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.

What will be the work done on an ideal gas enclosed in a cyliner, when

1.	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.
Answer» Solution :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