Entropy,  Efficiency and Mr. Spock

“… there is an art to flying”, said Ford, “or rather a knack. The knack lies in learning how to throw yourself at the ground and miss.”

Douglas Adams’ “A Hitchhiker’s Guide to the Galaxy.”

Many indicate that energy crops are inefficient, changing best 40-60 % of the enter calories to electrical energy. Why can’t we do higher?  Easy solution – the Second Law of Thermodynamics. The Second Law places bettering energy plant potency to a lot more than 65% – 70% in the identical class as   “throw yourself at the ground and miss”,  simple to mention – however unattainable to do.  

The First regulation of Thermodynamics is relatively easy, “Energy can neither be created nor destroyed.” The Second Law, “In any adiabatic transaction entropy must increase” is, whilst in large part unintelligible, crucial to working out of thermodynamic potency and efficiency. The time period adiabatic method no calories is added or subtracted from exterior assets. Entropy is a measure of the high quality of calories. Further as entropy at all times will increase it dictates the course of the glide of calories in any thermodynamic transaction. There are many transactions that would continue in opposite with out violating different Laws of Physics however the undeniable fact that entropy should at all times building up dictates that they’re irreversible, they may be able to best continue in a single course.

Spock, Temperature Scales, and Efficiency

To perceive entropy, we can flip to a global galactic elegance science instructor, Mr. Spock. Spock, warping previous earth at some point, was once shocked to be informed that entropy calculations weren’t taught in the 2d grade and incredulous that the majority earthlings didn’t perceive the temperature scales. Spock thus beams us aboard for a five-hour undertaking to discover Temperature, Entropy, Efficiency, and the Food Replicator.

Spock begins by way of mentioning that according to a survey of 348 Class M Planets the Fahrenheit Temperature Scale nonetheless holds the galactic file for many disorganized, ill-conceived scale ever. First, the thermometer was once made, temperatures had been categorized, and it was once “discovered” that water iced up at 320F and boiled at 2120F.

In 1742 Andres Celsius determined there should be a greater method. He constructed a thermometer and put it in freezing water and marked the that time as 00C and put it in boiling water and marked that time as 1000C and put 100 levels in between. This is the Centigrade or Celsius Scale

Both scales alternatively omit the most important level they don’t get started at 0 temperature. Which then raises the query, “Is there such a thing as zero temperature?”

Figure 1. Temperature Scales

The solution is sure, it’s the level the place all molecular movement ceases. To confuse  High School Students even additional we have now two scales beginning at  Absolute Zero, The Rankine Scale which makes use of levels the identical measurement at the Fahrenheit scale and the place 00R is minus 459.670F and the Kelvin Scale which makes use of levels that have the identical measurement as centigrade levels and the place 00Ok is minus 273.150C. Figure 1 displays a comparative take a look at Temperature scales. To simplify issues let’s suppose that absolute 0 is -4600F and that the earths reasonable temperature is +600F hanging earth at about 5200R. 

Once the scales are understood Spock begins  his entropy dialogue with two comfortable drink cans as proven in Figure 2, one can at 1000F and any other at 00F( the comfortable drink, from Vogon, is so concentrated that it does now not freeze even at 00F ). He places them in a superbly insulated field. Later, after a smash, part the elegance[1] returns and each cans are at 500F as proven in Figure 3. Spock then asks the query, “Will the cans in Figure 3. ever go back to their state in Figure 2? Clearly not.

Figure 2. Soft Drink Cans

Figure 3. Soft Drink Cans

But why not? If the cans went back to the 1000F – 00F state the First Law would not be violated, energy would neither been created nor destroyed. Common sense however tells us that the cans will not reverse their trip. The Second Law tells us they cannot reverse their trip.

As energy transfers from the hot can to the cold can the warmer, faster molecules slow down and the cooler, slower molecules speed up. Once the water molecules are all at 500F there is no way they can collide so that one molecule speeds another back up to the 1000F energy, the transition is irreversible. For a parallel example consider a demolition derby. Can you think of a way that two 50 mph cars could collide so that one of them ended up at 100 mph?

her example is a box with fifty White Balls lined up on one side and 50 Black Balls on the other side. Once you start shaking the box what is the probability that the Balls will ever reach their initial State. There is nothing to prevent this, but the probability of this outcome is exceedingly low. Next consider the probability that the several zillion molecules in the soft drink cans will return to their initial state and you can see why Thermodynamic Transactions increase entropy and flow in one direction.

