# Drawing a PV Diagram

imatreyu

## Homework Statement

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.

## 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
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?

imatreyu
Oh okay haha. . .P has to be half. . .

Thank you :)