4: Entropy and The Second and 3rd Law of Thermodynamics
- Page ID
- 508012
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 4.1: Energy Does not Determine Spontaneity
- There are many spontaneous events in nature. If you open the valve in both cases a spontaneous event occurs. In the first case the gas fills the evacuated chamber, in the second the gases will mix. The state functions \(U\) and \(H\) do not give us a clue what will happen. You might think that only those events are spontaneous that produce heat. The development of the new state function entropy has brought us much closer to a complete understanding of how heat and work are related.
- 4.2: Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Energy Dispersal
- An isolated system, one that does not exchange heat with its surroundings, not at equilibrium will evolve in a direction that increases the overall energy dispersion of the state. The system will reach equilibrium when the energy dispersal, or entropy (\(S\)), is maximum.
- 4.3: Unlike heat, Entropy is a State Function
- Entropy, \(S\), is a state function, so it does not depend on the thermodynamic path. We can take any path we want to calculate the entropy of a thermodynamic system.
- 4.4: The Second Law of Thermodynamics
- An isolated system is a little more than just adiabatic. In the latter heat cannot get in or out. In an isolated system nothing gets in or out, neither heat nor mass nor even any radiation, such as light. The isolated system is like a little universe all to itself.
- 4.5: We Must Always Devise a Reversible Process to Calculate Entropy Changes
- The second law of thermodynamics can be formulated in many ways, but in one way or another, they are all related to the fact that the state function entropy, \(S\), tends to increase over time in isolated systems. The second law has important consequences for the question of how we can use heat to do useful work.
- 4.6: Entropy Increases With Increasing Temperature
- The entropy of a system increases with temperature and can be calculated as a function of temperature if we know the heat capacity of the system.
- 4.7: The 3rd Law of Thermodynamics Puts Entropy on an Absolute Scale
- The 3rd law of thermodynamics says that a perfect (100% pure) crystalline structure at absolute zero (0 K) will have no entropy (\(S\)). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy. We can put entropy on an absolute scale.
- 4.8: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition
- For a general phase transition at equilibrium and constant temperature and pressure: \(\frac{\Delta_{trs}H}{T_{trs}}=\Delta_{trs}S\).
- 4.9: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions
- Since entropy is a state function (path independent), we can calculate entropy changes in a chemical reaction by taking the sum of the standard entropies of the products and subtracting the sum of the standard entropies of the reactants.