How Do You Calculate Work in a Reversible Ideal Gas Cycle?

[velvetymoogle]

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 temperature.
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.

Homework Equations

PV=nRT
PV/T = PV/T
W = -P(delta)V
H = 5/2RT
(delta)U = Q + W

The Attempt at a Solution

So I started off by finding the original volume.
V = nRT/P
V = (1 mole)(8.31 constant)(300 degrees Kelvin) / 4(1.013x10^5)
V = 0.0062 cubic meters.

Then for step (a), since it expands isothermally, PV must remain constant as well as T. W = P(delta)V. Since it's a constant, I can just multiply 4.013x10^5 by 0.0062. That gives me 2512.24 joules. It's positive because it's expanding.

This next part is where I get stuck. If the volume is compressed back to its original volume, that means pressure has to go back to its original as well since the temperature is constant, the number of moles can't change, and neither can a constant. What do I do for this step and the other 2?

Also, how would I draw the diagram?


Question 1: Is it correct to multiply 4 by 1.013x10^5 because our PV=nRT equation is not in atm and we need to convert it?

 

[t!m]

Regarding your question in red, it's all in the units.
$$R=8.314\frac{J}{K mol}=8.314\frac{m^3 Pa}{K mol}$$
So yes, you do need to convert from atm to Pa if you want to use R=8.314. Alternatively, you could use R=0.08206 L*atm / K*mol, leave P in atm and your volume would then be in L.

And I'd reconsider part (a). Remember - this is a reversible expansion. And technically dW=-Pext dV, where Pext is the external pressure the gas is expanding against. W=-P$$\Delta$$V only applies when Pext is constant.

 

[velvetymoogle]

Wait, I'm still confused. I've never done any of this before because my teacher doesn't teach and he sprung this on us within two days of the section. How would I figure out the work then for each part? How would I draw the diagram?