Changes in State for Gases

Changes in state for a gas can be followed from one point to another in a p/V diagram. For real-life cases, three axes for the variables p, V and T are required. With a change in state, we are moved along a 3-dimensional curve on the surface in the p, V and T space. However, to simplify, we usually consider the projection of the curve in one of the three planes. This is usually the p/V plane. Five different changes in state can be considered:

1. Isochoric process (constant volume)
2. Isobaric process (constant pressure)
3. Isothermal process (constant temperature)
4. Isentropic process (without heat exchange with surroundings)
5. Polytropic process (complete heat exchange with the surroundings)

Heating a gas in an enclosed container is an example of the isochoric process at constant volume.

Heating a gas in a cylinder with a constant load on the piston is an example of the isobaric process at constant pressure.

If a gas in a cylinder is compressed isothermally, a quantity of heat equal to the applied work must be gradually removed. This is unpractical, as such a slow process cannot occur.

An isentropic process exists if a gas is compressed in a fully-insulated cylinder without any heat exchange with the surroundings. It may also exist if a gas is expanded through a nozzle so quickly that no heat exchange with the surroundings has time to occur.

The isothermal process involves full heat exchange with the surroundings and the isotropic process involves no heat exchange whatsoever. In reality, all processes occur somewhere in between these extreme: the polytropic process. The relation for such a process is: