This essay will aim to define entropy, and explore its relevance in the context of the 2nd law of thermodynamics, with the objective of establishing that the idea behind entropy exists within the molecular structure of a working fluid; the phenomena of spontaneous combustion as well as the Carnot and Rankine cycles will be considered to further elaborate on the concept of entropy under the 2nd law of thermodynamics; and at the conclusion of this essay, a recommendation on the basis of the algebraic formula for entropy would be used to understand the idea behind modern research into energy management technology today.
Entropy and its concept under the 2nd law of thermodynamics
The concept of Entropy can be understood by examining the change in the molecular structure of substances undergoing a thermodynamic cycle, and also examining how its molecules interact at different stages of the cycle. Reynolds and Perkins (1977) considered entropy as the total degree of disorderliness of all the individual molecules of a working fluid; based on this concept, when considering the individual molecules of water being boiled at room temperature, it will be observed that its molecular structure and degree of random motion are different at liquid and vapour state. Cengel and Boles (2008) indicates that when a fluid is in its solid phase, its molecules are not exhibiting any random motion but are held together by a bond; but once there is a rise in temperature, it changes to liquid state and then vaporizes at saturation temperature; while its individual molecules start moving in a disorganised random motion, colliding with each other in the process and generating energy in the form of heat; the size of heat generated correlates with the speed of the random motion of its molecules; for this reason, if the random motion of the fluids molecules increase, more heat is generated. Entropy is the term used to express the degree of this random motion of the molecules of the fluid undergoing a thermodynamic process and at the point of highest entropy (vapour state), higher molecular chaos is achieved, and more heat is generated.
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Simonson (1993) elaborated this fact further, by deducing that an increase in entropy occurs when a fluid mixture in an isolated system changes from a non equilibrium state to an equilibrium state. As illustrated in figure 1, if a vapour at 100oC is mixed with another vapour at 50oc in an isolated system, with no heat energy loss outside the system boundary, it would mix and settle at an equilibrium temperature over time, as both fluids internal energy and degree of molecular disorderliness redistribute itself and changes.
Source: John Simonson, 1993. Foundations of Engineering pp 322
Furthermore, considering spontaneous combustion of fuel, the molecules of the hydro-carbon fuel generates heat once in the combustion process; at this point the individual molecules collide in a random, disorganised order. Once the heat has been generated and the energy within the fuel/air vapour mixture used up, it seizes to produce any more energy and remains in equilibrium with its environment; therefore, the internal energy within the fluid produced as heat, generated by the random collision motion of the individual molecules of the fluid, is lost to the environment and cannot be recovered. On further analysis, it will also be observed that at liquid state, there is high potential internal energy and lower entropy, and while at vapour form higher entropy occurs; furthermore, the changes in entropy between both states are greater than when in solid or pure crystalline form. Thus it can be inferred that the change in entropy between states of the working fluid in a process is greater than or equal to zero; this is in accordance with the second law of thermodynamics.
Bacon (1972) supports this concept of change and increase in entropy using the Clausius inequality theorem by indicating that a change in entropy occurs in an irreversible adiabatic process. Bacon (1972) further suggested that in the event of a reversible adiabatic process, no entropy change occurs and entropy equals to zero; and since entropy is an expression used to show the ratio of Heat over temperature, mathematically it could be expressed as:
S=Q/T (where ∑ (Q/T) ≥ 0 ≤ S)
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Where S= Entropy, Q= heat and T= change in temperature [absolute temperature in Kelvin].
Rogers and Mayhew (1992) analysed the concept of the 2nd law of thermodynamics and concluded that the 2nd law postulates that heat supplied in a thermodynamic cycle cannot produce a 100% equivalent work output; This supports the fact that energy is lost to the surroundings, and since a change of state occurs while energy is converted in an irreversible process within a fluid, the entropy of the fluid changes between states, and cannot be recovered but is lost to the surroundings. Reynolds and Perkins, (1977) further supported this concept by analysing that a process involving the transfer of heat energy to the environment results in a net positive increase in Entropy value.
The context of entropy in the 2nd law of thermodynamic can be explored further by recognising it as one of the properties used in deriving the state of a working fluid. Other properties include temperature, pressure, enthalpy and volume; it is also one of the properties used in calculating the amount of heat energy generated in a thermodynamic cycle phase, by referring to steam tables and thermal charts.
