Thermodynamics
Heat Capacity Relation
Mayer relation: C_p is always greater than C_v by R for ideal gases.
Variables
C_pJ/(mol·K)
Heat capacity (constant P)
Molar heat capacity at constant pressure
C_vJ/(mol·K)
Heat capacity (constant V)
Molar heat capacity at constant volume
RJ/(mol·K)
Gas constant
8.314
Derivation
At constant P, heat goes to both internal energy and work: C_p = (∂H/∂T)_p = C_v + R.
Your notes
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Common questions
What is the Heat Capacity Relation formula?
Heat Capacity Relation is written Cₚ = Cᵥ + R. Mayer relation: C_p is always greater than C_v by R for ideal gases. It belongs to Thermodynamics, under First Law.
What are the units in Cₚ = Cᵥ + R?
In SI units, C_p is heat capacity (constant p), measured in kg·m²/(s²·mol·K); C_v is heat capacity (constant v), measured in kg·m²/(s²·mol·K); R is gas constant, measured in kg·m²/(s²·mol·K).
How is the Heat Capacity Relation formula derived?
At constant P, heat goes to both internal energy and work: C_p = (∂H/∂T)_p = C_v + R. The result is Cₚ = Cᵥ + R.