# 8.7: Standard State Heat Capacities

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

We have observed that $$C_V$$ depends on volume and temperature, while $$C_P$$ depends on pressure and temperature. Compilations of heat capacity data usually give values for $$C_P$$, rather than $$C_V$$. When the temperature-dependence of $$C_P$$ is known, such compilations usually express it as an empirical polynomial function of temperature. In Chapter 10, we find an explicit function for the dependence of $$C_P$$ on pressure:

${\left(\frac{\partial C_P}{\partial P}\right)}_T=-T{\left(\frac{{\partial }^2V}{\partial T^2}\right)}_P$

If we have an equation of state for a substance, we can find this pressure dependence immediately. It is usually negligible. For ideal gases, it is zero, and $$C_P$$ is independent of pressure.

Compilations often give data for the standard state heat capacity, $$C^o_P$$, at a specified temperature. For condensed phases, this is the heat capacity for the substance at one bar. For gases, this is the heat capacity of the substance in its ideal gas standard state.

300 K 400 K $$\boldsymbol{a}\left(\mathrm{J}\right)$$ $$b\left(\mathrm{J}\boldsymbol{\ }{\mathrm{K}}^{-\boldsymbol{1}}\right)$$
C_s 0 0 -1.482 0.03364
$${\boldsymbol{H}}_{\boldsymbol{2}}\left(\boldsymbol{g}\right)$$ 0 0 27.853 0.00332
$${\boldsymbol{O}}_{\boldsymbol{2}}\left(\boldsymbol{g}\right)$$ 0 0 27.221 0.00722
$${\boldsymbol{CH}}_{\boldsymbol{4}}\left(\boldsymbol{g}\right)$$ -74.656 -77.703 21.167 0.04866
$${\boldsymbol{CH}}_{\boldsymbol{3}}\boldsymbol{OH}\left(\boldsymbol{g}\right)$$ -201.068 -204.622 21.737 0.07494

8.7: Standard State Heat Capacities is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Paul Ellgen via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.