In the 1000F/00F the 1000F molecules were in one can and the 00F molecules were in the other can, a state of order prevailed.  In the 500F/500F scenario disorder prevailed, everything was the same. 

This use of the terms “Order” and “Disorder” is complicated to many as they imagine that the ultimate state the place the whole lot is the identical will have to be a state of order whilst the preliminary state the place temperatures are other will have to be a state of dysfunction. But take into consideration two Marching Bands. Order is after they everyone seems to be covered up, dysfunction prevails when they’re all wandering round on the box. It is now and again more straightforward to view the Second Law in Terms of concentrated Energy and Dispersed Energy. In any Adiabatic Transaction Concentrated Energy will likely be dispersed, dysfunction will building up. In Thermodynamic transactions dysfunction at all times will increase. Entropy is a measure of the level of order and dysfunction.

Some might indicate that it’s simple to pay attention calories, merely put a pot of water on a range and boil it. But that isn’t an Adiabatic Transaction, you’ve gotten added warmth. If you come with the Heat enter from the Stove dysfunction and Entropy greater.

Now let’s believe the Soft Drink Can Experiment from a piece standpoint. A thermocouple is a tool that may generate electrical energy from temperature variations. In Figure 1 a thermocouple may extract calories from the cans because of the temperature distinction.  

But if we let the cans achieve 500F/500F state we have now eternally given up the alternative to extract calories from this 1000F – 00F temperature differential. The identical quantity of calories continues to be found in the 500F/500F state, calories can neither be created nor destroyed.  But by way of permitting the concentrated calories in the 1000F can to  mix with the decrease grade calories in the 00F the concentrated calories has dispersed, dysfunction has greater and we have now  eternally  misplaced the skill to  extract  helpful paintings from the preliminary  temperature distinction.

As effectively as having a amount equivalent to BTU’s or Joules calories has high quality. Entropy isn’t a “thing” It is a measure, a measure of high quality.  As we disperse the calories from a excessive temperature to a low temperature, we ruin that high quality and create entropy or already used up calories. The calories continues to be there, it has now not been destroyed, it is only of decrease high quality. In any thermodynamic transaction the whole calories enter is transformed into both helpful paintings or already used up calories or entropy. The trick for designing for optimum potency is to attenuate entropy technology and maximize exergy output or Exergy.

Here is the easy equation for paintings in a procedure the place fuel at a continuing strain is used to force a piston to do paintings.

dH=TdS+PdV

In this equation the first “d” is simply the mathematical image for differential or distinction and H is Enthalpy, the whole calories content material. So, dH method the trade in whole calories content material in the gadget, on this case the enter Energy. T represents temperature whilst dS method the trade in Entropy. PdV represents Pressure(P) occasions trade in quantity (dV). Note that during gadgets PdV is solely strain(lbs/feet2) * quantity (feet3) which when multiplied in combination give ft-lb which is figure.

Thus, the enter calories can both move into paintings (PdV) or entropy (TdS). The objective of gadget design is thus to attenuate entropy technology and maximize paintings.

Consider two weights tied to 2 ropes wound in several instructions round a pipe. As the weight heavier weight falls it turns the pipe which then lifts the different lighter weight. In this case maximum of the calories stays concentrated, it’s now in the lighter weight and now not a lot entropy has been created. Now believe the identical pipe and weight however this time the pipe drives a fan. In this example all the calories has long gone to combine up air molecules, it has long gone from concentrated to dispersed and can’t be used to do helpful paintings. All the enter paintings has created entropy, already used up calories.

Why can’t we simply make Heat Engines that don’t create Entropy?

Figure 4. Simple Piston Engine 

To solution this query Spock takes you to the Enterprise’s Museum of Ancient Technology the place he displays you the easy (however thermodynamically highest) piston engine proven in Figure 4. On the left-hand we have now a piston (blue) with a red weight on the best resting on 700F air. In the subsequent diagram a 7000F warmth is offered both by way of igniting gas or via a warmth exchanger. This warmth heats up the 700F air to 5000F lifting the piston and weight as the air expands. Note that by way of blending 7000F warmth with 700F air to create 5000F air we have now created entropy simply as we did with the comfortable drink cans. We have used a few of calories to warmth air, to not do paintings. As the air does paintings by way of increasing and lifting the piston and weight it cools to 2000F.

