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.

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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