Heat Capacities of Liquids and Vapors

By the use of an equation previously derived for the energy of vaporization of a liquid: ΔE=k(D_lⁿ—D_gⁿ) (in which k is a constant; n=5/3, and D_l and D_g are the molar densities of liquid and vapor, respectively), an expression is derived relating (∂ΔE/∂T)_sat to the difference in molar heat capacities at constant pressure of the liquid and vapor (ΔC_p). At low pressures this relation can be approximated by the equation ΔC_p=(∂ΔE/∂T)_s+ R (R is the gas constant, 1.986 cal./mole‐°A). Under these conditions ${\mathrm{(\partial \Delta E/\partial T)}}_s\text{=(5/3)ΔE(∂\hspace{0.17em}}\ln D_l{\mathrm{/\partial T)}}_s$ , and the resulting equation for ΔC_p is ${\mathrm{\Delta C}}_p\text{=(5/3)ΔE(∂\hspace{0.17em}}\ln D_l{\mathrm{/\partial T)}}_s\text{+1.99}$ . From known properties of liquids ΔC_p can be calculated using this last equation. These calculated values are found to be in good agreement with observed experimental values.