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@wikipedia


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

LaTeX Math Block
anchorMAYER
alignmentleft
 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 matter the Isobaric molar heat capacity (cP) and Isochoric molar heat capacity (cV) are identical:

LaTeX Math Block
anchorcompress
alignmentleft
 c_P = c_V


For the ideal gas it will take a form:

LaTeX Math Block
anchorIDEALGAS
alignmentleft
 c_P - c_V = R

where

LaTeX Math Inline
bodyR

Gas constant


Both 
incompressible matter and ideal gas are idealistic models but some real mattes come very close to conditions of 

LaTeX Math Block Reference
anchorcompress
 or 
LaTeX Math Block Reference
anchorIDEALGAS
 at engineering level of accuracy.

See also


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

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