The subsequent query is, “What now?” As our gadget is highest and lossless the 2000F air will stay at 2000F eternally and the piston won’t return to its authentic place to start out any other cycle. Thus an exhaust valve should open letting the 2000F excessive strain air out of the cylinder to combine with the 700F ambient air developing much more entropy because of the strain and temperature differentials between the 2000F pressurized piston air and the 700F outside-unpressurized  air. Note that each temperature and strain differentials can create entropy.

Spock then issues out we needed to let the air out of the piston to go back to the authentic state on order to run in a cycle. Another commentary of the Second Law makes use of this commentary: “ It is impossible to construct an engine, operating in a cycle, which takes heat from a high temperature reservoir and does work without exhausting heat into a low temperature reservoir.” Note that during each the consumption cycle and exhaust cycle we created entropy. Your subsequent query is why we will be able to’t simply design higher machines that don’t create as a lot entropy.

Figure 5. Vulcan Second Grade Entropy Kit

To solution that Spock will give you the Vulcan Second Grade Entropy Kit; 4 completely insulated Containers stuffed with a liquid at 1,0000 R (~5400F), and an ideal thermocouple as proven in Figure 5. He explains that he’s the use of the Rankine Temperature Scale as ALL Thermodynamic Calculations should be finished the use of a scale that begins at Absolute Zero.

Next you seek advice from a 7000R global. Here your thermocouple starts to paintings and extracts calories from the container.  But as calories is extracted the boxes cools. When the container reaches 7000R no extra calories may also be extracted. You had been thus in a position to extract 30%, of the boxes whole  calories.He first beams you (effectively insulated) onto a planet with a temperature of  1,0000R the place  you find that the thermocouple  can’t do any paintings with the warmth in container as the temperature on each ends of the thermocouple is 1,0000R.

Next you warp to a quite cooler however earth-like 400F global (5000R). On this global it is possible for you to to extract calories till the calories of the container reaches 5000R or 50% of the calories.

Finally, you get to the 00R global the place, effectively insulated, you find that the thermocouple can extract 100% of the calories from the container

Regardless of which global which Mr. Spock beams you to or what preliminary stipulations existed in the vials or what procedure was once used to warmth them,  you are going to briefly uncover one in all the basics regulations of thermodynamics and entropy: The most potency of any warmth engine is;

Efficiency (Max) = (Tin – Tout) / Tin.

Where Tin is the enter temperature and Tout is the exhaust temperature (the use of a scale that begins at Absolute 0.)  On the 7000R global our 1,0000R container would lead to a most theoretical potency of (1,000-700)/1000 or 0.3 = 30%. Thus, potency is an instantaneous serve as of the distinction between enter and output temperature, the higher the distinction the upper the potency.

You might suppose this isn’t proper. You simply, heated a substance from 700F (5300R) to 1000F (5600R) and you will have to have the ability to get again as a lot warmth as you installed. Sorry, your state of affairs is no other than if you happen to have been beamed to earth with a vial of liquid at 1000F (5600R). The most potency, the ratio of calories in-to energy-out is (560-530)/530. It makes no distinction what means you used to warmth the container, what means you employ to extract the warmth, what the preliminary stipulations had been and so on., the Formula offers the Maximum Theoretical Efficiency of any Heat Engine.

Efficiency (MAX) =(Tin-Tout)/Tin   

This issues out that we don’t have a World Energy Crisis, we have now a World Entropy Crisis. In a 600F (5200R) global we have now numerous calories. What we do have is an entropy Crisis as maximum of this calories is unavailable to be used as it’s already at or close to the ambient temperature.

Another method of having a look at thermodynamic potency is to believe an individual on a diving board fifteen toes above the backside of the pool. If the pool has ten toes of water the particular person can best trade one-third in their doable calories into kinetic calories as after they hit the water, they may be able to move no additional.  If the pool has 5 toes of water, then can trade two-thirds and if the pool has no water, they may be able to trade all their doable calories into kinetic calories with the attendant ugly penalties. Molecules having a warmth content material are the identical, after they cool all the way down to the ambient temperature they may be able to fall no additional, no extra calories may also be extracted, the calories continues to be there it simply can’t be extracted to do helpful paintings except you lower the outdoors ambient temperature.

