Free Expansion of an Ideal Gas

Free expansion of an ideal gas refers to the process in which a gas expands into a vacuum without any external work being done on it. This means that there are no forces acting on the gas, and as a result, the gas molecules can freely move and expand in all directions.

During free expansion, the gas expands rapidly and fills the available space. This process is irreversible, and the gas undergoes a change in volume, temperature, and pressure.

Free Expansion under Adiabatic Conditions

During free expansion under adiabatic conditions, the internal energy of the gas remains constant. This is because there is no heat transfer occurring between the gas and its surroundings. The absence of any external work being done on the gas also means that there is no change in the kinetic energy of the gas molecules.

The lack of heat transfer and external work during free expansion results in an isentropic process. This means that the entropy of the gas remains constant during the expansion.

Free Expansion under Isothermal Conditions

During free expansion under isothermal conditions, the temperature of the gas remains constant. This is because heat is allowed to transfer between the gas and its surroundings, keeping the temperature constant.

Although the temperature remains constant, the expansion still leads to a decrease in pressure and increase in volume. This is due to the fact that the gas molecules are spreading out into a larger space, resulting in a decrease in the frequency of collisions and therefore a decrease in pressure.

The internal energy of the gas also remains constant during free expansion under isothermal conditions. This is because the temperature remains constant, and there is no change in the average kinetic energy of the gas molecules.

Summary

- Free expansion of an ideal gas refers to the process in which a gas expands into a vacuum without any external work being done on it.
- During free expansion under adiabatic conditions, the internal energy of the gas remains constant, and the process is isentropic.
- During free expansion under isothermal conditions, the temperature of the gas remains constant, and the process leads to a decrease in pressure and increase in volume.
- In both cases of free expansion, the internal energy of the gas remains constant.