Efficiency of engine taking diatomic ideal gas through cycles

[jensgt]

Homework Statement

What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1 -------> 2 -------> 3 -------> 4 ------> 1 shown in the figure ?

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Homework Equations

e = W/Qh

The Attempt at a Solution

I know the answer is 10.5

I am trying to prep for a test today and this is the last thing from my homework that I don't understand...can someone explain to me how the answer is generated? I am sort of lost on it and I figure it has to be easier than it seems.

 

[mukundpa]

There are two isochoric and two isobaric processes in the cycle. Find temperatures at all four points and calculate the heat absorbed from the source and the net work done.
The efficiency is always less than one thus it must be 10.5%.

 

[jensgt]

How to find temp with no p or v numbers?

 

[mukundpa]

It is P₀V₀/nR at 1.

 

[jensgt]

I'm still confused...po is not a numerical value.

 

[mukundpa]

say P0V0/nR = T0 then what are temperatures at 2, 3 and 4 ?

 

[mukundpa]

these are 2T₀, 4T₀ and 2T₀ respectively.
Now find the heat absorbed in isochoric and isobaric processes using Q = n Cv ΔT and Q = n Cp ΔT