Thermodynamics - Cycle efficiency

[Jalo]

Homework Statement

Compute the efficiency of the following cycle:

Homework Equations

The Attempt at a Solution

I know there's an isothermic process between a and b, where heat comes into the system, let's call it Qh.
I also know that between b and c heat will leave the system, let's call it Qc.
The process from c to a is adiabatic.

The efficiency, n, is equal to:

η = 1- Qc / Qh = 1 - Qc / T2(S2-S1)

The problem is that I don't know how to compute Qc...
Any help would be highly appreciated.
Also, if anyone has a good book on the subject I'd appreciate.

Thanks.

 

[TSny]

The area enclosed by a cycle on a T vs S graph has a physical interpretation that will help to determine the efficiency.

 

[haruspex]

The text below the figure at http://en.wikipedia.org/wiki/Temperature–entropy_diagram should help.

 

[Jalo]

Thank you very much! Sadly I had no idea it had a physical interpretation..

 

[Radhakrishnam]

Don't use Carnot efficiency equation for the cycle; but use a more fundamental and simpler equation: efficiency = (W/Qh) = (work output from the engine / heat input to the engine). The numerator is obtained from the area of the triangle. You already know how to calculate (the denominator) the heat input to the engine (T2*delta S). The ratio of the two numbers gives the efficiency.

Caution: Cycles involving sloping straight line paths can sometimes be dangerous! For eg the efficiency calculation of similar cyclic triangular paths on PV plane (instead of TS plane) is a very complicated and controversial issue.