20.14:
Adiabatic Processes for an Ideal Gas
A thermodynamic process with no heat transfer inside or outside the system is termed adiabatic.
Thus, according to the first law of thermodynamics, the change in internal energy is the negative of the work done in an adiabatic process.
For instance, a fire piston consisting of a thermally insulated tube has one end closed, and the other end has a movable plunger.
If a small piece of cotton ball is placed inside the tube and the plunger is allowed to push down rapidly at room temperature, the cotton ball catches fire despite no heat being applied. This happens due to adiabatic compression.
Here, as the volume decreases, the work done becomes negative; hence, the internal energy change is positive, with a corresponding increase in gas temperature.
Conversely, when opening a bottle of cooled carbonated drink, the gas trapped in the bottle undergoes adiabatic expansion, resulting in the work done being positive.
As a result, the internal energy decreases with a corresponding temperature drop, condensing the evaporated vapor into a visible cloud.
20.14:
Adiabatic Processes for an Ideal Gas
When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its temperature does rise significantly. In fact, the temperature increase can be so large that the mixture can explode without the addition of a spark. Such explosions, since they are not timed, make a car run poorly—it usually “knocks.” As the ignition temperature rises with the octane of the gasoline, the usage of higher-octane gasoline is one way to overcome this issue.
Another interesting adiabatic process is the free expansion of a gas. Imagine a gas is confined by a membrane to one side of a two-compartment, thermally insulated container. When the membrane is punctured, the gas rushes into the empty side of the container, thereby expanding freely. As the gas expands “against a vacuum”, the pressure decreases (p = 0), it does no work, and, because the vessel is thermally insulated, the expansion is adiabatic. With Q = 0 and W = 0 in the first law, dU = 0, so the internal energy in the initial and final equilibrium states is the same for the free expansion. If the gas is ideal, the internal energy depends only on the temperature. Therefore, when an ideal gas expands freely, its temperature does not change.
Suggested Reading
- Young, H.D. and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. P. 640.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-2/pages/3-6-adiabatic-processes-for-an-ideal-gas