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Question
How will you calculate work done on an ideal gas in a compression, when change in pressure is carried out in infinite steps?
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Solution
- When an ideal gas is compressed, where the change in pressure is carried out in infinite steps i.e. through a reversible process, the work done can be calculated only through the observation of pressure vs volume plot of the process.
- Reversible process occurs in an infinite number of steps as the driving force and opposing force vary infinitesimally. The process could, at any moment, be reversed by an infinitesimal change in the system.
- The shaded area in the above graph represents the work done in the process, by calculating the area covered we can calculate the work done.
- Mathematically, this area can be represented by this equation,
Work done = shaded Area = Area of shape
w=−P V1∫V2dV
(here P is the pressure, which depends on given curve)
- When an ideal gas is compressed, where the change in pressure is carried out in infinite steps i.e. through a reversible process, the work done can be calculated only through the observation of pressure vs volume plot of the process.
- Reversible process occurs in an infinite number of steps as the driving force and opposing force vary infinitesimally. The process could, at any moment, be reversed by an infinitesimal change in the system.
- The shaded area in the above graph represents the work done in the process, by calculating the area covered we can calculate the work done.
- Mathematically, this area can be represented by this equation,
w=−P V1∫V2dV
(here P is the pressure, which depends on given curve)
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