Heat capacity ratio

In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas or κ (kappa), the isentropic exponent for a real gas. The symbol γ is used by aerospace and chemical engineers.

γ

=

C

P

C

V

=

C

¯

P

C

¯

V

=

c

P

c

V

,

{\displaystyle \gamma ={\frac {C_{P}}{C_{V}}}={\frac {{\bar {C}}_{P}}{{\bar {C}}_{V}}}={\frac {c_{P}}{c_{V}}},}

where C is the heat capacity,

C

¯

{\displaystyle {\bar {C}}}

the molar heat capacity (heat capacity per mole), and c the specific heat capacity (heat capacity per unit mass) of a gas. The suffixes P and V refer to constant-pressure and constant-volume conditions respectively.

The heat capacity ratio is important for its applications in thermodynamical reversible processes, especially involving ideal gases; the speed of sound depends on this factor.

Thought experiment

To understand this relation, consider the following thought experiment. A closed pneumatic cylinder contains air. The piston is locked. The pressure inside is equal to atmospheric pressure.