# Definition of Constant V and P Heat Capacities

The Constant Pressure Heat Capacity is definied by:
The Constant Volume Heat Capacity is defined by:
The Constant Volume Specific Heat is defined by:
The Constant Pressure Specific Heat is defined by:
The Heat Capacity Ratio is defined by:

The molar heat capacity of a substance is defined as the energy required to raise the temperature of a mole of a substance by one degree.

The specific heat of a substance is defined as the energy required to raise the temperature of a unit mass of a substance by one degree.

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### Ch 3, Lesson C, Page 2 - Definition of Constant V and P Heat Capacities

• Heat capacities are defined for two different types of processes. Cp is the heat capacity of a substance undergoing a process at constant pressure and Cv is the heat capacity of a substance undergoing a process at constant molar volume.
• For each of these two types of processes, two different heat capacities are commonly used.
• Molar Heat capacity or just heat capacity generally refers to the amount of energy required to heat up one mole of the substance by 1 degree.
• So, the units are often J/mole-K or kJ/mole-K or Btu/lbmole-oR.
• The amount of energy required to heat up a unit mass of a substance by one degree is called the specific heat.
• The units of specific heat might be cal/g-oC or Btu/lbm-oF or kJ/kg-K.
• The specific heat is just the heat capacity multiplied by the molecular weight.
• As a result, many engineers and scientists do not differentiate between the specific heat and the heat capacity.  The two terms are often used interchangeably.  The bottom line is that you need to keep your eyes on the UNITS.  That way you can be sure whether you really have a specific heat or a heat capacity !
• The mathematical definitions of heat capacity and specific heat are shown here.
• Remember that constant volume heat capacity is the rate at which the internal energy changes as the temperature changes in a constant volume process.
• The subscript V means constant molar volume.
• The constant pressure heat capacity is the rate at which the enthalpy changes as the temperature changes in a constant pressure process.
• The subscript P means constant pressure.
• Last, we define the heat capacity ratio, gamma.  Gamma is Cp over Cv.
• Since the moles or masses cancel, you get the same value for gamma whether you use heat capacities or specific heats.
• Now, that we have some mathematical definitions to work with, let’s see why heat capacities are useful.