Can a thermodynamic heat engine include all these processes?

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distalphalanx
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Homework Statement


Hi, I'm a new user and got this problem. Sorry to bother, but I couldn't find any relevant information from my Physics books..
The problem states: Build a heat engine using these processes: adiabatic, isothermal, isochoric and isothermal. The work-cycle of the engine must include all these cycles.You are allowed to use each process only once.
a) Name the processes, and draw your cycle into a pV-diagram.
b) At which processes does your engine do work and when is work done on it? At which processes does your engine emit heat, and when is heat added to the cycle?
c) How does the 1st and 2nd law of thermodynamics restrict the operation of your engine?

I know there's a simple solution to this problem, but I just can't figure it out right now..
Thanks in advance for your assistance!

Homework Equations


So basically, I have to figure out which of all thermodynamic cycles works with this principle with all these four elements used just once?
EDIT: basically I just need to know in which order I need to put the processes into my pV-diagram. When I got that clear, I'll probably be able to calculate the rest.

Q=W (1st Law of TD)
pv=nRT
p1V1=p2V2 (isothermal)
Q=W (isothermal)
dE= Q-W (inner energy)
V1/T1 = V2/T2 (isobaric)
p1/T1=p2/T2 (isochoric)
further explanation needed from some kind of guru =)

The Attempt at a Solution

 
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Discussion

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Try sketching the cycle on a PV diagram first.

The easy way to see this is starting from the Carnot cycle, where you replace one of the adiabatic steps with an isochoric (constant volume) step (two ways to do this). This wil have two isothermal steps, but you list isothermal twice, so I don't know if this is allowed. If you are to have only three steps, then you need to think about how you would arrange the three lines: isocharic (vertical), isotherm (gentle slope), adiabat (steeper slope than isotherm) between three points (I can see only one ways ot do this).
 
I would assume 4 processes as the problem states: adiabatic, isothermal at T1, isochoric and isothermal at T2.

You also need an equation of state for an adiabatic process.