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I could really use some help with this problem. I dont really know how to solve this
what is your thought process so far?
I dont really have one for this type of problem

If i see an example worked out i have a better understanding of how to approach it
okay so since the process is adibatic from AB to DC, there is no heat transfer taking place. Pressure is constant from BC and DA so they're isobaric

im not sure where to go from there
In physics problems you need to start from the end. You want to obtain the efficiency, so start from the definition of it, see (1).

Now (2), identify what the terms needed in (1) correspond to in your problem and write their expressions. DA and BC are isobaric processes, so write the expression for heat exchanged at constant pressure, here written by unit mass (if you are used to imagine the cycle opearting with a finite amount of gas just multiply this by the mass of the gas in the cycle, nothing changes in the end).

(2) represents a set of two equation with 6 variables, you need another 4 equations (aka relationships between variables) to solve it. The key is to express some variables using different variables. We choose to express the variables in the first equation as functions of the variables in the second equation.

Start by writing the relationships between the temperatures in a reversible adiabatic transformation (so, isoentropic) (3) and specialize for your problem (4).

Use the relationships for the pressures in isobaric processes (5) (quite simple) and subsitutute into one of the equations in (4) (we'll do it on the first one). Then, subsitute everything into the first equation in (2) and you will get (6).

The last step is substituting the full expressions for the heats (in and out) into (1) and you get (7). The end.
oh man this is super helpful, thank you!
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