19: The First Law of Thermodynamics
- Page ID
- 62253
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 19.1: Overview of Classical Thermodynamics
- This page covers the contributions of James P. Joule to thermodynamics, highlighting the relationship between work, heat, and internal energy, foundational for the First Law of Thermodynamics. It also explains pressure changes in ideal gases during temperature changes and volume expansions, noting pressure's status as a state variable.
- 19.2: Pressure-Volume Work
- This page explains work in physics as the force multiplied by the path element, discussing types like frictional and electrical work. It introduces pressure-volume work in a piston-cylinder system, detailing interactions of internal and external pressures. A sign convention is outlined, where positive values signify energy input and negative values signify energy output. Additionally, the page covers irreversible processes and their depiction on PV diagrams.
- 19.3: Work and Heat are not State Functions
- This page discusses how heat and work are path functions dependent on the process used. In piston compression and expansion, irreversible paths require more work than reversible ones due to imbalance in pressures. The page illustrates these concepts through isothermal processes, highlighting the differences in work for both compression and expansion. Reversible processes are ultimately shown to represent the minimum or maximum work that can be achieved in these scenarios.
- 19.4: Energy is a State Function
- This page explains that work and heat are not state functions, while internal energy is. It describes the first law of thermodynamics, which states that the change in internal energy (\(ΔU\)) equals the sum of work (\(w\)) and heat (\(q\)). Unlike work and heat, which are path-dependent, the change in internal energy depends solely on initial and final states. This leads to the conclusion that internal energy is conserved over cycles, reinforcing its classification as a state function.
- 19.5: An Adiabatic Process is a Process in which No Energy as Heat is Transferred
- This page explains the isothermal and adiabatic expansion of an ideal gas. Isothermal expansion maintains constant internal energy and relates reversible work to heat transfer. In adiabatic expansion, with no heat transfer, energy changes affect internal energy and cause temperature decrease. While both processes can lead to the same internal energy change, the work done differs, emphasizing that work is a path-dependent function.
- 19.6: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion
- This page explores the relationship between temperature and volume in the reversible adiabatic expansion of a monatomic ideal gas, like Argon. It illustrates that as volume increases, temperature decreases, using the ideal gas law to interconnect pressure, volume, and temperature.
- 19.7: Work and Heat Have a Simple Molecular Interpretation
- This page explores the relationship between changes in internal energy (dU) and work done under reversible conditions in thermodynamics. It references a section on the partition function, illustrating how its logarithmic derivative with respect to volume can be used to derive a system's pressure. The discussion emphasizes the significance of the partition function in calculating essential thermodynamic properties.
- 19.8: Pressure-Volume Work
- This page explains enthalpy (H) as a state function defined by H = U + PV, emphasizing its significance in heat exchange at constant pressure. It notes the relevance of pressure-volume work for gases and other work forms for different systems. The derivation indicates that ΔH relates to heat added (q_P), making enthalpy easier to measure than internal energy. The relationship between U and H is highlighted, particularly for gases, while they are approximately equal for condensed matter.
- 19.9: Heat Capacity is a Path Function
- This page explains the relationship between enthalpy and heat capacity at constant pressure through differentiation. It highlights the method of measuring heat capacity as a function of temperature to determine enthalpy, while noting challenges such as the need for reference points and complications during phase transitions, where enthalpy changes suddenly.
- 19.10: Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition
- This page explains enthalpy, focusing on the significance of changes in enthalpy (ΔH) rather than absolute values. It covers three processes: heating ice, melting, and heating water, including related ΔH calculations.
- 19.11: Enthalpy Changes for Chemical Equations are Additive
- This page explains Hess's Law, which states that enthalpy changes in a chemical reaction are additive due to enthalpy being a state function. It allows for the calculation of reaction heat, even for challenging reactions, and indicates that reversing a reaction changes the sign of enthalpy. The law is essential for estimating enthalpy by combining known reaction heats and highlights the necessity of balancing equations correctly.
- 19.12: Heats of Reactions Can Be Calculated from Tabulated Heats of Formation
- This page discusses the significance of reaction enthalpies and the role of Hess' Law in their calculation using standard enthalpy of formation. It explains ionization potentials and electron affinities for atoms, emphasizing their sequential nature and the importance of the first few values.
- 19.13: The Temperature Dependence of ΔH
- This page describes methods for calculating thermodynamic functions, particularly enthalpy changes at various temperatures using Kirchhoff's Law. It explains the relationship between enthalpy and heat capacity, offers an empirical model for heat capacity, and illustrates the integration process for determining enthalpy changes with examples involving lead and ammonia. Additionally, it provides experimental parameters for various substances to aid in these calculations.
- 19.14: Enthalpy is a State Function
- This page explains the relationship between heat (q_P), internal energy (ΔU), and pressure-volume work (PΔV) at constant pressure. It rearranges the expression for internal energy to show that heat can be represented as a change in enthalpy (H), defined as H = U + PV, thereby establishing enthalpy as a significant state function in thermodynamics.
- 19.E: The First Law of Thermodynamics (Exercises)
- This page discusses Werner Heisenberg's 1920s uncertainty principle, which highlights the inverse relationship between the precision of a quantum particle's position and momentum. The principle stems from the wave nature of matter, implying that accurate localization of quantum particles is impossible.
Thumbnail: A thermite reaction using iron(III) oxide. The sparks flying outwards are globules of molten iron trailing smoke in their wake. (CC SA-BY 3.0; Nikthestunned).