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Modern Engineering Thermodynamics

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462 CHAPTER 13: Vapor and Gas Power Cycles<br />

EXAMPLE 13.3<br />

The boiler on the toy steam engine shown in Figure 13.10 is heated by a 300. watt electrical heater and produces<br />

saturated vapor at 20.0 psia. If the exhaust steam from the engine is condensed at 14.7 psia, determine the maximum<br />

possible thermal efficiency and net power output of the engine, assuming it operates on (a) a Carnot cycle and (b) a<br />

Rankine cycle.<br />

FIGURE 13.10<br />

Example 13.3, toy steam engine.<br />

Solution<br />

a. A Carnot cycle is defined to be a reversible cycle, so it automatically represents the maximum possible performance.<br />

Equation (13.2) gives the Carnot cycle thermal efficiency as<br />

ðη T Þ Carnot = 1 – T L /T H<br />

where<br />

and<br />

T L = T sat ð14:7 psiaÞ = 212°F = 671:67 R<br />

Then,<br />

T H = T sat ð20:0 psiaÞ = 228:0°F = 687:67 R<br />

ðη T Þ Carnot<br />

= 1 − 671:67/687:67 = 0:0233 = 2:33%<br />

and since<br />

then<br />

ðη T Þ Carnot = ð _W net Þ Carnot / _Q boiler<br />

ð _W net Þ Carnot<br />

= ðη T Þ Carnot<br />

× _Q boiler = 0:0233ð300:Þ = 6:98 watts

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