Cyclic processes and their effeciency, Carnot cycle Lecture

Technology uses cyclic thermodynamic processes to describe the conversion of thermal energy to mechanical energy and vice versa.

During this process a medium undergoes periodically different changes of state, such as compression and expansion, evaporation and condensation, or heating and cooling over a period of time. In a cyclic process, the medium, after having undergone the different changes of state, goes back to its original state and can thus be reused repeatedly.

When a phase change occurs, more energy is converted than during simple heating or cooling. This means that phase change processes involve a higher energy density and require lower  differences in temperature.

Cyclic processes can be used in driving or driven machines. Driving machines convert thermal energy to mechanical energy, such as in steam power plants. Driven machines convert the supplied mechanical energy into thermal energy, like in a compression refrigeration system.

A cyclic thermodynamic process can be illustrated clearly by what are known as state diagrams. The most commonly used state diagrams are:

•     p-v diagram: pressure p against specifi c volume v, suitable for representing mechanical power. It is often used for reciprocating compressors and internal combustion engines with a purely gaseous working medium. Here, cyclic processes can be observed quite well because there is a fi xed relationship between volume change and time. The enclosed area is a measure for the mechanical work performed, also known as useful work.

•     h-s diagram: enthalpy h against entropy s, for representation of steam turbine processes. It is used for water steam and is well suited as a tool for designing steam turbines.

•     log p-h diagram: logarithmic representation of the pressure p against the specifi c enthalpy h, particularly well suited for cooling processes in refrigeration engineering, as heat fl uxes

can be read from the diagram directly as horizontal lines. For the vertical pressure scale, a logarithmic division is used, as this is a good way to represent phase limit curves.

• T-s diagram: a plot of temperature T against entropy s, used for the representation of the thermodynamic conditions. The direction of the cyclic process indicates the type of system, driving or driven machine. If the cycle goes clockwise, the system is a driving machine, and if it goes counter-clockwise, it is a driven machine. In the clockwise direction, heat is absorbed at a high temperature and released at a low temperature. In the counter-clockwise direction, heat is absorbed at a low temperature and released at a high temperature. If the system is operated in the counter-clockwise direction, it is thus suitable as a heat pump or refrigeration machine. As in the p-v diagram, the enclosed area is a measure of the useful work performed.

Examples of cyclic thermodynamic processes

Type

Driving or driven machine

Working medium

Aggregate state

Steam power plant

driving

water

liquid/gaseous

Internal combustion engine

driving

air/combustion gas

gaseous

Gas turbine

driving

air/combustion gas

gaseous

Stirling engine

driving

air, helium

gaseous

ORC power plant

(Organic Rankine Cycle)

driving

fl uorocarbons, hydrocarbons

liquid/gaseous

Refrigeration machine

driven

fl uorocarbons, hydrocarbons, ammonia, etc.

liquid/gaseous

Stirling refrigeration system

driven

air, helium

gaseous

bustion engine. In the case of the internal combustion engine, all changes of state take place in the same space: the cylinder. The changes of state occur one after the other.

     1 – 2        polytropic gas compression

Point 2 ignition with subsequent fuel combustion

medium is the fl uorohydrocarbon refrigerant R134a.

1   – 2       polytropic compression

2   – 3       isobaric cooling and condensation with 

                heat dissipation