OpenStax College Physics for AP® Courses, Chapter 15, Problem 8 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. In this process from point C to point D, the change in volume from C to D is less than zero and this means that the work is being done on the system— the system is being squished— and that means the work is going to be negative and the work is going to be the area under this curve so it consists of a rectangle which is the pressure at point C multiplied by this base, which is the volume at point D minus the volume at point C and then we add to that the area of this triangle which is one-half times the base V D minus V C times the height, which is the pressure at point D minus the pressure at point C and then we factor out the V D minus V C and we end up with V D minus V C times P C plus one-half P D minus P C and then distribute the one-half into the brackets there and then P C minus one-half P C is positive one-half P C and then we can factor out the one-half and we can write this formula here which is actually the formula for the area of a trapezoid, which I guess I could have started with but anyway, we got there one way or the other. So we have one-half times 1.0 times 10 to the minus 3 cubic meters— that's the volume at point D— point D here by the way... minus 4.0 times 10 to the minus 3 cubic meters at point C and then multiply that by the pressure at point C, which is 0.6 times 10 to the 6 newtons per meters squared plus 1.0 times 10 to the 6 newtons per meters squared and we end up with negative 2400 joules is the work done by the system and this terminology "by" and "on," you have to be careful with it. So I really mean negative 2400 joules work done by the system or you could say, positive 2400 joules of work done on the system.