For energy crops if the inlet temperature of a turbine is  10400F (about 15000R) and the outlet (ambient air) temperature is 400F ( about  5000F Rankine) the most theoretical potency it might download is (1,500-500)/1500 or 1,000/1500 or about 33%. Since it’s unattainable to build a plant working at the most theoretical potency (there are losses) energy crops perform at decrease efficiencies than the Maximum Theoretical Efficiency. Due to low temperature equivalent to those energy crops in the 1940’s operated at about 33% potency. Today plant temperatures are upper leading to upper efficiencies.

As outlet temperature isn’t controllable the major driving force of contemporary turbine design is thus the quest for upper inlet temperatures the use of unmarried crystal steel blades with thermal and ceramic coatings. These blades are cooled by way of decrease temperature steam circulating within the blade and additionally escaping from tiny holes close to the Leading Edge forming a protecting cooler layer on the floor of the blades.

An attention-grabbing reality is that many Electric Markets crops should record Summer and Winter Qualified capability (Peak Output) as in the wintry weather crops have decrease Outlet Temperatures and therefore upper potency and subsequently upper output.

The skill to deal with excessive temperatures is one in all the major the explanation why fuel generators are extra environment friendly than steam generators equivalent to utilized in coal crops. For example, the turbine inlet temperature of a fuel fired Mitsubishi 501J is set 2,9000F whilst in a supercritical coal plant it’s about 1,3000F. Temperature alternatively isn’t the complete tale. Coal crops alternatively have a lot upper inlet pressures which is able to additionally carry out paintings. And, as defined under, coal crops should additionally take care of the Heat of Vaporization. The quantity of calories had to convert 1000C water to steam.

Nucear crops run at low temperatures (about 5700F however, once more, at upper pressures than fuel generators) and therefore low efficiencies as the zirconium cladding on the gas rods would soften at upper temperatures. Next technology nuclear crops having ceramic gas or different enhancements letting them run at a ways upper temperatures and efficiencies.

Figure 6. Space Suit Refill

Spock subsequent explains that paintings may also be finished, and entropy can be created, by way of variations in strain as he walks you to the Enterprise Space Suit Oxygen Refill Tanks.  When you arrive Spock takes 3 tanks, one empty and the different two at 3,000 PSI. First, he hooks the tanks in combination (“B” in Figure 6) and the ensuing strain in the tanks is two,000 PSI.

Next Spock takes 3 different tanks having the identical preliminary stipulations and hooks one 3,000 PSI tank to the empty tank leading to the two tanks every having 1,500 PSI (“C” in Figure 6). He then hooks the 1,500PSI tank to the final 3,000 PSI tank (“D” in Figure 6) and each finally end up at 2,250 PSI which is 250 PSI upper than simply hooking all 3 tanks in combination.

Why? By protecting one 3,000 PSI tank in reserve you didn’t divulge it to the decrease strain of the empty tank developing entropy or already used up calories. Every SCUBA Diver is accustomed to this procedure as that is the method Dive Shops fill SCUBA Tanks. You will see this procedure once more, the use of temperature relatively than strain, once we talk about Feedwater Heaters in Power Plants.

Adding Heat at the Highest Possible Temperature.

Figure 7. Adding Heat at the Highest Possible Temperature

Spock then comes to a decision to turn you any other experiment which has main implications for powerplant design. Although Spock hates kilos as they, like the Fahrenheit Scale, are irrational he comes to a decision as he’s in geostationary orbit over the U.S it’ll be ok. But he issues out that kilos and Fahrenheit in combination result in an much more irrational unit, the British Thermal Unit or BTU. A BTU is the quantity of warmth required to extend the temperature of 1 pound of water one level of Fahrenheit.

Spock then will give you 4 one-pound boxes of water, “A”, “B”, “C”, and “D”. as proven in the Bottom Box of determine 7. Next, he will give you two BTU’s which you employ to lift the temperature of Containers “B” and “D” 10F as proven in the heart field.  “B” and “D” are actually one 10F level warmer than “A” and “C”.

