The thermal efficiency can only be 100%(complete conversion of heat into work) if 2R=0, and a basic question is what is the maximum thermal efficiency for any arbitrary cycle? we examine this for two cases, the Carnot cycle and the Brayton (or Joule) cycle which is a model for the power cycle in a jet engine 1A. 2 Carnot Cycles A Carnot cycle is shown below. It has four processes. There are two adiabatic reversible legs and two isothermal reversible legs. We can construct a Carnot cycle with many different systems, but the concepts can be shown using a familiar working fluid, the ideal gas. The system can be regarded as a chamber filled with this ideal gas and with a piston 易 T Reservoir Insulating stand Figure A-2: Carnot cycle- thermodynamic diagram on left and schematic of the different stages in the cycle for a system composed of an ideal gas on the right The four processes in the Carnot cycle are whi system is at temperature T2 at state(a). It is brought in contact with a heat reservoir which is just a liquid or solid mass of large enough extent such that its temperature does not change appreciably when some amount of heat is transferred to the system. In other words, the heat reservoir is a constant temperature source(or receiver)of heat. The system then undergoes an isothermal expansion from a to b, with heat absorbed 22 2) At state b, the system is thermally insulated (removed from contact with the heat reservoir) and then let expand to c. During this expansion the temperature decreases to T. The heat exchanged during this part of the cycle, Lbc =0 3)At state c the system is brought in contact with a heat reservoir at temperature T. It is then compressed to state d, rejecting heat o, in the process 4)Finally, the system is compressed adiabatically back to the initial state a. The heat exchange Oda =0 The thermal efficiency of the cycle is given by the definition Q (A.2.1) In this equation, there is a sign convention implied. The quantities QA, Qr as defined are the magnitudes of the heat absorbed and rejected. The quantities Q1, Q2 on the other hand are defined with reference to heat received by the system. In this example, the former is negative and the latter is positive. The heat absorbed and rejected by the system takes place during isothermal processes and we already know what their values are from Eq(A 1.1)1A-3 The thermal efficiency can only be 100% (complete conversion of heat into work) if QR = 0, and a basic question is what is the maximum thermal efficiency for any arbitrary cycle? We examine this for two cases, the Carnot cycle and the Brayton (or Joule) cycle which is a model for the power cycle in a jet engine. 1.A.2 Carnot Cycles A Carnot cycle is shown below. It has four processes. There are two adiabatic reversible legs and two isothermal reversible legs. We can construct a Carnot cycle with many different systems, but the concepts can be shown using a familiar working fluid, the ideal gas. The system can be regarded as a chamber filled with this ideal gas and with a piston. P V Q1 T1 T2 T2 Q2 Q2 T1 Q1 a b d c 1 2 4 3 Reservoir Insulating stand Reservoir Figure A-2: Carnot cycle – thermodynamic diagram on left and schematic of the different stages in the cycle for a system composed of an ideal gas on the right The four processes in the Carnot cycle are: 1) The system is at temperature T2 at state (a). It is brought in contact with a heat reservoir, which is just a liquid or solid mass of large enough extent such that its temperature does not change appreciably when some amount of heat is transferred to the system. In other words, the heat reservoir is a constant temperature source (or receiver) of heat. The system then undergoes an isothermal expansion from a to b, with heat absorbed Q2 . 2) At state b, the system is thermally insulated (removed from contact with the heat reservoir) and then let expand to c. During this expansion the temperature decreases to T1. The heat exchanged during this part of the cycle, Qbc = 0. 3) At state c the system is brought in contact with a heat reservoir at temperature T1. It is then compressed to state d, rejecting heat Q1 in the process. 4) Finally, the system is compressed adiabatically back to the initial state a. The heat exchange Qda = 0. The thermal efficiency of the cycle is given by the definition η =− =+ 1 1 1 2 Q Q Q Q R A . (A.2.1) In this equation, there is a sign convention implied. The quantities Q ,Q A R as defined are the magnitudes of the heat absorbed and rejected. The quantities Q ,Q1 2 on the other hand are defined with reference to heat received by the system. In this example, the former is negative and the latter is positive. The heat absorbed and rejected by the system takes place during isothermal processes and we already know what their values are from Eq. (A.1.1):