4: Models of Thermodynamics
- Page ID
- 104104
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In Chapter 4, we expand the Energy-Interaction Model to include thermodynamics, connecting macroscopic properties like pressure, volume, and temperature to internal energy changes. We explore work done on fluids, the Ideal Gas Law, and introduce key thermodynamic concepts, such as enthalpy and heat capacity. Using PV diagrams, we analyze processes like isothermal, isobaric, and adiabatic. The Second Law of Thermodynamics is introduced, linking entropy to probability, highlighting how energy disperses in natural processes. This foundation connects thermodynamic principles to real-world phenomena, with implications across physics, chemistry, and biology.
- 4.1: Where We Are Headed
- We approach thermodynamics using the Energy-Interaction Model, linking particle-based models to applications across sciences. Thermodynamics, while complex, demystifies phenomena like entropy, ∆H, and Gibbs Energy, offering insights into systems from cells to stars. With statistical models, we address questions about phase changes, reaction energetics, and more, often making predictions from known data rather than direct experiments, illustrating thermodynamics' powerful applicability.
- 4.2: Work and Pressure
- We revisit work as force over displacement and extend it to fluids. For fluids under pressure, work is calculated as force times area and displacement, or W=−∫PdV, where the negative sign indicates work done on the system during compression. In constant-pressure cases, work simplifies to W=−PΔV. Graphical interpretation shows work as the area under the pressure-volume curve, useful for visualizing energy exchanges in thermodynamic processes.
- 4.3: Ideal Gas Model
- The Ideal Gas Model describes gas behavior with assumptions of random motion, negligible volume, and no intermolecular forces. The Ideal Gas Law, PV=nRT, links macroscopic properties like pressure, volume, and temperature. Heat capacity differs at constant volume and constant pressure, with C_P exceeding C_V by R. This model bridges microscopic particle behavior and macroscopic thermodynamics, allowing predictions of work and heat requirements in gas processes.
- 4.4: Intro Model of Thermodynamics
- We introduce thermodynamics with the First Law, where internal energy change equals heat added and work done. State variables like pressure, volume, and temperature define a system's thermodynamic state, independent of process paths. PV diagrams graphically represent processes, showing work as area under curves. In cycles, state variables return to initial values, making net internal energy change zero. Thermodynamic cycles help visualize energy transfers in processes involving gases and fluids.
- 4.5: Thermodynamics processes
- We explore thermodynamic processes: isochoric (constant volume, no work done), isobaric (constant pressure, work done by W=−PΔV), isothermal (constant temperature, work found by integrating W=−nRTln(V_f/V_i)), and adiabatic (no heat transfer, work changes internal energy). Each process has distinct energy transfer characteristics shown in PV diagrams. These concepts apply widely, from gas expansion to biological and atmospheric phenomena.
- 4.6: Second Law of Thermodynamics
- We introduce entropy and the Second Law of Thermodynamics, stating that entropy of a closed system never decreases. Entropy measures energy dispersion; it increases as systems move toward equilibrium. Heat transfer changes entropy, visualized in TS diagrams, where the area under the curve represents heat. Statistically, entropy links to the number of microstates, favoring the most probable macrostates, explaining why systems evolve toward higher entropy.
- 4.7: Looking Back and Ahead
- We conclude by linking entropy to probability, explaining that large systems naturally evolve to high-entropy states due to overwhelming probability. Living systems maintain order by transferring entropy to their surroundings, aligning with the Second Law. Looking ahead, we’ll apply energy conservation to fluid flow and electric circuits, drawing parallels to living systems. We’ll also explore momentum conservation and dive into Newton’s Laws to understand forces and motion over time.