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  Low Temperature and Third Law of Thermodynamics, Physics tutorial

Low Temperature Physics:

Low temperature physics is the specialized area of physics which deals with behavior of materials at low or extremely low temperature. Low temperature, in this context, is temperature low enough to observe phenomena like superconductivity and super-fluidity.

Liquefaction of Gases:

Liquefaction of gases is process by which substances in their gaseous state are converted to liquid state. Liquefaction of gases can be attained:

  • By compressing gas at temperatures less than critical temperature;
  • By making gas do some kind of work against an external force, thereby causing gas to lose energy and change to the liquid state; and
  • By making the gas do work against its own internal forces, this also causing it to lose energy and liquefy.

When gases are liquefied, they can then be stored and transported in much more compact form than in gaseous state. One type of liquefied gas that we are familiar with is Liquefied Natural Gas (LNG). In principle, any gas can be liquefied, so their compactness and ease of transportation has made them popular for the number of other applications.

Applications of Liquefaction:

Liquefied gases are used in the following application:

  • Fuel for rocket engines e.g. liquefied oxygen and hydrogen;
  • For welding operation e.g. liquid oxygen and acetylene;
  • Aqualung devices e.g. combination of liquid oxygen and liquid nitrogen;
  • For research application (cryogenics) e.g. liquid helium is widely used for the study of behaviour of matter at temperatures close to absolute zero.
  • Liquid nitrogen for low temperature refrigeration.

Maintenance of Low Temperature:

Method on maintaining low temperature is by using liquefied gases as heat sink. For instance, some gases liquefy at quite low temperatures (like nitrogen liquefied at 77 K, hydrogen at 20K, helium at 4.2 K). If such gases are liquefied, liquid can be utilized as bath to maintain experiment at these temperatures.

Phenomena at Low Temperature:

Two known phenomena at low temperature are superconductivity and superfluidity.

Superconductivity in Metals:

At a temperature low enough, most metals as well as many alloys and compounds enters a state at which their resistant to flow of current disappears (i.e. they become a superconductor). This state is called superconductivity in metals. Most metals in the periodic table, many alloys and compounds show this behavior. Implication of superconductivity is that if a superconductor is a wire loop and a current is generated in that loop, then it flows for years with no significant decay.

Superfluidity:

At the temperature low enough, materials enter the state whereby they become fluid which flows with no viscosity. Superfluidity can only be observed at much lower temperatures than temperature at which superconductivity is observed. For instance helium-4 doesn't display superfluid-behavior until it reaches temperature below 2 K. When the material becomes superfluid, following will be observed:

  • As superfluids have no internal viscosity, the vortex formed within superfluid persists forever.
  • The superfluid has zero thermodynamic entropy and infinite thermal conductivity, meaning that no temperature differential can exist between two superfluids or two parts of the same superfluid.
  • A superfluid can also climb up and out of a container in a one atom-thick layer if the container is not sealed.
  • A conventional molecule embedded within a superfluid can move with full rotational freedom, behaving like a gas.

Application of Low Temperature Phenomena

Applications of Superconductivity

Superconductivity promises the whole lot of applications but limitation to this is how to maintain this temperature as whole of these applications are at room temperature in everyday world. Most important real application of low temperature physics is super-conducting magnet. This is being utilized for magnetic resonance imaging (MRI) and particle accelerators. Other applications are in;

  • Super sensor,
  • Quantum computing,
  • Loss less power transmission line.

We know that energy loss on the transmission line is I2R. Imagining using super conduction as transmission cable, meaning that R = 0 i.e. I2R = 0.

Applications of Superfluidity:

Superfluidity doesn't have wide range of application as superconductivity. Two areas of applications are in dilution refrigerators and spectroscopy.

Nernst Heat Theorem:

Third law of thermodynamics describes the behavior of systems that are in internal equilibrium, as temperature approaches absolute zero (i.e. 0 K).

Consider the chemical reaction taking place in the container at constant pressure, and that container makes contact with the heat reservoir at the temperature T. If temperature of system increases as a result of reaction (i.e. if reaction is exothermic) there will be a heat flow to reservoir until temperature of system reduced to its original value T. Heat bath or reservoir is so large that its temperature doesn't change considerably when heat flow in or out of it.

For the process at constant pressure heat gain or lost is increase or decrease in enthalpy. Then

ΔH = Hf - Hi = -Q

Minus sign in right hand side of equation indicates that heat flows out of system. Heat of reaction is generally given as ΔH. ΔH is positive for the endothermic reaction and negative for exothermic reaction.

Change in Gibbs function and change in enthalpy are related as

Gf - Gi = Hf - Hi + T[(∂(Gf - Gi))/∂T]P

Written as

ΔG = ΔH + T[(∂(ΔG))/∂T]P

This means that change in enthalpy and change in Gibbs function are equal only when T[(∂(ΔG))/∂T]P approaches zero. Nernst suggested that, in limit, as temperature approaches zero, changes in enthalpy and Gibbs function are equal. As

(∂ΔG/∂T)P = -ΔS

So that limT→0(S1 - S2) = 0

This means that chemical reactions at a temperature of absolute zero take place with no change in entropy.

Planck later extended this to suppose that, not only does ΔG → ΔH , but that, as T → 0 , enthalpy and the Gibbs function of system approach each other asymptotically in such a manner that, in limit, as T→0, G→H and (∂G/∂T)P→0

i.e. limT→0 S = 0

Third Law of Thermodynamics:

Nernst's heat theorem and Planck's extension of it, though derived from observing behavior of chemical reactions in solids and liquids, is now believed to apply quite usually to any process. Equation is called as third law of thermodynamics.

Statement of Third Law of Thermodynamics:

The third of thermodynamics defines that it is impossible to decrease temperature of material body to absolute zero of temperature in the finite number of operations.

This is third law of thermodynamics, and it is inevitable result of Planck's extension of Nernst's heat theorem. Third law is sometimes known as unattainability statement of third law.

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