Heat Capacity Relation
Mayer relation: C_p is always greater than C_v by R for ideal gases.
Variables
Derivation
At constant P, heat goes to both internal energy and work: C_p = (∂H/∂T)_p = C_v + R.
Your notes
Constants in this formula
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- Cv = 2 J/(mol·K) (Heat capacity (constant V))
- R = 8.314 462 618… J/(mol·K) (Gas constant)
Result: Cp = 10.314463 J/(mol·K)
Other thermodynamics formulas with the same quantities
- Work (Isothermal Process) (First Law) shares Gas constant
- Internal Energy (Ideal Gas) (First Law) shares Gas constant
- Ideal Gas Law (Kinetic Theory) shares Gas constant
- Root Mean Square Speed (Kinetic Theory) shares Gas constant
- Entropy Change (Ideal Gas) (Entropy) shares Gas constant
- Most Probable Speed (Kinetic Theory) shares Gas constant
Where this formula is listed
- Thermodynamics formulas, under First Law, alongside Work Done by Gas, Work (Adiabatic Process) and Enthalpy.
- In the thermodynamics list it comes after Adiabatic Process and before Work (Adiabatic Process).
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Heat Capacity Relation formula?
Heat Capacity Relation is written C_p = C_v + 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 C_p = C_v + 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 C_p = C_v + R.