5: The Second Law
- Page ID
- 84322
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 5.1: Introduction to the Second Law
- The text discusses fundamental principles of thermodynamics as articulated by Rudolf Clausius???specifically, the conservation of energy and the increase of entropy. It delves into the second law of thermodynamics, which introduces the concept of entropy and how it influences our perception of time and irreversible processes. The discussion includes spontaneous processes, which occur without external forces and may not be predicted solely by energy changes.
- 5.2: Heat Engines and the Carnot Cycle
- The document discusses the concept of heat engines, particularly focusing on Sadi Carnot's theoretical model of a heat engine, the Carnot cycle, which examines the conversion of heat into work and the limitations imposed by the Second Law of Thermodynamics. The text explains the Carnot cycle's four reversible stages and presents formulas to calculate engine efficiency, emphasizing that perfect conversion of heat to work is not practical.
- 5.3: Entropy
- The page discusses the Carnot engine and its relationship with temperature and efficiency. It explains how the total heat transferred in the cycle is derived, showing that heat (q) is not a state function due to its net change around a closed cycle being non-zero. However, when considering the sum of q/T, it results in zero, which aligns with the behavior of a state function.
- 5.4: Calculating Entropy Changes
- This page explains how to calculate entropy changes for different thermodynamic processes, such as isothermal, isobaric, isochoric, adiabatic changes, and phase transitions. It provides formulas for the entropy change in each case and includes examples to illustrate the calculations.
- 5.5: Comparing the System and the Surroundings
- It is oftentimes important to calculate both the entropy change of the system as well as that of the surroundings. Depending on the size of the surroundings, they can provide or absorb as much heat as is needed for a process without changing temperature. As such, it is oftentimes a very good approximation to consider the changes to the surroundings as happening isothermally, even though it may not be the case for the system (which is often smaller).
- 5.6: Entropy and Disorder
- The concept of entropy is commonly interpreted as a measure of chaos or randomness in a system, corresponding to the dispersal of energy. Ludwig Boltzmann developed a statistical approach, proposing an equation, S = k ln(W), to calculate entropy based on the number of energetically equivalent states a system can achieve. This equation is a significant contribution to thermodynamics, even etched on Boltzmann???s grave. An example application involves calculating the entropy of a 1.
- 5.7: The Third Law of Thermodynamics
- The page discusses the Third Law of Thermodynamics, emphasizing that a perfectly ordered crystal at 0 K has zero entropy. This is different from other thermodynamic functions like enthalpy, which requires an arbitrary reference point for zero. It introduces a formula to calculate absolute molar entropies using heat capacity and discusses the Debye Extrapolation method to estimate entropies and heat capacities near absolute zero K. An example with SiO??? is provided to demonstrate the calculation.
- 5.8: Adiabatic Compressibility
- Chapter 4 discusses isothermal compressibility, \(\kappa_T\), an important thermodynamic quantity that aids in understanding various thermodynamic processes. The text explores historical insights by Isaac Newton, who miscalculated the speed of sound due to an assumption of isothermal compression, rather than adiabatic compression as later corrected by Pierre-Simon Laplace.
- 5.E: The Second Law (Exercises)
- This page consists of a series of thermodynamics problems related to various processes including isothermal, isobaric, isochoric, and adiabatic expansions or compressions of ideal gases, as well as phase changes of water. It covers topics such as calculating work, heat, changes in internal energy, enthalpy, and entropy for each process.
- 5.S: The Second Law (Summary)
- The chapter's learning objectives include describing a Carnot engine and deriving its efficiency; defining entropy and calculating its changes under various conditions; relating entropy to disorder within a crystal; stating the Third Law of Thermodynamics for entropy calculations at specific temperatures; and understanding the difference between isothermal and adiabatic compressibility, particularly in relation to sound wave propagation in gases.