Rogers and Mayhew (1992) shows that although the, the 1st law of thermodynamics indicates that heat is converted to work, the 2nd law further establishes the fact that energy loss occurs while producing work, and this concept can be illustrated as shown below:
Source: Rogers and Mayhew, 1992. Engineering Thermodynamics
QH =W + Qc ↑
QH: The energy Input.
W: work [Useful energy]
Qc: Energy lost in the form of heat.
From the illustration in figure 1, the expression of heat loss can be derived from entropy; thus mathematically establishing a relationship between entropy and the 2nd law of thermodynamics.
Mathematically; Q = Sâˆ†T.
Where S= Entropy, Q= heat and âˆ† T= change in temperature [absolute temperature in Kelvin].
From the formula, it is observed that the Entropy of a working fluid during a thermodynamic energy conversion process, is a function of the value of heat generated in the process; thus the expression 'Entropy in thermodynamics as a function of heat generated, during an energy conversion process' is justified. Entropy is generated when a working fluid is not in thermodynamic equilibrium and at a higher temperature from its normal equilibrium temperature e.g. water at room temperature compared with superheated steam at 515oC, or liquid methane at -160oC compared with methane vapour at room temperature. As a consequence, energy generated in the form of heat is lost to the environment; Furthermore, working fluids undergo changes in their thermodynamic equilibrium when used in energy converters (engines) to convert useful energy to a form of work; for instance, a fuel and air mixture in the combustion chamber of a 2-stroke or 4 stroke diesel engine has a steady entropy value until spontaneous combustion occurs at higher temperature prior to the power stroke; It will also be noticed that while the piston is at top-dead centre, there is a higher temperature within the cylinder compared to, when at bottom dead centre of its stroke. This imbalance in temperatures causes the fuel/air mixture to generate and release energy in the form of heat, while increasing the entropy in the process and producing work [thrust force] on the piston and connecting rod.
The mathematical equation derived from the 2nd law of thermodynamic and entropy can also be used in deriving the value of work and heat in thermodynamic cycles, and this is considered as part of design parameters used in calculating cycle efficiency (Æž) or performance coefficients (COP) for steam power plants, refrigerating plants, diesel and spark ignition engines. Most engine performances and corresponding entropies can be illustrated in any of the five thermodynamic cycles in general use today, and the value of entropy is used in generating temperature -entropy (T-S) diagrams, which are used with steam tables and Mollier charts in analysing energy conversion efficiency against energy input and work.
The significance of entropy can be further examined by analysing the change in entropy within the context of the 2nd law of thermodynamics using the Carnot and Rankin cycles.
THE CARNOT CYCLE:
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The Carnot cycle is a basic steam cycle for conventional steam engines running on saturated steam; the cycle involves generating steam by heating the working fluid [water] to its saturation temperature. The steam generated is then used to power the steam engine and thereafter is condensed, then pumped and reheated.
The Carnot Cycle
Source: http://chemwiki.ucdavis.edu/Wikitexts/HOPE_343/Carnot_Cycle (accessed 24/02/2011)
From figure 2, the entropy and temperature is used to generate a diagram illustrating the thermodynamic process occurring at each stage of the Carnot cycle.
At stage 1 to 2: Heat is applied to water at temperature (T h) over a constant pressure; thereby increasing entropy, and generating saturated steam at stage 2.
Stage 2 to 3: The saturated steam (working fluid) is used to generate work in a simple steam engine; it will also be noticed that while useful energy in the form of work is being converted, no entropy change occurs because the process is adiabatic.
Stage 3 to 4: The working fluid is then condensed/ cooled in a heat exchanger after all the useful energy has be converted to work in the engine; It can also be observed that on cooling the working fluid, the entropy decreases. The cycle then starts over again with the water being pumped from stage 4 to 1.
Polak (1983) indicates that the Carnot cycle satisfies the concept of an ideal cycle producing work and generating a change in entropy during isothermal expansion of a working fluid, however Bacon (1972) shows that the cycle is not a realistic concept for gas cycles due to the fact that its thermal efficiency is presently unattainable. It is important to note that based on the 2nd law, the entropy of a working fluid is transferred to the environment thereby registering a net increase in entropy to the environment, or cooling medium in the condenser. From the illustration of the Carnot cycle, it can be observed that a change in entropy (âˆ†S) also registered an energy transfer (q); in conformity with the 2nd law, not all the energy (q in) supplied in the process was converted into useful work; thus a part of the energy was lost as heat (q out).