Now Spock will give you any other BTU and a call as proven in the best Box. You can use your BTU to lift Container ”A” one level in order that it’s now equivalent in temperature to Container  “B” as proven in the left portion of the best field. Or, on the proper in the best field you’ll be able to go away Container  “C” at its’ authentic temperature and lift Container  “D” any other one level. Spock then asks you which of them possibility is best possible.

Having been via the Spock demonstration with comfortable drink cans you briefly acknowledge that the lift Container “D” possibility is best possible.  With an excellent thermocouple shall we get calories from the “C-D” configuration and it might decay to the “A-B’ State as energy was removed. While in the “A-B” state we have now eternally misplaced the calories which may be received from the “C-D” temperature differential.  This experiment and Space Suit Oxygen Refill experiment display any other elementary outcome of the Second Law: it’s at all times extra environment friendly so as to add further strain at the easiest strain and further warmth at the easiest temperature as much less entropy is created. 

An attention-grabbing tale about entropy is how one industries quest to lower entropy radically remodeled any other Industry. Early jet engines equivalent to the ones used on the Boeing 707 and 727 airplane compressed air, injected gas right into a combustion chamber and then expelled the excessive temperature and high-pressure air out the again offering thrust. As a lot of the excessive temperature and excessive strain dissipated into the setting 707 engines had been amongst the most productive machines ever invented for changing jet gas into noise and entropy.

The answer was once to put turbine blades in the scorching fuel pathway changing the in the past wasted calories into shaft horsepower. The shaft ran to the entrance of the Engine and grew to become a big “Fan” (propeller) forcing air backwards outdoors the engine however within a shroud. The “High Bypass” Engine was once born. This configuration is the reason why trendy airplane engines are such a lot wider. Today whilst you fly a 777 or 787 you might be flying a propeller pushed airplane, over 90% of the thrust cones from the Fan hugely bettering calories potency and airplane vary.

How did this variation the Electric Utility Industry? Before the 1970’s the plant with the easiest potency was once most often the biggest plant. These crops price over one thousand million bucks to construct and best massive well-financed corporations may input the business.  With the introduction of the High Bypass Engine engineers briefly found out that one may take away the fan, insert a generator, and use the engine for energy technology.  The least expensive, most productive plant to construct was once now an Aeroderivative Gas Turbine. Further development time for a coal plant was once measured in years. For an LM-6000 Aeroderivative it was once months. The Gar Turbine Unit was once standardized, and manufacturing unit constructed; construct the basis, the fuel and electrical infrastructure, hook it up and you had been in the electrical trade. Competition arrived and the business modified eternally. All of this as a result of the airways had been getting uninterested in having to make a gas forestall in Bangor, Maine on the long ago from Europe

Power Plants, The Brayton and Rankine Cycles

Figure 8. Typical Coal Plant (Rankine Cycle)

Figure Eight displays a one-line schematic of a Rankine Cycle Coal Plant which displays a number of cases of “adding heat at the highest possible temperature.” Let ‘start with the turbine exhaust, the steam coming out of the Low-Pressure Turbines (the Yellow Triangle LP Turbines in the diagrams).

From the LP Turbines the steam exhausts into a condenser vacuum where it condenses into water. The “vacuum” condition is so that the steam condenses at a lower temperature decreasing exhaust temperature and pressure hence increasing efficiency and plant output. Once the condensate water leaves the Condenser (flowing through the blue dashed line) it enters the feedwater heaters, devices designed specifically to add heat at the highest possible temperature.  

The feedwater heaters, (the green cylinders, four in this diagram) take extraction steam from the turbines and use it to heat the feedwater. The first stage feedwater heater extracts low temperature steam from the LP Turbine and increases the water temperature through a heat exchanger mechanism. After passage through the Boiler Feed Pump, which increases the pressure up to about 2,000PSI, the feedwater comes to the next stage of feedwater heating which takes even higher temperature steam raising the water temperature even further. The remaining feedwater heaters continue the process, taking the increasingly hotter feedwater and adding increasingly higher temperature. steam.

The water then pass through the economizer where even hotter exhaust gas raises the temperature even further, the water then proceeds to the steam drum where it descends to the bottom of the boiler and then passes upward through the  “Waterwall”, hundreds of vertical pipes, welded together to from the boiler walls where it picks up even more heat. From the waterwall the water returns to the steam drum where it either turns to steam or makes another circuit through the waterwall.

