What will be the work done on an ideal gas enclosed in a cyliner, when it is compressed by a constant external pressure, `p_("ext")` in a single step as shown in figure ? Explain graphically.

Explanation

Suppose total volume of the gas is `V_(i)` and pressure of the gas inside cylinder is p. After compressionby constant external presure `p_("ext")` in a single step, final volume of the gas becomes `V_(f)`
Then W is the work done on the system by movment of the piston, then
`W = p_("ext") (-DeltaV)`
`W = -p_(ext)(V_(t)-V_(i))`

This can be calculated from p-V graph as shown in the figure. Work done is equal to the shaded area `ABV_(f)V_(i)`
This can be calculated from p-V graph as shown in the figure. Work done is equal to the shaded are `ABV_(f)V_(i)` ,
The negative sign in the expression is required to obtain conventional sign for W which will be positive. Because in case of compression work is done on the system, so `DeltaV` will be negative.