Thus: Qin=W + Q out
And using algebra; W=Qin - Q out
Thermal efficiency coefficient (Æž) = work/Energy input
È = (Q in - Q out)/ Q in
È =âˆ†S (T (1, 2)-T (3, 4) /âˆ†s T1, 2 (Carnot Cycle change in entropy is the same at both stages of heat transfer)
È =T (h) -T (l) / T (h)
From the illustration of the Carnot cycle, the property of entropy and temperature has been used in deriving the formula for Work done, heat energy lost and thermal energy efficiency coefficient; the numerical value of entropy can be derived from mollier chart or steam tables if other properties of the fluid like pressure and enthalpy is known.
Figure 3: Rankine Cycle
Source: http://commons.wikimedia.org/wiki/File:Rankine_cycle_with_superheat.jpg (accessed 25/02/2011)
Figure 3 illustrates the Rankin Cycle, and it is the basis for showing a more realistic thermodynamic process in a steam generating plant. Again, the significance of entropy during the different stages of the cycle is shown.
Stage 1 to 2: The water is pumped at 8 bar through a series of heat exchangers and then on to the boiler at approximately 220oC where it is heated till saturation temperature point; as the water is heated, the entropy gradually rises.
Stage 2 to 3: Part of the heat generated in the boiler furnace is transferred to the water in the boiler, and at saturated liquid temperature, it begins to boil, till saturated vapour temperature is achieved; the water then flashes off into saturated steam. It will also be noticed that as the water is heated up, its entropy rises.
Stage3 to 3*: The saturated steam is further heated by the exhaust gas from the boiler furnace in the super heater, thereby gaining more heat energy, resulting in an increase in temperature, pressure and entropy. At this stage, dry superheated steam is generated at a temperature of approximately 515oC.
Stage 3*to 4*: The high energy steam is transferred to the steam turbine where its high pressure energy is converted into kinetic energy in the turbine blades, which then spins the turbine wheels; thereby transmitting torque to the shaft and gear box. As the steam passes each stage of the turbine, energy from the steam is converted into work, until all the useful energy the turbine is capable of converting is used up.
Stage 4*to 1: The steam is condensed/cooled in a heat exchanger and it changes into water. As the working fluid passes through this stage, unused heat energy in the working fluid is lost at the condenser and entropy is lost to the cooling medium. Again a net increase in entropy to the environment occurs, thereby obeying the 2nd law of thermodynamics.
The change in entropy of a working fluid in the Diesel cycle is similar to the description of entropy change during spontaneous combustion of fuel as explained in earlier in this report. The concept of the 2nd law and entropy change also occurs in spark ignition and Jet propulsion engines, illustrated in the Otto and Brayton thermodynamic cycles respectively. However, energy management technology over the years are being researched and developed in an attempt to reduce, circumvent or limit net-energy losses over a period of time, by converting or transferring a percentage of the energy into another form of useful work; for instance the use of exhaust gas from diesel engines for driving turbo chargers, wind technology, fuel cell technology, and even re-introduction of exhaust gas into the combustion process to reduce specific fuel consumption. But since 2nd law of thermodynamics is a fundamental law, energy and consequently entropy is lost to the environment and cannot be reconverted into useful work.
Based on the analysis of entropy in the context of the 2nd law of thermodynamics, it is clear to deduce that entropy can only be clearly defined by examining the molecular activities of working fluids at different stages in a thermodynamic cycle; entropy exists as molecular chaos, and the heat loss generated from its effect is not 100% converted to useful work, but lost to the environment. For this reason, it has also been established that entropy is a function heat generated during an energy conversion process, and it is mathematically expressed as the ratio of heat and temperature. Based on this analogy, it is recommended that entropy can be reduced by either reducing the quantity of heat loss, or raising the working temperature of the working fluid; with this concept in mind, researches are being conducted to find innovative ways of improving engine efficiency and reducing the net entropy loss to the environment, thereby circumventing the 2nd law of thermodynamics; however, based on the fact that the 2nd law is a fundamental principle, it applies to all thermodynamic processes in energy converters existing today.