# Work done in Brayton cycle

I am studying Brayton cycle. In Brayton cycle, heat addition and exhaust is carried out at constant pressure. Now, the efficiency is $$\eta=\frac {w_{net}}{q_{in}}$$ My book, while calculating $$w_{net}$$ for efficiency takes into account only the compressor work and the turbine work. My doubt is shouldn't the work in constant pressure heat addition and extraction be also taken into account.

Thanks

I have added the image of book problem. The book is Engineering Thermodynamics by Cengel Boles. It is an example problem. In (c) part I have to calculate efficiency. Just have a look at it.

• Yes, the work is present not only during compression and expansion, but also during heating and cooling at constant pressure. Could you please write down the calculations? Maybe there is some term which cancel out. – Doriano Brogioli May 31 at 11:39
• Has the book stated any assumptions? – user207455 May 31 at 13:05
• I have added the image. Please have a look at it. @SolarMike – Tojrah May 31 at 13:16
• Rigorously, it seems wrong, if we consider the operation performed in a piston with four phases. However, considering how it is performed in reality, it is probably correct, as @BobD explains. I still have a doubt, if the efficiency (with the usually reported formula) is calculated for the "ideal" piston cycle or for the "real" compressor-turbine cycle. When I will have time, I will calculate it. – Doriano Brogioli May 31 at 14:03
• @DorianoBrogioli What makes you think work is done during the constant pressure processes? The volume changes are not against anything (like expansion of a gas in a piston/cylinder). Your basically dealing with heat exchangers. Also why are you referring to the efficiency of an "ideal" piston cycle? The Brayton Cycle involves shaft work (compressor and turbine). – Bob D May 31 at 20:30

The Brayton cycle (or Joule cycle) represents the operation of a gas turbine engine.

For the gas turbine operation the constant pressure heat addition process is an idealization of the combustion process. No pressure volume work is involved

The constant pressure heat extraction process simply cools the air to its original state. Its basically a condenser. Again no pressure volume work is involved.

Bottom line, the constant pressure processes are basically heat exchange processes where

$$Q=C_{p}\Delta T$$

Here is another resource for the Brayton Cycle

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node27.html

Hope this helps.

• So what does the area under that curve indicate? It is clear that it is a non zero quantity – Tojrah May 31 at 15:08
• Area under which curve? 1-4 or 2-3? – user207455 May 31 at 15:17
• Each of them.... – Tojrah May 31 at 15:41
• @Tojrah The area under the TS diagram (2-3 and 1-4) is heat. – Bob D May 31 at 19:05
• @Tojrah The constant pressure processes are basically heat exchangers. See my edit. – Bob D May 31 at 19:17