Third law of thermodynamics — Safekipedia Adventurer

The third law of thermodynamics tells us about what happens to a closed system as it gets very, very cold. It says that when a system's temperature reaches absolute zero, its entropy — a measure of how much the system’s energy is spread out — approaches a fixed value. This value does not change based on other factors like pressure or magnetic fields.

At absolute zero, which is zero kelvin, a system must be in its lowest possible energy state. Entropy is linked to the number of ways the system’s energy can be arranged, called microstates. Usually, there is just one best arrangement, known as the ground state, and at absolute zero the entropy becomes exactly zero.

However, if a system does not settle into a perfect order — for example, if it becomes glassy — some entropy might remain even at very low temperatures. This remaining entropy is called the residual entropy of the system. The third law helps scientists understand the limits of how cold things can get and how energy behaves at these extreme temperatures.

Formulations

The third law of thermodynamics has several ways to explain it. One simple idea is from a scientist named Planck. He said that when you cool a perfect crystal down to the coldest possible temperature, its disorder (called entropy) will stop changing.

Another idea comes from Nernst. He studied liquids and solids and found that when you get very close to the coldest temperature possible, any changes in disorder also become almost nothing. This means the disorder stays the same no matter what you do to the material, as long as it's very cold.

There are other ways to describe this law, but they all point to the same basic truth: at the coldest possible temperature, called absolute zero, the disorder of a system reaches its lowest point.

History

The idea behind the third law of thermodynamics was created by a chemist named Walther Nernst between 1906 and 1912. It is sometimes called the Nernst heat theorem. This law tells us that when a system reaches a temperature of absolute zero, its ability to disorder (called entropy) becomes a fixed number. At absolute zero, a system is in its simplest energy state.

In 1923, two scientists, Gilbert N. Lewis and Merle Randall, explained the law in another way. They said that if we think of the entropy of basic building blocks as zero at absolute zero, then real materials can also have zero entropy at that temperature if they form a perfect crystal. Some crystals can have a little bit of leftover entropy because of tiny imperfections.

Explanation

(a) Single possible configuration for a system at absolute zero, i.e., only one microstate is accessible. Thus S = k ln W = 0. (b) At temperatures greater than absolute zero, multiple microstates are accessible due to atomic vibration (exaggerated in the figure). Since the number of accessible microstates is greater than 1, S = k ln W > 0.

The third law of thermodynamics says that when a pure substance is a perfect crystal and its temperature gets very close to zero, its entropy—which measures how much the parts can be arranged in different ways—also gets very close to zero. This is because in a perfect crystal, every piece stays in the same place and moves very little when it is super cold.

The third law also helps scientists understand entropy at any temperature. It gives them a starting point at absolute zero. By comparing other temperatures to this zero point, they can find the entropy at those temperatures.

Consequences

The third law of thermodynamics tells us that as a system gets very cold, close to absolute zero (which is zero kelvin), its entropy — a measure of how much the system’s energy is spread out — approaches a constant value. This means that at absolute zero, the system must be in its lowest possible energy state.

One important idea from the third law is that it is impossible to reach absolute zero in a finite number of steps, no matter how careful we are. Even with very advanced methods, we would need an infinite number of steps to actually reach zero kelvin.

∫ T 0 T C ( T ′ , X ) T ′ d T ′ = C 0 α ( T α − T 0 α ) . {\displaystyle \int _{T_{0}}^{T}{\frac {C(T',X)}{T'}}dT'={\frac {C_{0}}{\alpha }}(T^{\alpha }-T_{0}^{\alpha }).}

lim T → 0 C ( T , X ) = 0. {\displaystyle \lim _{T\to 0}C(T,X)=0.}

S ( T , V ) = S ( T 0 , V ) + 3 2 R ln ⁡ T T 0 . {\displaystyle S(T,V)=S(T_{0},V)+{\frac {3}{2}}R\ln {\frac {T}{T_{0}}}.}

C V = π 2 2 R T T F {\displaystyle C_{V}={\frac {\pi ^{2}}{2}}R{\frac {T}{T_{\text{F}}}}}

T F = 1 8 π 2 N A 2 h 2 M R ( 3 π 2 N A V m ) 2 / 3 . {\displaystyle T_{\text{F}}={\frac {1}{8\pi ^{2}}}{\frac {N_{\text{A}}^{2}h^{2}}{MR}}\left({\frac {3\pi ^{2}N_{\text{A}}}{V_{\text{m}}}}\right)^{2/3}.}

C V = 1.93.. R ( T T B ) 3 / 2 {\displaystyle C_{V}=1.93..R\left({\frac {T}{T_{\text{B}}}}\right)^{3/2}}

T B = 1 11.9.. N A 2 h 2 M R ( N A V m ) 2 / 3 . {\displaystyle T_{\text{B}}={\frac {1}{11.9..}}{\frac {N_{\text{A}}^{2}h^{2}}{MR}}\left({\frac {N_{\text{A}}}{V_{\text{m}}}}\right)^{2/3}.}

L = L 0 + C p T {\displaystyle L=L_{0}+C_{p}T}

S ( T , x ) = S l ( T ) + x ( L 0 T + C p ) {\displaystyle S(T,x)=S_{l}(T)+x\left({\frac {L_{0}}{T}}+C_{p}\right)}

α V = 1 V m ( ∂ V m ∂ T ) p . {\displaystyle \alpha _{V}={\frac {1}{V_{m}}}\left({\frac {\partial V_{m}}{\partial T}}\right)_{p}.}

( ∂ V m ∂ T ) p = − ( ∂ S m ∂ p ) T {\displaystyle \left({\frac {\partial V_{m}}{\partial T}}\right)_{p}=-\left({\frac {\partial S_{m}}{\partial p}}\right)_{T}}

lim T → 0 α V = 0. {\displaystyle \lim _{T\to 0}\alpha _{V}=0.}