is a measure of the magnitude of the dispersion of energy of a system among the number of possible ways or scenario the system can contain energy. In other words, the entropy is more of a measure of chaos or dispersal of a system, and microstates are referred as the different scenarios of the system. Note that the entropy and the number of microstates are correlated, more specifically: S = klnW

(Equation 1)

where k is the Boltzmann constant (1.38 ×10-23 J/K). From the equation, it can be inferred that the larger the number of scenarios (W) means greater entropy. This is where it gets interesting: at absolute zero, a system would have zero entropy value, which means zero molecular action. In other words, the atoms are at rest.

Now, the negative absolute temperature, as the law of entropy suggests, is impossible. However, proponents of statistical thermodynamics and mechanics argues that the concept of negative absolute temperature rests on the definition of absolute temperature.

According to statistical mechanics, temperature is a macroscopic property; the microstates determine the temperature of the system. Indeed, entropy is correlated with temperature, more specifically:

1T = change in entropychange in energy=∂S∂E

(Equation 2)

For instance, consider a system with N number of atoms with two energy states. This means that there is only one possible scenario that the system would have the lowest energy possible – all atoms are in their lower energy state. Since entropy is proportional to the natural logarithm of the number of scenarios, the entropy for this state would be zero(ln1)=0). Moreover, since energy in this case is quantized – a shift on an atom from an energy state to the other causes one unit of shift to the total energy of the system – it can be inferred that the entropy would be maximized if half of the atoms are in their higher state and the other half in their lower state.

In the case of the system of N atoms with two energy states, an addition of energy means that one or more atoms would go from their lower energy state to higher energy state. This means that more energy means more atoms shifting from lower energy state to higher energy state. However, at the moment where there is an addition of energy while half of the atoms are in their higher energy state, entropy would decrease. To understand why, let us examine (Equation 2) closely.

The equation tells us that the temperature is related to the slope of the graph of entropy and energy. As we can see (see figure 1), the entropy is highest when energy is at half (half of the atoms in their lower energy state and half in their higher energy state). Entropy suddenly decreases exponentially after that, and the slope jumps from positive values, then zero, then negative values. Since temperature and the slope is indirectly proportional, at this particular point, the temperature jumps from positive infinity to negative infinity, thus, creating a system with negative absolute temperatures.

Figure 1. The probable graph of entropy versus energy of the example system.

## What does this mean?

Technically, the negative absolute temperatures are hotter than when the system is in the positive temperature. Going back to our example system, the negative temperature regions have higher number of atoms in their higher energy state than when the system is in positive temperature. This means that when the system is in contact with another system, the direction of the heat flow would be from the higher energy (negative absolute temperature) to lower energy (positive absolute temperature) (Doss np).

## References:

Braun, S. et al. "Negative Absolute Temperature for Motional Degrees of Freedom." Science 339 (2013): 52-55. Print.

Doss, Heide. "Below Absolute Zero: Negative Temperatures Explained." PhysicsCentral. American Physical Society, 2015. Web. 28 February 2015.

Chang, Raymond & Overby, Jason. General Chemistry, 6th Edition. New York, NY: The McGraw-Hill Companies, 2011. Print.

Manzano, Daniel. "Quantum Thermodynamics IV: Negative absolute temperatures." mappingignorance. 26 November 2014. Web. 28 February 2015.

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