# Drawing a PV Diagram

by imatreyu
Tags: gas, pv diagram
 P: 82 1. The problem statement, all variables and given/known data One mole of an ideal gas at an inital tempreature of 300K and pressure of 4 atm is carried through the following reversible cycle: a) It expands isothermally until its volume is doubled. b) It is compressed to its original volume at constant pressure. c) It is compressed isothermally to a pressure of 4 atm. d) It expands at constant pressure to its original volume Make a plot of this cycle process on a PV diagram and calculate the work done by the gas per cycle. 2. Relevant equations 3. The attempt at a solution Okay so step a. means that while Vo goes to 2Vo the pressure doubles as well, yes? And step b means that the pressure is the same but the volume goes to Vo. And so then step C should mean that since P is returning to its initial, the gas returns to Vo too, right? But if that's true, then D doesn't make sense since it has already returned to Vo. Please help! Once I get the diagram correct, I'm just going to use the area to find the work done.
Mentor
P: 11,202
 Quote by imatreyu Okay so step a. means that while Vo goes to 2Vo the pressure doubles as well, yes?
Take a look at the PV = nRT equation. If T is held constant (isothermal), how must P and V relate to each other?

 And step b means that the pressure is the same but the volume goes to Vo. And so then step C should mean that since P is returning to its initial, the gas returns to Vo too, right?
Again, take a look at PV = nRT. What's the current volume and pressure when step C begins? How do P and V vary when the compression (or expansion) is isothermal?
 P: 82 Oh okay haha. . .P has to be half. . . Thank you :)

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