letters to nature 338 NATURE | VOL 399 | 27 MAY 1999 | www.nature.comWith Ṁ 2 suppressed, the performance of the engine is measured as a function of p 1c and the temperature of the helium immediately below the hot heat exchanger, T h,gas . Figure 3 shows the thermal efficiency 2 , h ¼Ẇ res =Q h , where Ẇ res is the acoustic power delivered to the resonator. The maximum thermal efficiency of h ¼ 0:30 occurs near jp 1 =p m j ¼ 0:06 at T h;gas ¼ 725 ЊC with the engine delivering 710 W to the resonator. This corresponds to 42% of the theoretical maximum Carnot efficiency 2 . At the most powerful operating point, jp 1 =p m j ¼ 0:10, 890 W is delivered to the resonator with h ¼ 0:22.Although this engine already shows a large increase in efficiency over previous heat engines without moving parts, we anticipate further improvements through research on flow separation losses 17,18 and regenerator inefficiency. We have also built one refrigerator 19 according to the same principles, and we expect that it will give performance comparable to that of commercially successful refrigeration equipment. Ⅺ

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