3.4: Specific Heat
- Page ID
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Latent heat is the term for the amount of heat released from changes in phase, but what about changes in temperature unassociated with phase changes? These portions are the slanted lines in the figure above where energy is going into the system and the temperature is responding. Specific heat or heat capacity (\(C\)) is the term for the amount of heat required to raise the temperature of a substance by a certain amount. Typically this is defined at a constant pressure (\(C_p\)) or a constant volume (\(C_v\)).
Some substances, such as water, require a particularly large amount of heat energy in order for the temperature to change. The heat capacity of a substance is the ratio of heat energy that is absorbed to the corresponding rise in temperature. The specific heat is the heat capacity of a substance per a unit mass. Basically, specific heat is the amount of heat that is needed in order to raise the temperature of one gram (g) of a substance by one degree Celsius, or Kelvin.
For example, the specific heat of pure water is 4186 Joules per degree Kelvin per kilogram (J·K-1·kg-1), while the specific heat of dry air at sea level (\(C_{pd}\)) is about 1004 J·K-1·kg-1. The specific heat of dry air at constant volume (\(C_{vd}\)) is equal to 717 J·kg–1·K-1. This means that it takes much more energy to raise 1 kg of water by 1°C than it does for 1 kg of dry air. Remember that Celsius and Kelvin have a linear relationship so the change in temperature of one degree Celsius is the same as a change of one degree Kelvin (\(K = { }^{\circ} \mathrm{C}+273\)).
The difference in specific heat capacity of water and land leads to different annual cycles of air temperature and water temperature in Hawaii. The heat capacity of sea water is about 3985 J·K-1·kg-1 while the heat capacity of land is typically less than 1000 J·K-1·kg-1. This means that land heats up faster and cools down faster while the ocean takes longer to warm and also takes longer to cool.
The warmest temperatures in Hawaii typically follow the solar cycle with a slight lag. The warmest temperatures in the Northern Hemisphere occur during the time periods where the Sun’s angle is highest and the length of day is longest as we discussed in Chapter 2. This typically corresponds to June through August. However, the warmest ocean temperatures lag the land temperatures significantly by a few months because water takes more energy to warm. The warmest ocean temperatures occur from August through October.
There is some feedback where the warm ocean temperatures affect land temperatures as well, but it all comes down to the difference in specific heat.