As the water changes to steam a huge amount of energy is required. A Calorie is defined as the amount of heat necessary to raise one gram of water one degree centigrade. As we heat the feedwater it’s One Calorie in keeping with Degree Centigrade; then we hit 1000 Centigrade. To trade that one gram of 1000C water to 1000C steam takes any other 540 Calories. So, to head from 700Farenheit (210C) to 2120F (1000C) took (100-21) or 79 Calories/gram. To trade the water to steam took any other 540 Calories in keeping with gram, over 7 occasions as a lot. Although this turns out like an enormous waste of calories when seen from a temperature standpoint we have now received a lot, we have now modified water to steam and the that steam has the skill to do paintings because it strikes via the generators.

After leaving the Steam Drum the steam is going via the First Stage Superheater and after all to the Last Stage Superheater which is simply above the flame entrance the place the freshest stem choices up the freshest warmth. All of this to “Add heat at the highest possible temperature.

After leaving the Superheater the steam travels to the first stage or High Pressure (HP) Turbine. After passing through the HP turbine it returns to the boiler to be reheated (adding heat at the highest possible temperature) and then to the Intermediate Pressure Turbine. As the steam cools it expands. To constantly reduce the pressure so as to keep the steam as a vapor each row of turbines blades is larger than the one before it increasing the volume as the pressure drops. Finally, after leaving the IP Turbine the steam has expanded so much that it usually requires two low pressure turbines.

After the steam it is exhausted from the LP Turbine it goes into the condenser and it is here that a major heat loss occurs. Remember the 540 calories per gram it took to turn the water to steam? When we turn that steam back into water, we get an instant replay but in reverse. To turn 700F (about 200C) steam back into 700F Water we emit 540 calories per gram. The condenser brings in colder water from a lake, river, or ocean. This water travels through the inside of thousands of condenser tubes to extract the 540calorie per gram heat generated from condensing the water and in doing so the cooling water rises about 400Fcreating large amounts of entropy.

This water can be returned to the source but is usually to hot so it must go through a cooling tower where the water falls through the air and vaporizes it again gives up 540 calories. Thus, as the steam system is a closed circuit, the 540 calories per gram used to vaporize the water is all rejected to the condenser and then to the cooling tower.

Figure 9. Combined Cycle Cogeneration Plant (Brayton and Rankine Cycle)

Everything we have learned about entropy is utilized in a Combined Cycle Plant. In a Combined cycle plant as shown in Figure 9 we utilize two different Thermodynamic Cycles. The first (the “Brayton” Cycle)  

 Uses a fuel turbine to energy a generator. The fuel turbine exhaust alternatively is set 10000F and nonetheless accommodates a lot useable calories.

Note that during the Brayton Cycle there may be no reason why to show water into steam with the attendant losses as there may be in a Rankine Cycle Unit. The scorching gases run at once via the turbine generating paintings. Thus, a natural Brayton Cycle Unit equivalent to a fuel turbine does now not have a necessity for cooling water.  The Brayton cycle may now not be run in a standard coal plant as the molten ash and particulate subject would quickly ruin the turbine blades. Thus, the push for coal gasification in order that the next potency Brayton Cycle can be used for coal.

In a Combined Cycle Unit, the scorching turbine exhaust is then run via a Heat Recovery Steam Generator or HRSG the place the exhaust calories is used to show water to steam which then runs a turbine the use of a standard Rankine Cycle. By the use of the Rankine Cycle, we keep away from discharging 10000F air into the setting developing huge entropy. as an alternative we use it to do paintings. The undeniable fact that those gadgets use the Brayton Cycle on the entrance finish and the Rankine Cycle on the again finish is the place the identify “Combined cycle comes from. As the Brayton Cycle portion of the plant does not need cooling water a combined cycle unit only uses about 40% of the cooling water as an equivalent coal plant.

Due to the differences in efficiencies  modern combined cycle plants can generate one kw-hr with just less than 7,000 BTU’s/kw-hr while a Coal plant normally requires about 10,000 BTUS/kw-hr (this number is referred to as the plants “Heat Rate.) This lower fuel usage also translates into lower CO2 emissions.

