8.1: Thermodynamic Properties
- Page ID
- 19315
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A container of air of fixed mass confined to a volume stores energy. We can shrink the volume of the air. This process requires energy, and the shrunken volume of air stores more energy. We can increase the gas pressure, for example, by exerting a force on a piston within which air is confined. This process requires energy, and the air under pressure stores more energy. We can take the fixed volume of air and heat it too. It takes energy to heat the air, and the hotter air stores more energy. Similarly, we can shake the container of air. Again, this process requires energy, and the energy from shaking is stored in the internal energy, the random motion, of the air molecules.
To talk about thermodynamic energy conversion, we need to define four fundamental properties of a system: volume, pressure, temperature, and entropy. All of these properties depend on the current state, not the past history, of the sample. These properties can be classified as intensive or extensive [2, p. 10]. An intensive property is independent of the size or extent of the material. An extensive property depends on the size or extent [2, p. 10].
| Units for Pressure |
|---|
| 1 \(\frac{N}{m^2}\) = 1 Pa |
| 1 bar = \(10^5\) Pa |
| 1 mmHg= 133.322 Pa |
| 1 atm = 101 325 Pa |
| 1 psi = \(6.894757 \cdot 10^3\) Pa |
Volume \(\mathbb{V}\) is an extensive property measured in \(m^3\) or liters where \(1 L = 0.001 m^3\). Pressure \(\mathbb{P}\) is an intensive property measured in the SI units of pascals where 1 Pa = \(1\frac{N}{m^2}\). Pressure is also measured in a wide variety of other, non-SI, units such as bars, millimeters of mercury, or standard atmospheres as listed in Table \(\PageIndex{1}\). Pressure measures are often specified in comparison to the lowest possible pressure, of a complete vacuum, and such pressure measurements are called absolute pressure measurements [102, p. 15-17]. In some cases, values are specified as the difference above the local atmospheric pressure, and these measurements are called gauge pressure measurements [102, p. 15-17]. In other cases, values are specified as the difference below the local atmospheric pressure, and these measurements are called vacuum pressure measurements [102, p. 15-17]. Unless otherwise specified, the term pressure in this text refers to absolute pressure, not gauge or vacuum pressure.
| Symbol | Quantity | Unit | Ext/int |
|---|---|---|---|
| \(\mathbb{V}\) | Volume | \(m^3\) | Extensive |
| \(\mathbb{P}\) | Pressure | Pa | Intensive |
| \(S\) | Temperature | K | Intensive |
| \(T\) | Entropy | \(\frac{J}{K}\) | Extensive |
| Symbol | Name | Value and Unit |
|---|---|---|
| \(k_B\) | Boltzmann constant | \(1.381 \cdot 10^{-23} \frac{J}{K}\) |
| \(\mathbb{R}\) | Molar gas constant | \(8.314 \frac{J}{mol \cdot K}\) |
| \(N_a\) | Avogadro constant | \(6.022 \cdot 10^{23} \frac{1}{mol}\) |
Temperature \(T\) is an intensive property measured in either the SI units of degrees Celsius or kelvins. By definition, we can relate the two units by
\[T_{\left[^{\circ} \mathrm{C}\right]}=T_{[\mathrm{K}]}-273.15 \nonumber \]
[68]. We can also measure temperature in the non-SI unit of degrees Fahrenheit. Temperature in degrees Celsius and temperature in degrees Fahrenheit are related by
\[T_{[^{\circ} \mathrm{C}]} = \left( \frac{T_{[^{\circ} \mathrm{F}]} - 32}{1.8} \right) . \nonumber \]
As with absolute pressure measurements, temperature in kelvins is said to be measured on an absolute temperature scale because the lowest possible temperature is given by zero kelvin. All temperatures are either absolute zero or have positive values. We use the term temperature to describe a property of a system. We use the term heat transfer to describe the process of transferring energy from a hot to a cold object. Entropy \(S\) is measured in units \(\frac{J}{K}\), and it is an extensive property. Intuitively, entropy is a measure of the lack of order or organization of a material. The atoms in an amorphous material are less ordered than the atoms in a crystal of the same composition, so the amorphous material has more entropy.
Some further definitions will be needed. The symbol \(\mathbb{N}\) represents the number of atoms or molecules of a substance. While it is not usually considered a fundamental thermodynamic property, it is a useful property of a sample. Sometimes it is specified in the units of mols instead of by the number of atoms or molecules. The Avogadro constant
\[N_a = 6.022 \cdot 10^{23} \frac{1}{mol} \nonumber \]
is a constant which is used to convert a number given to the number per mol. The molar gas constant is
\[\mathbb{R} = 8.314 \frac{J}{mol \cdot K}. \nonumber \]
The Boltzmann constant is
\[k_B = 1.381 \cdot 10^{-23} \frac{J}{K}. \nonumber \]
These three constants are related by
\[k_B = \frac{\mathbb{R}}{N_a}. \nonumber \]