topic: nernst heat theorem and third law of thermodynamics
TRANSCRIPT
BPT-201 (semester II) THERMAL PHYSICS………… Credits: 4
Topic: Nernst Heat Theorem and Third Law of thermodynamics
Dr Neelam Srivastava Department of Physics (MMV Section)
Banaras Hindu University [email protected]
Third law of thermodynamics Like second law, third law also has many equivalent alternate
statements. Third law can be seen as an inference from thermochemical observations
• 1. “It is impossible to attain the absolute zero by any finite sequence of thermodynamic process”
• 2. “every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances,” by 1923, Lewis and Randall
• 3. The limit of equilibrium entropies of all thermodynamic systems and also the limit of equilibrium entropy-changes of all thermodynamic systems in all reversible isothermal processes between equilibrium states tend to zero
• Definition ‘1’ can also be given as that-Third law prohibits 100% conversion of heat into work.
• This is very obvious since there is no sink of 0K temperature.
• Hence for all other sinks some amount of heat will be rejected.
• So η will never be 1 or 100% conversion of heat into work not possible.
•
Born June 25, 1864, Briesen, Prussia [now Wąbrzeźno, Poland] Died November 18, 1941, Zibelle, Germany [now Niwica, Poland]
• On the basis of data available in literature Nernst inferred a postulate known as the Nernst heat theorem.
• Nernst analyzed the of differences between enthalpy and (ΔH) and Gibbs free energy (ΔG), for particular reactions at a series of temperatures.
• Richards Experiment showed that • Nernst analyzed all such data and came with his postulate
as discussed in coming slides
• Let us start from Gibbs; Helmholtz equation
• At T=0 or when =0 the above equation gives • In this context Nernst came with an postulate that in
the neighborhood of absolute zero =0 • mathematically it is written as • ∆G can either increase or decrease and hence two
curves are shown in next slides • Nernst further suggested that as the absolute zero is
reached ∆G and ∆H become asymptotically equal • Which gives
• So Nernst Heat Theorem is mathematically stated as • and • Let us differentiate the Gibbs Helmholtz relation w.r.t. T • • We will get • or or • Since Nernst assumed that Gibbs’ potential converges to
a limiting value as T tends to zero and will have same sign i.e. will have opposite
sign. Variation of ∆G and ∆H with temperature are given in next slide
• Nernst theorem has important consequences • Let us start from Gibbs potential • That means we will get • Hence from Nernst’s Heat theorem we get • • That means Nernst equation results in a statement—In
the neighborhood of absolute zero, all processes would occur without a change in entropy
• i.e. From Nernst theorem we can reach to the statement of Third law of Thermodynamics
Consequences of Third Law of Thermodynamics
All expansion coefficients tend to zero as T →0 • The isobaric expansivity or the volume coefficient of
expansion α is given by • Using Maxwell’s thermodynamic equations we get • which leads to • So isobaric volume expansivity tends to zero when T→0 • We know that relation between coefficient of linear
expansion (λ) and coefficient of volume expansion (α) is given as α=3λ i.e. we will also get
• The pressure coefficient (β) at constant volume will also tend to zero →
All heat capacities tend to zero as T →0 • If heat capacity is given by C then we get following
• That means Cp and Cv both tend to zero as T tends to
zero. • These results were experimentally verified by Nernst. • The classical prediction of C due to equipartition theory
says C=R/2 per mole per degree of freedom which seems to fail at low temperature.
• i.e. equipartition theory fails at low temperature
Cp-Cv →0 asT →0 T →0
• As we know • Using the relation we will get
• Hence
• i.e. Cp-Cv =0 as T →0 • Thus third law implies the confluence of Cp and Cv near absolute zero. • These results have been confirmed experimentally also.
Surface tension tends to have a constant value as T →0 • The surface tension (ϒ) satisfy following thermodynamic
relation
• Which gives • means surface tension (ϒ) will tend to have a
constant value
Does ideal Gas remain ideal when T →0 ? • We know for an ideal gas Cp-Cv=R • But in previous slides we have seen • That means ideal gas laws are not followed. • we have also seen that Cp and Cv both tend to zero as
T tends to zero hence • Entropy of an ideal gas is given by where ‘A’ is a constant • This equation indicates that when T →0 S → -∞ • Which has no physical meaning. This indicates the
degeneracy of an ideal gas and indicates that gas model should be revised
• The statement of third Law “It is impossible to attain the absolute zero by any finite sequence of thermodynamic process” can be mathematically proved also.
• To prove this let us assume we have a sink at temperature at 0k and we are having Carnot engine working between ‘0’K to some temperature T following 1234 cycle.
Unattainability of absolute zero
• For the cyclic procedure we know • S0 ∆S= ∆ S12+ ∆ S23+ ∆ S34+ ∆ S41 and we know ∆S12=Q/T
• Being adiabatic process ∆ S23=∆ S41 =0 • Nernst theorem says that ∆ S34=0 as it is carried out
T=0 K • i.e. • But this violation of 2nd law. That means our
assumption to have a sink at 0 K was wrong or we can zero K is not possible or it confirms the Unattainability of absolute zero