2: Work, Heat, and the First Law
- Page ID
- 477356
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 2.1: Overview of Classical Thermodynamics
- Joule was able to show that work and heat can have the same effect on matter – a change in temperature! It would then be reasonable to conclude that heating, as well as doing work on a system will increase its energy content, and thus it’s ability to perform work in the surroundings. This leads to an important construct of the First Law of Thermodynamics: The capacity of a system to do work is increased by heating the system or doing work on it.
- 2.2: Pressure-Volume Work
- Work in general is defined as a product of a force FFF and a path element dsdsds. In the case of a cylinder, the movement of the piston is constrained to one direction, the one in which we apply pressure (\(P\) being force \(F\) per area \(A\)). We can therefore introduce the area of the piston, \(A\), and forget about the vectorial nature of force. This form of work is called pressure-volume (\(PV\)) work, and it plays an important role in the development of our theory.
- 2.3: Work and Heat are not State Functions
- Heat and work are both path functions: they depend on the path taken. In order to calculate the heat transfer or work being done on/by a system, the path taken must be known.
- 2.4: Thermodynamic Systems
- A thermodynamic system—or just simply a system—is a portion of space with defined boundaries that separate it from its surroundings (see also the title picture of this book). The surroundings may include other thermodynamic systems or physical systems that are not thermodynamic systems.
- 2.5: Internal Energy
- The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy. This is contrast to external energy which is a function of the sample with respect to the outside environment (e.g. kinetic energy if the sample is moving or potential energy if the sample is at a height from the ground etc).
- 2.6: The Joule Experiment
- Joule's experiment concluded that dq=0 (and dT=0) when a gas is expanded against a vacuum. And because dV>0 for the gas that underwent the expansion into an open space, the internal pressure must also be zero!
- 2.7: Enthalpy
- Enthalpy is defined as the sum of the internal energy and the product of the pressure times the volume: H = U + PV. Many experimental studies of enthalpy occur at constant pressure, under which conditions it can be shown that the change in enthalpy is the change in heat. In this section we will derive the relationship between enthalpy and heat, and then describe constant-pressure calorimetry experiments, introduce molar heat capacity at constant pressure, and then relate the constant-pressure an
- 2.8: Thermochemistry
- Thermochemistry is an extremely useful application of thermodynamics because it allows us to use previously gathered data to estimate the enthalpy changes of processes that we have not yet done, or that are unknown to us. The two most common applications are the use of Hess's Law to combine the enthalpy changes of entire chemical equations, and the combination of the enthalpy changes of formation of the pure substances involved in a process.
- 2.9: Reaction Enthalpies
- Reaction enthalpies are important, but difficult to tabulate. However, because enthalpy is a state function, it is possible to use Hess’ Law to simplify the tabulation of reaction enthalpies. Hess’ Law is based on the addition of reactions. By knowing the reaction enthalpy for constituent reactions, the enthalpy of a reaction that can be expressed as the sum of the constituent reactions can be calculated.
- 2.10: Lattice Energy and the Born-Haber Cycle
- An important enthalpy change is the lattice energy. This is the energy necessary to take one mole of a crystalline solid to ions in the gas phase. A very handy construct in thermodynamics is that of the thermodynamic cycle. This can be represented graphically to help to visualize how all of the pieces of the cycle add together. A very good example of this is the Born-Haber cycle, describing the formation of an ionic solid.
- 2.11: Energy Basics
- Energy is the capacity to do work (applying a force to move matter). Heat is energy that is transferred between objects at different temperatures; it flows from a high to a low temperature. Chemical and physical processes can absorb heat (endothermic) or release heat (exothermic). The SI unit of energy, heat, and work is the joule (J). Specific heat and heat capacity are measures of the energy needed to change the temperature of a substance or object.
- 2.12: Measuring Heat
- When we want to measure the heat added to a system, measuring the temperature increase that occurs is often the most convenient method. If we know the temperature increase in the system, and we know the temperature increase that accompanies the addition of one unit of heat, we can calculate the heat input to the system. Evidently, it is useful to know how much the temperature increases when one unit of heat is added to various substances.
- 2.13: Temperature Dependence of Enthalpy
- It is often required to know thermodynamic functions (such as enthalpy) at temperatures other than those available from tabulated data. Fortunately, the conversion to other temperatures isn’t difficult.
- 2.14: The Joule-Thomson Effect
- Joule and Thomson conducted an experiment in which they pumped gas at a steady rate through a lead pipe that was cinched to create a construction. A cooling was observed as the gas expanded from a high pressure region to a lower pressure region was extremely important and lead to a common design of modern refrigerators. Not all gases undergo a cooling effect upon expansion.
- 2.15: Adiabatic Changes
- As noted in Topic 2A, an adiabatic change is a change that occurs with no transfer of heat. In other words, under adiabatic conditions \(q =0\) and \(\Delta U = w_{ad}\). In this section, we will derive formulas to calculate the changes in temperature and the changes in pressure that occur during adiabatic changes.