The ratio of specific heats is a fundamental thermodynamic property of a gas, often denoted by the symbol gamma ($\gamma$) or sometimes $k$. This ratio is defined as the specific heat at constant pressure ($C_p$) divided by the specific heat at constant volume ($C_v$).

In thermodynamics, specific heat ($C$) refers to the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). There are two primary specific heats relevant to gases:

• Specific Heat at Constant Pressure (\(C_p\)): This is the heat required to raise the temperature of a unit mass of gas by one degree while keeping the pressure constant. When heat is added at constant pressure, the gas expands and does work, so more heat is needed compared to constant volume.
• Specific Heat at Constant Volume (\(C_v\)): This is the heat required to raise the temperature of a unit mass of gas by one degree while keeping the volume constant. In this case, no work is done by the gas against external pressure.

Ratio of Specific Heats for Air

The ratio of these two specific heats, $\gamma$, is given by the formula:

$$\gamma = \frac{C_p}{C_v}$$

This ratio is also known as the adiabatic index because it appears in the equations describing adiabatic processes (processes where no heat is exchanged with the surroundings).

Specific Heat Value for Air

Air is primarily composed of nitrogen ($\text{N}_2$) and oxygen ($\text{O}_2$), both of which are diatomic gases. For an ideal diatomic gas, the degrees of freedom ($f$) are typically considered to be 5 (3 translational and 2 rotational degrees of freedom at moderate temperatures). The theoretical value of $\gamma$ for an ideal gas can be related to its degrees of freedom using the formula:

$$\gamma = 1 + \frac{2}{f}$$

For a diatomic gas where $f=5$:

$$\gamma = 1 + \frac{2}{5} = 1 + 0.4 = 1.4$$

The experimentally determined value for the ratio of specific heats for air at standard conditions is very close to this theoretical value. It is commonly taken as approximately 1.41 (or sometimes 1.40). This value is crucial in many engineering calculations, especially in fields like aerodynamics, acoustics, and internal combustion engines.

Therefore, based on standard experimental values and theoretical understanding for diatomic gases like air, the ratio of the two specific heats of air is approximately 1.41.