Work done BY the gas in a cyclic thermodynamic process

[Aletag]

Homework Statement

What is the work done by the gas in the cycle shown below?

Relevant Equations

V1=3L, V2=5L, P1=1atm, =P2=2atm

Since the assignment asks the work done by the gas, that should be equal to P1*(V2-V1) aka the area under the P1 line. Do I have to subtract the work done to the system or is this the solution already? If so, why do I need P2?

 

[kuruman]

P1*(V2-V1) is the work done by the gas only for the leg of the cycle from V1 to V2. For the complete cycle you must add to this the work done by the gas for the other three legs. That's why you need P2.

 

[Cutter Ketch]

I get what you are saying and I see the emphasis in the title of the post on the word “BY”, but I suspect you need to read the question as what NET work is done by the gas. Sure, maybe they could have specified explicitly, but that is not an unreasonable way to ask the question particularly when they say “in the cycle”. That is going to mean “net” (i.e. all the way around the cycle) every time.