Cyclic Processes A cyclic process is one that

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Cyclic Processes A cyclic process is one that periodically returns to its initial state

Cyclic Processes A cyclic process is one that periodically returns to its initial state 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 1. law: Cyclic equilibrium processes are represented by closed lines in state space P Work done during one cycle from a->b and back a b V = area of

Heat Engines Heat engine: any cyclic process that absorbs heat |Qin|, rejects heat |Qout|,

Heat Engines 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 Heat in |Qin| Heat out |Qout|

What you get Energy efficiency: (in the textbook the efficiency is called “e”, I

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

from state 1 2 Heat absorbed at the hotter isotherm from state 2 3

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

Efficiency of the Carnot engine: For the adiabatic processes we obtain: 2 3 4

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

(Although derived for the special case when the working substance is an ideal gas,

(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)

Stirling engines Flywheel Piston Four processes of a Stirling engine 1 Heating at constant

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

Efficiency of the ideal Stirling engine: Constant volume processes need not to be considered

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 4 2 3 Ideal Stirling engine has the same energy efficiency as the Carnot cycle

Gas turbine aircraft used in propel ships electrical power generator etc. Work provided by

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 ne o Turb gi n e t je

Fuel in Heat in Steam engine Work out closed system Air in gas turbine

Fuel in Heat in Steam engine Work out closed system Air in gas turbine open system 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 Exhaust gas gas turbine Heat exchanger Heat out

PV diagram of the gas turbine (Brayton or Joule cycle) 1 2 Process in

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

(in general) Efficiency of the gas turbine: 2 3 Heating the gas (by burning

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