carnot cycle

Carnot engine

Carnot cycle is an important reversible thermodynamic cycle with two essential isothermal and adiabatic process, carnot cycle is the most efficient of all heat engines. As stated in 2^nd law of thermodynamics,  not all energy transformation is not perfect some are lost inform of heat, this is where the concept of heat engines arise,  according to carnot principle large percentage of the heat can be used for doing work.  For the carnot engine to be efficient the process must be reversible and involve no change in entropy.

Using an ideal gas as a working substances, contained in a cylinder with a conducting base and non-conducting walls covered by by non-conducting moveable piston. A carnot cycle is established in the following state

Stage one

·         The circle is started at stage 1 where the system is at temperature TH. It is brought into contact with a heat reservoir at the same temperature and a reversible isothermal process is performed by the system to state 2. for an ideal gas , this should be an isothermal expansion in which heat Qin is given to the system by the reservoir  and a work W2 is done by the system.

Stage two

·         The system is now removed from the reservoir contact and thermally isolated so that it perform a reversible adiabatic  process to state c, this is also an expansion if the working substance is an ideal gas  and so work W1 is done by the system at the expense of its internal energy and the temperature falls to TL . The heat flowing into the system is zero.

Stage three

·         The system is now bought into contact with heat reservoir at a temperature TL and is allowed to perform a reversible isothermal compression to stage 3. Heat Qout flows out of the system and a work W1 is done on the system,.

Stage four

·         A further reversible adiabatic compression is performed on the ideal gas , so that it returns to its initial state a , here the workdone on the system is W2  and no heat enters no leave the system, zero heat change.

·          since the gas return to its original state  at A  therei is no in the internal energy of the gas  at the end of the the cycle . From the first law of thermodynamics , then the net workdone in a cycle  = heat gained by the gas  = Qin=Qout, the net workdone is represented by the shaded area abcd in the figure above, all heat engine , refrigerators works on this principles.

Note: carnot principle is an idealization which does not hold in real life, there is no any single engine that comply 100%  with carnot cycle,  in most cases the reversible isothermal process are very slow that they cannot be used to run real life system,  3^rd law of thermodynamics get it that system tend to disordered from ordered, meaning increasing entropy while carnot principle require zero entropy and this means carnot engines does not exist in real life. In real life  heat engine, there may be a friction between moving part, conduction of heat between moving part etc, all this will result to change in heat content and temperature which is not 100%  in line with carnot cycle.