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@wikipedia


Amount of of 
heat to  to be supplied to a given amount of a material to produce a unit change in its its temperature:

LaTeX Math Block
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 C =  \frac{\delta Q}{\delta T} 
SymbolDimensionSI unitsOil metric unitsOil field units

LaTeX Math Inline
bodyC

M L2 T−2 Θ−1J/KJ/K

 BTU/°F°R


Heat Capacity depends on the way the 
heat is  is transferred and as such is not a table property of the matter.


The two major
 heat transfer processes are isobaric and isohoric which define which result in different values of heat capacity:

C_V
LaTeX Math Inline
body

Isobaric heat capacity (CP)

Isochoric heat capacity

LaTeX Math Inline
bodyC_p

(CV)


Both
 

LaTeX Math Inline
bodyC_
p
P
 
and 
LaTeX Math Inline
bodyC_V
 are proportional to
the the amount of the matter chemical substance involved in a Heat Transferheat transfer process and as such are not the material properties.

The ratio 

LaTeX Math Inline
body\gamma = C_P/C_V
 is called a Heat Capacity Ratio (γ) or Adiabatic Index (γ) or Isentropic expansion factor (κ) and is a material property.


Based on Mayer's relation the Isobaric heat capacity is always greater than Isochoric heat capacity:

LaTeX Math Block
anchor1
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C_P \geq C_V


One can relate them to material properties through the known material mass  

LaTeX Math Inline
bodym
 or a material volume 
LaTeX Math Inline
bodyV
 or material amount of substance 
LaTeX Math Inline
body\nu
:

Molar Heat Capacity Specific heat capacityVolumetric Heat Capacity
Molar Heat Capacity 
LaTeX Math Block
anchorcMol
alignmentleft
c = C/\nu
LaTeX Math Block
anchorcm
alignmentleft
c_m = C/m
LaTeX Math Block
anchorcV
alignmentleft
c_
V
v = C/V


Overall, there are totally six different intensive physical properties related to heat capacity:


Molar Heat Capacity Specific heat capacityVolumetric Heat Capacity
Isobaric (V= const)

Isobaric molar heat capacity 

LaTeX Math Block
anchor
cMol
1
alignmentleft
c_
M
P = C_P/\nu
Isobaric specific heat capacity
LaTeX Math Block
anchor
Cp
1
alignmentleft
C_p= m \cdot
c_{
mp
Pm} = 
V \cdot c_{vp}
C_P/m
Isobaric volumetric heat capacity
LaTeX Math Block
anchor
KMZQT
1
alignmentleft
C_V= m \cdot
c_{
mV
Pv} = 
V \cdot c_{vV}
C_P/V
Isochoric (P = const)

Isochoric molar heat capacity

LaTeX Math Block
anchor
KMZQT
1
alignmentleft
C
c_V = 
m \cdot c_{mV} = V \cdot c_{vV}

LaTeX Math Inline
body--uriencoded--c_%7Bmp%7D

Isobaric specific heat capacity

LaTeX Math Inline
body--uriencoded--c_%7BmV%7D

Isochoric specific heat capacity

LaTeX Math Inline
body--uriencoded--c_%7Bvp%7D

Isobaric volumetric heat capacity

LaTeX Math Inline
body--uriencoded--c_%7BvV%7D

Isochoric volumetric heat capacity
C_V/\nu
Isochoric specific heat capacity
LaTeX Math Block
anchor1
alignmentleft
c_{Vm} = C_V/m
Isochoric volumetric heat capacity
LaTeX Math Block
anchor1
alignmentleft
c_{Vv} = C_V/V


See also

...

Physics / Thermodynamics / Thermodynamic process / Heat Transfer

...

Specific heat capacity ] Volumetric Heat Capacity ][ Molar Heat Capacity ][ Mayer's relation ]