How do you show the efficiency of an engine is x?

[lilliebeth]

Homework Statement

A hypothetical engine, with an ideal gas as the working substance, operates in the cycle shown in the diagram, show the efficiency of an engine is :

n= 1 - 1/$\gamma$ ((1-(P₃\P₁))/(1-(V₃/V₁)))

The diagram is basically a section the bottom left quadrant of a circle with an adiabatic process for 3 to 1 to make it a cycle

Homework Equations

ΔU = Qout -Qcold - Work
PV=nRT
gamma = Cp/Cv

The Attempt at a Solution

I really have no idea how to start this

 

[TSny]

Hi lilliebeth. Welcome to PF. To be sure of how you are labeling the states 1, 2, and 3 could you please answer the following?

The process from 1 to 2 is what type of process? (constant volume, constant pressure, or what?)
Does heat flow in or out of the engine in going from 1 to 2?

The process from 2 to 3 is what type of process?
Does heat flow in or out of the engine for this process?

To get started, you should add another relevant equation: the equation for the efficiency of an engine. That will help you decide what you need to calculate.