The Third Law of Thermodynamics

1. The Third Law of Thermodynamics • “If the entropy of every element in its stable state at T = 0is taken as zero, every substance has a _______entropy which at T = 0 may become zero, and does become zero for all perfect _______substances, including compounds.” _______Heat Theorem “The entropy change accompanying transformation between condensed phases in equilibrium, including chemical _______, approaches zero as T 0. Practical consequence: Set S(0) = 0 for _______by convention. Apply Nernst to determine S(0) for all else. • “It is impossible to reach absolute zero in a _______number of steps.” The 1st Law says U cannot be _______or _______. The 2nd Law says S cannot _______. The 3rd Law says zero _______cannot be reached. Modified by Jed Macosko

2. But In general, i.e. any path  Even more generally, Conditions for: _________equilibrium ____________equilibrium The _______Inequality Given and Substitute into the 1st Law: __________Equation of Thermodynamics All _______differentials, so path independent. Pex dV P Equal for _______change Clausius Inequality Modified by Jed Macosko

3. The Fundamental ______of Thermodynamics Reversible change but true for all paths since dV exact with Combine  or This fundamental equation generates many more _________. Example 1: Comparison with  Example 2: Consider that dU is exact and cross __________. which is a _______relation use this relation here Example 3: cyclic rule… …again… …and again! Modified by Jed Macosko

4. How Entropy Depends on T and V  Compare with 0 for ideal gases For _____substance, assuming CV is T ___________ For _______ gases, (eqs 3.7.4, 6.1.6) Modified by Jed Macosko

5. Compare with 0 for ideal gases Entropy Depends on T and P (not in text) First problem: replace_____;second problem: replace_____. Use and both are solved!  But  Modified by Jed Macosko

6. irreversible ice, T water, T reversible ice, 0°C water, 0°C rev. rev. Entropy Changes in __________ Processes Entropy is a __________function, so DS(sys) = S2 – S1__________of path This can be used to calculate DS for an irreversible process. • Consider isothermal expansion of a gas from V1 to V2: reversibleandirreversible cases For the reversible case For the irreversible case e.g. for __________expansion, w = 0  • Consider freezing of __________water at T < 273 K Modified by Jed Macosko

7. P, T, V2 n2 P, T, V1 n1 P, ___,V1+V2 n1+ ___ leads to Entropy of __________ • Consider the mixing of two ideal gases : In general This expression applies to the arrangement of objects (__________) just as well as __________(gases and liquids). For example, arrange N identical atoms in N sites in a crystal: Compare with the arrangement of two types of atoms, A and B. Application of ________approximation: do the math! Modified by Jed Macosko

8. if CPis  constant curves coincide at0 K, a consequence of the Nernst Heat Theorem X1 S X2 • Alter X isothermally. Entropy changes. • Restore X by a reversible adiabatic process. • Repeat cycle. 0 0 T T1 Using Entropy to Achieve Low T To achieve lower temperatures, S must be reduced. Choose some property X that varies with S, i.e. S= f(X,T). This could be the pressure of a gas or, for example, the magnetic moment of a paramagnetic salt (whose energy varies with magnetic field). Modified by Jed Macosko