What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, pext in a single step as shown in figure? Explain graphically.
Suppose total volume of the gases is Vi and pressure of the gas inside cylinder is p. After compression by constant external presure, (pext) in a single tap, final volume of the gas becomes Vf.
Then volume change,
If W is the work done on the system by movement of the piston, then
This can be calculated from p-V graph as shown in the figure. Work done is equal to the shaded area
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 will be negative.
