What is the relationship between work and pressure in a PV graph?

[pulkit707]

If in PV graph work goes down and then goes up please tell sign of work done and why?My teacher says no matter what preesure is if volume is increasing then work is positive but w=nRTln(p1/p2) and w=nRTln(v2/v1) also .

 

[Chandra Prayaga]

The graph that you have shown does not correspond to the formulas you have written. Both formulas are valid only for isothermal processes in an ideal gas. For all processes in a gas, the work done is given by

W = ∫ pdV where the limits of integration are from an initial volume to a final volume. If there is an increase in the volume, then the integral is positive, and the work is positive. The integral is equal to the area under the curve, and in both parts of your diagram, the volume is increasing.