Thermodynamic cycles and their analysis

[Urmi Roy]

Homework Statement

1. In Air compressor cycles, the work done is calculated by integrating vdp and not pdv(like we'd do in otto cycle or any other thermodynamic cycle)...why?

2. In Rankine cycle. we calculate work done by making use of enthalpy calculations whereas in brayton cycle and other cycle, we use P,V,T relations.
Again, in rankine cycle, which seems similar to refrigeration cycle, we primarily use T-S diagrams whereas in refrigeration cycles, we use P-H diagrams...basically, why do we use different methods of analysis/tools of analysis in theses similar situations?

Homework Equations

The Attempt at a Solution

1. I read briefly that pdv is used for non-flow processes whereas vdp is used for flow processes...but then the same kind of things happen in otto cycle and aircompressor cycle (neither of these is a thermodynamic cycle even though they are both mechanical cycles).

2. I have no idea...

 

[mark726]

I would like to provide some insight into the reasoning behind these different methods of analysis in the various cycles mentioned.

1. The reason for using vdp in air compressor cycles is because it is a flow process, where the volume of the gas is changing continuously. In this case, the work done is given by the integral of vdp, as it takes into account the change in volume throughout the process. On the other hand, pdv is used for non-flow processes, where the volume remains constant and the pressure changes. In the case of Otto cycle, the volume of the gas remains constant during the compression and expansion processes, hence pdv is used.

2. The different methods of analysis used in the various cycles are based on the type of process and the properties that are important for that particular process. In Rankine cycle, enthalpy is used because it is a flow process and enthalpy takes into account both the internal energy and the work done by the system. In Brayton cycle, the focus is on the pressure and temperature changes, hence P-V-T relations are used. Similarly, in refrigeration cycles, the focus is on the temperature and enthalpy changes, hence P-H diagrams are used. These different tools of analysis are used to simplify the calculations and make them more applicable to the specific process being analyzed.