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Cyclic Processes

Cyclic Processes. A cyclic process is one that periodically returns to its initial state. 1. law:. Change of a state function in one cycle is zero. in particular. In a cyclic process heat transferred to a system equals the work done by it.

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Cyclic Processes

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  1. Cyclic Processes A cyclic process is one that periodically returns to its initial state 1. law: Change of a state function in one cycle is zero in particular In a cyclic process heat transferred to a system equals the work done by it Cyclic equilibrium processes are represented by closed lines in state space P Work done during one cycle from a->b and back a = area of b V

  2. Heat Engines Heat in Heat out |Qin| |Qout| Heat engine: any cyclic process that absorbs heat |Qin|, rejects heat |Qout|, and does a positive amount of work W in each cycle Steam engine Total heat transferred to the system In one cycle Work out

  3. Energy efficiency: 1 Carnot engine in an ideal gas Th 2 4 3 Tc What you get (in the textbook the efficiency is called “e”, I prefer “”) What you have to invest With adiabats Heat absorbed at the hotter isotherm 1 isotherms Heat rejected at the colder isotherm 2 No heat transferred during adiabatic processes 3

  4. from state Heat absorbed at the hotter isotherm 1 2 from state No heat exchange because of adiabatic change 2 3 from state Heat rejected at the colder isotherm 3 4 from state No heat exchange because of adiabatic change 4 1

  5. Efficiency of the Carnot engine: 1 Th 2 4 3 Tc For the adiabatic processes we obtain: 2 4 3 1

  6. (Although derived for the special case when the working substance is an ideal gas, this result is true for all Carnot engines) Nicolas Léonard Sadi Carnot (1796–1832)

  7. Stirling engines displacer displacer displacer displacer Flywheel Four processes of a Stirling engine Heating at constant volume 1 Piston expansion 2 Cooling at constant volume 3 Displacer compression 4

  8. Efficiency of the ideal Stirling engine: Constant volume processes need not to be considered in the net heat transfer when isochoric heat transfer processes take place inside a regenerator such that isotherms 1 2 4 3 Ideal Stirling engine has the same energy efficiency as the Carnot cycle

  9. Gas turbine aircraft used in propel ships electrical power generator etc. Work provided by the turbine is used to drive the compressor and to do useful work like: Turbo-prop engine - rotate a propeller or - increase the kinetic energy of the outgoing gas Turbojet engine

  10. gas Fuel in Heat in Steam engine closed system gas turbine open system Work out Air in Work out Exhaust gas Heat out No particle exchange with surrounding Matter exchange with surrounding Idealization of the gas turbine as a closed system Heat in Fuel in Heat exchanger burner gas turbine gas turbine gas Exhaust gas Heat exchanger Heat out

  11. PV diagram of the gas turbine (Brayton or Joule cycle) 1 2 Process in the compressor adiabatic compression 2 3 adiabates 2 3 Heating the gas (by burning the fuel) 3 4 Adiabatic expansion in the turbines 4 1 4 1 Real engine: exhaust gases out fresh air in Here: cooling exhaust gas return it to the engine at atmospheric pressure

  12. Efficiency of the gas turbine: 2 3 4 1 (in general) 2 3 Heating the gas (by burning the fuel) Q exchange only at Adiabatic changes Q=0 cooling 4 1 2 3 4 1 and Adiabatic changes: Efficiency of gas turbine determined by pressure ratio

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