During an adiabatic process the pressure of a gas is found...

During an adiabatic process the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_{p} / C_{V}$ for the gas is
(a) $\frac{3}{2}$
(b) $\frac{4}{3}$
(c) 2
(d) $\frac{5}{3}$

Key Concepts

Ideal Gas Behavior

Ideal gas behavior is based on the ideal gas law, which relates pressure, volume, and temperature of a gas under the assumption that the gas molecules do not interact except through elastic collisions. This model simplifies the analysis of thermodynamic processes and allows for clear derivations of relationships, such as those observed in adiabatic transformations.

Adiabatic Index

The adiabatic index, denoted by ? (gamma), is defined as the ratio of the specific heats at constant pressure and constant volume (C?/C?). This ratio is critical in characterizing adiabatic processes in ideal gases, as it determines the proportional relationships among pressure, volume, and temperature during such processes.

Specific Heats

Specific heats refer to the quantities C? and C?, which are the amounts of heat required to raise the temperature of a unit mass of a substance by one degree at constant pressure and constant volume, respectively. These properties are intrinsic to the substance and are fundamental in analyzing energy changes during various thermodynamic processes.

Adiabatic Process

An adiabatic process is a thermodynamic transformation in which the system exchanges no heat with its surroundings, so any change in its internal energy is solely due to work done. This property leads to unique relationships among pressure, volume, and temperature compared to processes where heat transfer occurs.

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