In this case, the system and the surroundings are not in equilibrium and work done by the gas in expanding is W = ∫PextdV which is not the negative of the work done by the surroundings because of this pressure difference over the boundary. The surroundings applies a force F = PextA on the system so for the gas to expand it must do work against this force.kelvin490 said:If the external pressure is not equal to the system's pressure, how to evaluate the work done?
Yes, the external pressure is zero (vacuum) so typically the gas expands into a container and there is nothing preventing it from doing so. So no force on the gas from the surroundings, no work done.In addition, we know that in free expansion the work done by the system and the surrounding are zero. Is it due to the fact that W = -∫PdV where P is the external pressure?
CAF123 said:In this case, the system and the surroundings are not in equilibrium and work done by the gas in expanding is W = ∫PextdV which is not the negative of the work done by the surroundings because of this pressure difference over the boundary. The surroundings applies a force F = PextA on the system so for the gas to expand it must do work against this force.
I think that would only true if they were constantly in equilibrium throughout the process. In which case there is a well-defined pressure and Wgas on surr = ∫PsurrdV = -Wsurr on gas = ∫PgasdV if Pgas = Psurr. Perhaps someone else could clarify this though.kelvin490 said:Does it mean that the work done by the gas and that done by the surrounding have equal magnitude W= ∫PextdV but just different sign (assume massless piston)
If the set up is vertical, then as the gas expands the piston gains gravitational potential energy. This energy will have to be supplied by the gas.What if the piston is not massless?
This all depends on what you call the system. If the system is the gas, then the Pext is the force per unit area on the base of the piston, and the piston is regarded as part of the surroundings. If the system also includes the piston, then Pext is the force per unit area on the top of the piston, and the piston is regarded as part of the system and not part of the surroundings.kelvin490 said:Thanks both, your answers are very useful. Now I know that W= ∫PextdV because we can only be sure what the external pressure is, while the internal pressure varies spatially. By conservation of energy if we figure out the work received by surrounding we know the work done by the system.
Now I am interested in the case that the piston consumed some of the energy during expansion. If the piston gains PE or have friction, that means the work done by the system equals the energy consumed by piston plus the work done on surrounding. If we use W= ∫PextdV would we underestimate the work done by the gas?
The problem of gas expansion refers to the behavior of gases when they are heated or cooled. When a gas is heated, its molecules gain kinetic energy and move faster, causing the gas to expand. Conversely, when a gas is cooled, its molecules lose energy and move slower, causing the gas to contract.
The problem of gas expansion is important in science because it helps us understand and predict the behavior of gases in various situations. It is also a key concept in many scientific fields such as chemistry, physics, and meteorology.
The relationship between temperature and gas expansion is direct. As the temperature of a gas increases, its volume also increases, and vice versa. This relationship is described by Charles' Law, which states that at a constant pressure, the volume of a gas is directly proportional to its absolute temperature.
The problem of gas expansion affects everyday life in many ways. For example, it explains why a balloon expands when it is filled with hot air and shrinks when it is placed in a cold environment. It also plays a role in weather patterns, as changes in temperature can cause air to expand and rise, leading to changes in air pressure and precipitation.
Yes, the problem of gas expansion can be controlled and manipulated. In fact, many everyday devices such as refrigerators and air conditioners rely on this principle to function. By changing the temperature and pressure of a gas, we can control its volume and use it for various practical purposes.