Physical Chemistry Third Edition

140 3 The Second and Third Laws of Thermodynamics: Entropy

If no adiabatic process can lead to zero temperature, one might ask if some other

kind of process might lead to zero temperature. Unless a heat reservoir already exists

at zero temperature, conduction of heat away from an object cannot do the job, since

heat flows from a hotter to a cooler object. A refrigerator cannot do the job, since

its coefficient of performance must be less than that of a Carnot refrigerator, which

approaches zero as the lower temperature approaches zero. We therefore conclude

that no process can cause a system to attain 0 K, which is therefore calledabsolute

zero. The unattainability of absolute zero is a consequence of both the second and

third laws.

Isotherm at T 50

(also a reversible adiabat)

Reversible adiabat

0

T

X

Figure 3.12 Reversible Adiabats Sho-
wing the Unattainability of Zero Temp-
erature.

Very low temperatures have been attained by adiabatic demagnetization. The first

step of this process, invented by Giauque, consists of magnetizing an object isother-

mally. The magnetization process decreases the entropy, since it aligns magnetic dipoles

in the material and reduces the randomness of the system. Heat flows from the object to

a heat reservoir during the magnetization. Once the object is magnetized, it is adiabati-

cally insulated and then removed from the magnetic field that has magnetized it. During

the adiabatic demagnetization, which approximates a reversible process, the entropy

remains nearly constant and the temperature drops. Carrying out this process repeatedly

has achieved temperatures of less than 0.000001 K (1μK) in the nuclear spins of a

magnetizable system. Recent studies of ultralow temperatures have involved opposing

laser beams that effectively stop the translational motion of atoms, thus lowering their

temperature so far as this motion is concerned. Saubamea and coworkers have achieved

an effective temperature of 3× 10 −^9 K (3 nK).^5

Absolute Entropies

According to the third law as stated by Lewis, we can consistently set the entropy of any

pure perfect crystalline substance equal to zero at zero temperature. The entropy change

to bring a sample of a pure substance from zero temperature in a perfect crystalline

form to some specified state is called theabsolute entropyof that substance at that state.

For any substance

S(T 1 )

∫T 1

0

dqrev

T

(3.5-1)

whereS(T 1 ) is the absolute entropy of the substance at temperatureT 1. If there is no

solid-solid phase transition betweenT0 andTT 1 and if the final and initial states

are at the same pressure, we can write for a solid substance

Sm(T 1 )−

∫T 1

0

CP, m

T

dT (solid substance) (3.5-2)

Inspection of Eq. (3.5-2) shows that the heat capacity must approach zero as the temper-

ature approaches zero in order to prevent divergence of the integral. Heat capacity data

are difficult to obtain at very low temperatures, but all experimentally determined heat

capacities tend toward zero as the temperature approaches zero. If no data are available

(^5) See for example J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen-Tannoudji,
Phys. Rev. Lett., 75 , 4194 (1995).