a cold (low-entropy one), decreasing the entropy of the heat source and increasing that of the heat sink. Propulsive efficiency Propulsive efficiency is defined as the ratio of work done on the fluid to the propulsive power, i.e. thrust times velocity of the vehicle. In generic terms, the propulsive power can be calculated as follows: where represents thrust and the flight speed. The thrust can be computed from intake and exhaust massflows ( and ) and velocities ( and ): The work done by the engine to the flow, on the other hand, is the change in kinetic energy per time. This does not take into account the efficiency of the engine used to generate the power, nor of the propeller, fan or other mechanism used to accelerate air. It merely refers to the work done to the flow, by any means, and can be expressed as the difference between exhausted kinetic energy flux and incoming kinetic energy flux: The propulsive efficiency can therefore be computed as: Depending on the type of propulsion used, this equation can be simplified in different ways, demonstrating some of the peculiarities of different engine types. The general equation already shows, however, that propulsive efficiency improves when using large massflows and small velocities compared to small mass-flows and large velocities, since the squared terms in the denominator grow faster than the non-squared terms. The losses modelled by propulsive efficiency are explained by the fact that any mode of aero propulsion leaves behind a jet moving into the opposite direction of the vehicle. The kinetic energy flux in this jet is for the case that . Jet engines The propulsive efficiency formula for air-breathing engines is given below. It can be derived by setting in the general equation, and assuming that . This cancels out the mass-flow and leads to: where is the exhaust expulsion velocity and is both the airspeed at the inlet and the flight velocity. For pure jet engines, particularly with afterburner, a small amount of accuracy can be gained by not assuming the intake and exhaust massflow to be equal, since the exhaust gas also contains the added mass of the fuel injected. For turbofan engines, the exhaust massflow may be marginally smaller than the intake massflow because the engine supplies "bleed air" from the compressor to the aircraft. In most circumstances, this is not taken into account, as it makes no