8.4: First Law of Thermodynamics
- Page ID
- 18986
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The idea of energy conservation was introduced in Sec. 1.3. Most discussions of thermodynamics also begin with the same idea. The rst law of thermodynamics is a statement of energy conservation. Energy can be stored in the material polarization of a capacitor, the chemical potential of a battery, and in many other forms. People studying thermodynamics and heat transfer, however, often make some drastic assumptions. They classify all energy conversion processes as heat transfer or other where the primary component of the latter is mechanical work. At the beginning of introductory thermodynamics courses, all forms of energy besides heat transfer and mechanical work are ignored. Charging a capacitor, discharging a battery, and all other energy conversion processes are grouped in with mechanical work when writing the rst law of thermodynamics. The rst law of thermodynamics is typically written as
\[\text{(change in int. energy) = (heat in) − (work and other forms)}. \nonumber \]
\[\Delta \mathbb{U} = \mathbb{Q} - W \label{8.4.2} \]
Each term of the Equation \ref{8.4.2} has the units of joules. The symbol \(\mathbb{Q}\) represents the energy supplied in to the system by heating, and \(-W\), with the minus symbol, represents the mechanical work in to the system as well as all other forms of energy into the system. The quantity \(\Delta \mathbb{U}\) represents the change in internal energy of the system. In a closed system the total energy is conserved. In a closed system, energy is either stored in the system (for example as potential energy or another form of internal energy), is transfered in or out as heat, or is transfered in or out as another form such as mechanical work [109, p. 51].
As an example, consider the closed system shown on the left part of Fig. \(\PageIndex{1}\) comprised of a cylinder with a piston and a heater. Assume the cylinder contains a fixed volume of gas inside. Suppose the heater is used to transfer 100 J of energy into the piston in an hour while the piston is forced to remain in a fixed position. After the hour, the internal energy of the gas will be 100 J greater than before. Again suppose the heater is used to transfer 100 J of energy into the gas, but this time assume the piston is allowed to move thereby expanding the gas volume. After the hour, the internal energy of the gas will be the original energy of the gas, plus the 100 J supplied by the heater, and minus a factor due to the mechanical work done by the piston.
The first law of thermodynamics says two things. First, energy is conserved. Second, energy can be stored, converted to mechanical work, or converted to heat. We know energy can be converted to other forms too, like electrical or electromagnetic energy. While introductory thermodynamics classes do not usually do so, we can add other devices to the piston as shown on the right part of Fig. \(\PageIndex{1}\). We can include a battery and put a resistor inside to convert the chemical energy to electrical energy, and the resistor can heat the air in the piston. We can put a mass and a spring in the piston and convert potential energy of a compressed spring to kinetic energy by removing a clip which holds the spring compressed. In a closed system when all energy conversion processes are considered, energy must be conserved.