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Measurements of heat capacities at very low temperatures provide data for thecalculation from Eq. (5.13)

of entropy changes down to 0 K. When thesecalculations are made for different crystallineforms of the same chemical species, the entropy at 0 K appears to be the same for all forms.

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When the form is noncrystalline, e.g.,amorphous or glassy, calculations show that theentropy of the more random form is greaterthan that of the crystalline form. Suchcalculations, which are summarized elsewhere,lead to the postulate that the absolute entropy iszero for all perfect crystalline substances atabsolute zero temperature .

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While the essential ideas were advancedby Nernst and Planck at the beginning of the

twentieth century, more recent studies at very low temperatures have increased confidence inthis postulate, which is now accepted as thethird law.

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I f the entropy is zero at T = 0 K, thenEq. (5.13) lends itself to the calculation of absolute entropies. With T = 0 as the lowerlimit of integration, the absolute entropy of agas at temperature T based on calorimetricdata is:

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This equation is based on the suppositionthat no solid-state transitions take place and

thus no heats of transition need appear. Theonly constant-temperature heat effects arethose of fusion at T f and vaporization at T v.When a solid-phase transition occurs, a term A

Ht/ Tt, is added.

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A dditional Information

The Third Law of Thermodynamics means that asthe temperature of a system approaches absolute zero,its entropy approaches a constant (for pure perfect

crystals, this constant is zero). A pure perfect crystal isone in which every molecule is identical, and themolecular alignment is perfectly even throughout thesubstance. Only ferromagnetic, antiferromagnetic, anddiamagnetic materials can satisfy this condition.For non-pure crystals, or those with less-than perfectalignment, there will be some energy associated with theimperfections, so the entropy cannot become zero.

What is the third law of thermodynamics?

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A dditional Information

The Third Law of Thermodynamics can bevisualized by thinking about water.

Water in gas form has molecules that can movearound very freely. Water vapor has very high entropy(randomness).

As the gas cools, it becomes liquid. The liquid watermolecules can still move around, but not as freely. Theyhave lost some entropy.

When the water cools further, it becomes solid ice.

The solid water molecules can no longer move freely, butcan only vibrate within the ice crystals. The entropy is nowvery low.

What is the third law of thermodynamics?

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A dditional Information

As the water is cooled more, closerand closer to absolute zero, the vibration ofthe molecules diminishes. If the solid waterreached absolute zero, all molecular motionwould stop completely. At this point, thewater would have no entropy (randomness)

at all.

What is the third law of thermodynamics?

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The absolute temperature scale is defined in terms of theperformance of a Carnot engine (equation 5.7)

I nstrumental in the derivation of Eq. (5.7) is a second-law statementsuch as I t is impossible to completely convert heat into work in acyclic process. Equation (5.7) is therefore subject to this constraintand would not be valid for TC= 0 where QC would be zero.Therefore, the logical structure of thermodynamics does not permitzero absolute temperature and since the laws of thermodynamics are

based on statements from the physical world and have provenreliable in dealing with the physical world, it may be stated that zeroabsolute temperature is unattainable.

A dditional Information

Proving zero absolute temperature is unattainable

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A dditional Information

The Second Law, in part, implies that heat can neverspontaneously move from a colder body to a hotter body . So, as

a system approaches absolute zero, it will eventually have todraw energy from whatever systems are nearby . If it drawsenergy, it can never obtain absolute zero . So, this state is notphysically possible, but is a mathematical limit of the universe .

Proving zero absolute temperature is unattainable