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Modern Engineering Thermodynamics

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13.6 Rankine Cycle with Superheat 467<br />

Degree of superheat<br />

T H<br />

T L<br />

T<br />

Carnot cycle<br />

1<br />

A<br />

Rankine<br />

cycle with<br />

superheat<br />

3,4s 2s<br />

p<br />

4s<br />

3<br />

Carnot cycle<br />

1<br />

2s<br />

T H = Constant<br />

T L = Constant<br />

s<br />

(a) Temperature−entropy diagram for Carnot<br />

and Rankine cycles with superheat<br />

v<br />

(b) Pressure−volume diagram for Carnot<br />

and Rankine cycles with superheat<br />

FIGURE 13.15<br />

A comparison between the Carnot cycle and the isentropic Rankine cycle with superheat.<br />

The degree of superheat is defined to be the difference between the actual superheated vapor temperature and the<br />

saturation temperature at the pressure of the superheated vapor; that is,<br />

<br />

<br />

Degree of superheat of superheated<br />

= T − T<br />

vapor at temperature T and pressure p<br />

sat ðpÞ (13.10)<br />

For example, in Figure 13.15a, the degree of superheat is T 1 – T A . The degree of superheat that can be used in<br />

any particular heat engine design is limited only by the engine’s ability to resist high temperatures. This has led<br />

to the industrial development and use of high-temperature alloys and ceramics for critical heat engine<br />

components.<br />

EXAMPLE 13.5<br />

In the 1890s, the Lancashire Steam Motor Company (now called British<br />

Leyland) manufactured the lawn mower shown in Figure 13.16, which<br />

was powered by a Rankine cycle steam engine. If it had a superheated<br />

boiler outlet state of 100. psia and 500.°F, and a condenser pressure of<br />

1.00 psia, then find<br />

a. The degree of superheat at the boiler outlet.<br />

b. The equivalent Carnot cycle thermal efficiency of the lawn mower.<br />

c. The isentropic Rankine cycle thermal efficiency of the lawn mower.<br />

Solution<br />

A system sketch is shown in Figure 13.17.<br />

FIGURE 13.16<br />

Example 13.5, steam-powered lawn mower.<br />

W P<br />

Q H<br />

4 1<br />

Boiler<br />

Condenser<br />

3<br />

2<br />

Q L<br />

(a) Equipment schematic<br />

1<br />

T<br />

W E<br />

3,4s<br />

2s<br />

s<br />

(b) T–s thermodynamic state diagram<br />

FIGURE 13.17<br />

Example 13.5, system sketch.<br />

(Continued )

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