Ideal Gases in Adiabatic Processes

Definition: Adiabatic Process

An adiabatic process is a process in which no heat flows into or out of the gas.

$$Q=0$$

Theorem: Pressure and Volume in an Adiabatic Process

The pressure $p$ and volume $V$ of an ideal gas in an adiabatic process are related by

$$p{V}^{\gamma }=\text{const},$$

where $\gamma =\frac{C_p}{C_V}$ is the ratio of the gas’s molar heat capacity in an isobaric process to its molar heat capacity in an isohoric process.

PROOF

TODO