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@wikipedia


Universal relation between Isobaric molar heat capacity (cP) and  Isochoric molar heat capacity (cV):

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anchorMAYER
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 c_P - c_V = V_m \, T \, \frac{\alpha_V^2}{\beta_T}

where


LaTeX Math Inline
bodyT
temperature

LaTeX Math Inline
bodyV_m

molar volume

LaTeX Math Inline
body\beta_T

isothermal compressibility

LaTeX Math Inline
body\alpha_V

thermal expansion coefficient


For incompressible substances the Isobaric molar heat capacity (cP) and  Isochoric molar heat capacity (cV) are identical:

LaTeX Math Block
anchor1GBHB
alignmentleft
 c_P = c_V


For the ideal gas it will take a form:

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anchorIDEALGAS
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 c_P - c_V = R

where

LaTeX Math Inline
bodyR

Gas constant


See also


Physics / Thermodynamics / Thermodynamic processHeat Transfer / Heat Capacity / Molar heat capacity

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