The conclusion from either of these arguments is that a cycle designed for maximum thermal efficiency is not very useful in that the work(power)we get out of it is zero A more useful criterion is that of maximum per unit mass(maximum power per unit mass flow). This leads to compact propulsion devices. The work per unit mass is given by Work/unit mass=cp[(T-T)-(Ta-Ta)I Max turbine temp Atmospheric temperature (Design constraint) The design variable is the compressor exit temperature, Tb, and to find the maximum as this is varied, we differentiate the expression for work with respect to Th dwork d dT dT dTb dTh The first and the fourth term on the right hand side of the above equation are both zero( the turbine entry temperature is fixed, as is the atmospheric temperature). The maximum work occurs where the derivative of work with respect to Tb is zero dwork To use Eq (A 4.1), we need to relate Ta and Tb. We know that Th ence dT, -TT dT T Plugging this expression for the derivative into Eq (A 4. 1) gives the compressor exit temperature for maximum work as T=TaT. In terms of temperature ratio Compressor temperature ratio for maximum work Tb T The condition for maximum work in a Brayton cycle is different than that for maximum efficiency The role of the temperature ratio can be seen if we examine the work per unit mass which is delivered at this condition Work/unit maSS=CpITC-VTaTc Ta Tc+T Ratioing all temperatures to the engine inlet temperature Work /unit mass= c To find the power the an produce, we need to multiply the work per unit mass by the mass flow rate 1A-101A-10 The conclusion from either of these arguments is that a cycle designed for maximum thermal efficiency is not very useful in that the work (power) we get out of it is zero. A more useful criterion is that of maximum work per unit mass (maximum power per unit mass flow). This leads to compact propulsion devices. The work per unit mass is given by: Work unit mass c T T T T pc b d a / = − [ ] ( ) − − ( ) Max. turbine temp. Atmospheric temperature (Design constraint) The design variable is the compressor exit temperature, Tb , and to find the maximum as this is varied, we differentiate the expression for work with respect to Tb : dWork dT c dT dT dT dT dT b dT p c b d b a b = −− +       1 . The first and the fourth term on the right hand side of the above equation are both zero (the turbine entry temperature is fixed, as is the atmospheric temperature). The maximum work occurs where the derivative of work with respect to Tb is zero: dWork dT dT b dT d b = =− − 0 1 . (A.4.1) To use Eq. (A.4.1), we need to relate T and T d b. We know that T T T T T T T T d a c b d a c b = = or . Hence, dT dT T T T d b a c b = − 2 . Plugging this expression for the derivative into Eq. (A.4.1) gives the compressor exit temperature for maximum work as T TT b ac = . In terms of temperature ratio, Compressor temperature ratio for maximum work: T T T T b a c a = . The condition for maximum work in a Brayton cycle is different than that for maximum efficiency. The role of the temperature ratio can be seen if we examine the work per unit mass which is delivered at this condition: Work unit mass c T T T T T T T p c ac T a c a c a / =− − +      . Ratioing all temperatures to the engine inlet temperature, Work unit mass c T T T T T p a c a c a / = −+      2 1.  To find the power the engine can produce, we need to multiply the work per unit mass by the mass flow rate: