6.2: Definition of Temperature
- Page ID
- 30066
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Many physical processes depend on temperature. A few can be used to define absolute temperature \(T\). The unit of \(T\) is the kelvin, which has the symbol K. The fundamental processes used for defining an absolute temperature scale over the range of temperatures found in the ocean include (Soulen and Fogle, 1997): 1) the gas laws relating pressure to temperature of an ideal gas with corrections for the density of the gas; and 2) the voltage noise of a resistance \(R\).
The measurement of temperature using an absolute scale is difficult, and the measurement is usually made by national standards laboratories. The absolute measurements are used to define a practical temperature scale based on the temperature of a few fixed points and interpolating devices which are calibrated at the fixed points.
For temperatures commonly found in the ocean, the interpolating device is a platinum-resistance thermometer. It consists of a loosely wound, strain-free, pure platinum wire whose resistance is a function of temperature. It is calibrated at fixed points between the triple point of equilibrium hydrogen at 13.8033 K and the freezing point of silver at 961.78 K, including the triple point of water at 0.060\(^{\circ}\)C, the melting point of Gallium at 29.7646\(^{\circ}\)C, and the freezing point of Indium at 156.5985\(^{\circ}\)C (Preston-Thomas, 1990). The triple point of water is the temperature at which ice, water, and water vapor are in equilibrium. The temperature scale in kelvin, \(T\), is related to the temperature scale in degrees Celsius, \( t[^{\circ}\text{C}]\), by: \[t[^{\circ}\text{C}] = T [\text{K}] - 273.15 \nonumber \]
The practical temperature scale was revised in 1887, 1927, 1948, 1968, and 1990 as more accurate determinations of absolute temperature became accepted. The most recent scale is the International Temperature Scale of 1990 (ITS-90). It differs slightly from the International Practical Temperature Scale of 1968 (IPTS-68\). At 0\(^{\circ}\)C they are the same, and above 0\(^{\circ}\)C ITS-90 is slightly cooler. \(t_{90} - t_{68} = -0.002\) at 10\(^{\circ}\)C, \(-0.005\) at 20\(^{\circ}\)C, \(-0.007\) at 30\(^{\circ}\)C, and \(-0.010\) at 40\(^{\circ}\)C.
Notice that while oceanographers use thermometers calibrated with an accuracy of a millidegree, which is 0.001\(^{\circ}\)C, the temperature scale itself has uncertainties of a few millidegrees.