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

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

where

temperature

molar volume

Isothermal Compressibility

thermal expansion coefficient


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

 c_P = c_V


For the ideal gas it will take a form:

 c_P - c_V = R

where

Gas constant


Both 
incompressible matter and ideal gas are idealistic models but some real mattes come very close to conditions of  or  at engineering level of accuracy.

See also


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

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