11: Heat Engines
- Page ID
- 7283
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 11.1: Introduction
- This page explores the theoretical framework of heat engines, detailing their operation through ideal processes like reversible adiabatic expansions. It defines engine efficiency as the ratio of work done to heat supplied and emphasizes that no engine can attain 100% efficiency, presenting the Carnot cycle as the ideal model.
- 11.2: The Carnot Cycle
- This page explains the Carnot cycle's significance in defining an absolute temperature scale that aligns with the ideal gas temperature scale. It elaborates on the isothermal and adiabatic processes of the Carnot engine, deriving the cycle's efficiency based on the source and sink temperatures. It also discusses the creation of a temperature function to establish the absolute scale, highlighting the relationship between efficiency and heat transfer.
- 11.3: The Stirling Cycle
- This page details a thermodynamic cycle for an ideal gas in a cylinder with a porous partition, comprising four stages: isothermal compression, constant volume heating, isothermal expansion, and constant volume cooling. It explains how heat transfer occurs at each stage and derives the cycle's efficiency based on specific heat capacities and temperature differences, referencing ideal gases such as diatomic gas and helium.
- 11.4: The Otto Cycle
- This page explains the Otto cycle, which is similar to a car engine's operation and consists of two isochoric and two adiabatic processes. It describes the cycle's progression from air and gasoline intake at constant pressure, through adiabatic compression, ignition, adiabatic expansion for work production, and exhaust expulsion. The summary highlights that the cycle's efficiency can be affected by compression temperature limits, which pose risks of spontaneous ignition.
- 11.5: The Diesel Cycle
- This page explains the Diesel cycle, which compresses air to high temperatures before fuel injection for combustion. It outlines the cycle’s phases: intake, adiabatic compression, fuel injection, constant pressure expansion, and exhaust. The page also details performance metrics like net work, stroke volume, and efficiency equations, and includes an exercise to calculate efficiencies for different thermodynamic cycles under given conditions.
- 11.6: The Rankine Cycle (Steam Engine)
- This page explains the operation of the Titfield Thunderbolt, which utilizes an engine similar to the Rankine cycle. It details how work output is influenced by the working substance and temperature. Internal combustion engines are compact due to high operating temperatures, unlike bulkier steam engines that work at lower temperatures.
- 11.7: A Useful Exercise
- This page outlines the structured analysis of heat engine cycles, focusing on four stages: isotherm, adiabat, isochor, and isobar. It details the distinct characteristics of heat, work, and internal energy in each stage, emphasizing their relationships for evaluating engine efficiency. Additionally, it highlights the impact of heat addition or loss and work done or received on internal energy changes. The page recommends using T:S plane diagrams for clearer assessment of work and heat transfer.
- 11.8: Heat Engines and Refrigerators
- This page covers the principles of heat engines, refrigerators, heat pumps, and air conditioners, detailing their efficiencies and functions in heat transfer. It explains concepts like the Carnot engine, the coefficients of performance, and compares the roles of different systems in managing heat. Environmental impacts of refrigerants are discussed, alongside practical applications and performance metrics of these devices.
- 11.9: Entropy is a Function of State
- This page covers the absolute temperature scale within a reversible Carnot heat engine framework, illustrating the relationship between heat exchange and the temperatures of the heat source and sink. It emphasizes that the ratio of heat absorbed and released corresponds to the temperature ratio.