Section 2 Applications

**Chapter 6**

*Jack Denur*

**Abstract**

Improving Heat-Engine

Performance via High-

Temperature Recharge

Perfect (reversible) cyclic heat engines operate at Carnot efficiency. Perfect reversible) nonheat engines and noncyclic heat engines operate at unit (100%) efficiency. But a usually necessary, although not always sufficient, requirement to achieve reversibility is that an engine must operate infinitely slowly, i.e., quasi-statically. And infinitely slow operation, which implies infinitesimally small power output, is obviously impractical. Most real heat engines operate, if not at maximum power output, then at least closer to maximum power output than to maximum efficiency. Endoreversible heat engines delivering maximum power output operate at Curzon-Ahlborn efficiency. Irrespective of efficiency, engines' work outputs are in almost all cases totally frictionally dissipated as heat immediately (e.g., an automobile operating at constant speed) or on short time scales. But if a heat engine's work output must be frictionally dissipated, it is best to dissipate it not into the cold reservoir but at the highest practicable temperature. We dub this as hightemperature recharge (HTR). This is not always practicable. But if it is practicable, it can yield improved heat-engine performance. We discuss improvements of the Carnot and Curzon-Ahlborn efficiencies achievable via HTR, and show consistency with the First and Second Laws of Thermodynamics. We reply to criticisms of HTR.

**Keywords:** Carnot efficiency, Curzon-Ahlborn efficiency, entropy,

**1. Introduction, overview, and general considerations**

high-temperature recharge (HTR)

**107**

First Law of Thermodynamics, Second Law of Thermodynamics, heat engines,

Perfect (reversible) cyclic heat engines operate at Carnot efficiency [1–7]. Perfect (reversible) nonheat engines and noncyclic (necessarily one-time, singleuse) heat engines operate at unit (100%) efficiency. A simple example of a noncyclic heat engine is the one-time expansion of a gas pushing a piston. (If the expansion is isothermal, the heat is supplied from the internal energy of a reservoir; if is adiabatic, the heat is supplied from the internal energy of the gas itself. A polytropic expansion is intermediate between these two extremes.) Other examples include rockets: the piston (payload) is launched into space by a one-time power stroke (but typically most of the work output accelerates the exhaust gases, not the payload) and firearms: the piston (bullet) is accelerated by a one-time power stroke and then discarded (but some, typically less than with rockets, of the work output
