Path Dependent Work
Path Dependent Work - Related Videos
01:22
Mean free path and Mean free time
0 Views •
2025
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path." The mean free path varies inversely with the density of the molecules because when there are more molecules inside a volume, they have a greater chance of colliding with each other, thus reducing the mean free path. Additionally, the mean free path is inversely related to...
01:21
Path Between Thermodynamics States
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2023
Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1: In the first process for path A to C, the gas is kept at constant temperature T. It undergoes an expansion from volume V1 to V2. The work done by an ideal gas is expressed as Substituting for pressure as nRT/V from the ideal gas equation and integrating the terms, the work done by an ideal gas at constant temperature is obtained as In the second process, for path A to B, the...
07:26
Foraging Path-length Protocol for Drosophila melanogaster Larvae
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Cited by 18 •
2016
We provide a detailed protocol for a Drosophila melanogaster foraging path-length assay. We discuss the preparation and handling of test animals, how to perform the assay and analyze the data.
03:48
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion
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2020
Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
01:10
Interference: Path Lengths
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2023
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same. Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
FAQs
The calculation must follow the object's actual trajectory. At each point, the force contributes according to its component along the small displacement, and these contributions are summed through an integral along the route. When the force changes with position or represents a nonconservative interaction, two routes connecting the same endpoints can therefore produce different total work.
Friction makes the specific route important because it is a nonconservative interaction. As an object moves over a rough surface, the associated work cannot be represented solely by a potential energy determined by the endpoints. Accounting for that contribution requires tracking energy transferred through heat or other forms, which identifies the dissipative part of the process.
Conservative forces provide the useful comparison: their work is determined by the initial and final positions, so a potential-energy description can capture that transfer. Path-dependent work signals that this shortcut is not sufficient for the interaction being analyzed. Physicists must then retain information about the trajectory and account for energy transfers that potential energy alone does not describe.
To evaluate path-dependent work, first specify the force and the trajectory connecting the two positions. Next, resolve the force relative to each incremental displacement and integrate those contributions along the stated path. The result belongs to that particular route, so changing the trajectory requires a new calculation rather than simply reusing the value from another path.
On a rough surface, the relevant outcome is not only the object's change in position but also how the motion proceeds between positions. A different route can alter the work associated with friction, even when the endpoints match. This analysis helps separate mechanical energy transfer from energy that leaves the mechanical description as heat or another form.
Comparing routes with identical endpoints is a practical way to diagnose whether a force contribution is conservative. If calculated work changes when the route changes, endpoint positions do not fully characterize the energy transfer. If it remains fixed, the behavior is consistent with the conservative-force framework, and potential energy can be used for that contribution.