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 compression by constant external pressure, `(p_("ext"))` in a single step, final volume of the gas becomes `V_(f)`.
Then volume change, `Delta v = (V_(f) - V_(i))`
If W is the work done on the system by movement of the piston, then
`W = P_("ext") (-Delta V)`
`W = - p_("ext") (V_(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 this 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 `Delta V` will be negative