H

Where:

nth = Cycle efficiency

Th = Initial temperature at which heat is added to cycle

TL = Final temperature at which heat is rejected from cycle Qin = Heat energy input Qout = Heat energy rejected

The following example shows ideal cycle efficiency based on Equation 2-8, given an initial temperature, Th = 540°F, and a final temperature, Tl = 40°F. Temperatures are expressed in degrees R (°F + 460 = °R).

1,000

Figure 2-2 shows the Carnot cycle with steam as the working fluid based on the temperatures shown in the above example. The figure includes both a pressure-volume (PV) diagram and a temperature-entropy (Ts) diagram, indicating the relationship between pressure and temperature as measures of energy. As shown, the four basic steps are similar to that of the Carnot heat engine.

Fig. 2-2 Carnot Cycle with Steam as Working Fluid. Source: Babcock &Wilcox

Fig. 2-1 Temperature-Entropy Diagram for Carnot Heat Engine.

Fig. 2-2 Carnot Cycle with Steam as Working Fluid. Source: Babcock &Wilcox

Step A-B Isentropic compression

Step B-C Constant pressure (hence, constant temperature heat addition) Step C-D Isentropic expansion

Step D-A Constant pressure (hence, constant temperature heat rejection) Figure 2-3 shows the pressure-volume and temperature-entropy diagrams for Carnot, Otto, Diesel, and Brayton gas

s = ENTROPY

(A) CARNOT CYCLE PHASES a - b ISENTROPIC COMPRESSION b - c ISOTHERMAL EXPANSION c - d ISENTROPIC EXPANSION d - a ISOTHERMAL COMPRESSION

s = ENTROPY

s = ENTROPY

V = VOLUME

s = ENTROPY

(A) CARNOT CYCLE PHASES a - b ISENTROPIC COMPRESSION b - c ISOTHERMAL EXPANSION c - d ISENTROPIC EXPANSION d - a ISOTHERMAL COMPRESSION

(B) OTTO CYCLE PHASES a - b ISENTROPIC COMPRESSION b - c CONSTANT VOLUME HEAT ADDITION c - d ISENTROPIC EXPANSION d - a CONSTANT VOLUME HEAT REJECTION

V = VOLUME

(B) OTTO CYCLE PHASES a - b ISENTROPIC COMPRESSION b - c CONSTANT VOLUME HEAT ADDITION c - d ISENTROPIC EXPANSION d - a CONSTANT VOLUME HEAT REJECTION

s = ENTROPY

V = VOLUME

s = ENTROPY

(D) BRAYTON CYCLE PHASES b ISENTROPIC COMPRESSION c CONSTANT PRESSURE HEAT ADDITION d ISENTROPIC EXPANSION a CONSTANT PRESSURE HEAT REJECTION

V = VOLUME

s = ENTROPY

V = VOLUME

s = ENTROPY

(C) DIESEL CYCLE PHASES a - b ISENTROPIC COMPRESSION b - c CONSTANT PRESSURE HEAT ADDITION c - d ISENTROPIC EXPANSION d - a CONSTANT VOLUME HEAT REJECTION

(D) BRAYTON CYCLE PHASES b ISENTROPIC COMPRESSION c CONSTANT PRESSURE HEAT ADDITION d ISENTROPIC EXPANSION a CONSTANT PRESSURE HEAT REJECTION

Fig. 2-3 P-V and T-s Diagrams for Carnot, Otto, Diesel, and Brayton Gas Cycles. Source: Babcock & Wilcox c b b d a cycles. Work for each cycle is again represented by area A-B-C-D. Note that mean effective pressure (MEP) is the work of the cycle divided by the displacement.

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