Question
How will you calculate work done on an ideal gas in a compression, when the change in pressure is carried out in infinite steps?

Answer

When compression is carried out in infinite steps with the change in pressure, it is a reversible process.
Work done can be calculated from pV -plot when pressure is not constant.
A pV plot of the work of compression which is carried out by the change in pressure in infinite steps during compression from the initial volume, $V _{ i }$ to the final volume, $V _{ f }$ is shown in the figure. The work done on the gas is represented by the shaded area.
Image

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