Many large combined cycle plants stop there but others, located near industrial facilities or areas needing central heat, go even further in utilizing waste heat for other purposes. These units are known as Cogeneration or “Cogen” amenities. In determine 9 the HRSG has two further outputs. Fist a few of the exhaust is distributed to any other facility to energy a dryer and separate warmth exchanger segment is positioned in the HSRG to offer scorching water to the buyer.

Why does this make sense? Entropy. Methane burns at about 3,5000F.  Going again to the comfortable drink cans take into consideration the calories eternally misplaced by way of burning methane at 3,5000F and blending it with 700F air to get 2900F air for the dryer when the energy plant exhaust is to be had for no added calories. On a in keeping with unit foundation one in all the biggest entropy turbines round is in your home, burning methane at 3,5000F to warmth 700F air to 1200F or so that you can warmth your house. Many towns equivalent to Boston and New York thus have Cogen crops and use their waste warmth to provide central warmth.

TS Diagrams

Figure 10. TS Diagram Brayton Cycle

A great way to visualise Entropy is thru a TS Diagram (Temperature – Entropy Diagram, S stands for Entropy) as in Figure 10. which displays a TS Diagram for the Brayton Cycle utilized by a fuel turbine. Thermodynamics majors might suppose that is an extraordinary having a look TS Diagram and it’s. I’ve began T at absolute 0. Normally, as in Figure 11, under appearing a superheat Rankine Cycle we begin T slightly under the lowest temperature in the cycle as we all know there may be numerous area under the diagram (along with saving calories engineers like to save lots of paper area.) But by way of operating the curve to Absolute Zero all of the calories curious about the transaction is proven.  The house categorized W is the paintings finished in the transaction the Area categorized OE is the different calories in the transaction.

Point 1 in Figure 10. signifies the temperature and entropy of the inlet air. The trail between Points 1 and 2 is the place the air is compressed and heated in the turbine compressor. The trail from 2-Three is the combustor whilst 3-Four is the fuel increasing via the turbine doing paintings. Path 4-1 is the exhaust increasing and cooling again to atmospheric strain and temperature.

An attention-grabbing side of TS Diagrams is that the house bounded by way of 1-2-3-4 Curve is the paintings being finished in the transaction. You night time surprise why a TS Diagram would display paintings however take note the equation given above for paintings and entropy.

dH=TdS+PdV

It is apparent from this equation that each one the calories in the transaction is going into paintings or entropy. If you view the aircraft in the TS Diagram as the whole temperature – entropy probabilities

the house outdoors house 1-2-3-Four equals TdS and the house within 1-2-3-Four is the same as the paintings finished.

These diagrams additionally give us a very simple strategy to visualize Efficiency – W/(W+OE). From Figure Nine one can see that the house 1-2-3-Four or paintings is decided by way of inlet and outlet temperatures and entropy generated.   

Some might indicate that producing extra entropy (Going additional alongside the X Axis will building up the house below the curve and thus extra paintings. That is only a subject of scale. I’ve run the curve all the way down to Absolute Zero to turn all the calories of the substance curious about the transaction together with its latent calories sooner than it was once heated. If you lengthen the house additional alongside the entropy axis you additionally building up the 1-2-3-Four house but additionally building up the “OE” Area proportionally and the ratio of labor to whole calories stays consistent.

The larger the distinction between Tin and Tout the largerthe house below the TS Curve with regards to the house below the line 1-Four line and the larger the potency.

The best strategy to building up the paintings -to-total calories or potency is to lift the 2-Three line by way of operating at the next inlet temperature or decrease the 1-Four line by way of operating at a decrease outlet temperature. Lowering line 1-Four is the reason why we produce a vacuum in the condenser in order that the steam will condense at a decrease temperature thus gaining potency.

Figure 11. TS Diagram Rankine Cycle

Figure 11 displays the TS Diagram for a Superheat Rankine Cycle as utilized in a Coal Plant. Superheat merely implies that warmth is implemented to a fuel above a temperature the place all the liquid has transformed to vapor. In Figure 11 There is a upside “U” formed curve in the background. That curve is a steam curve and displays the state of water as both Water or Steam.  Simplistically, the whole lot to the Left of the Peak of the Curve is water (1-2-3) whilst the whole lot to the Right(5-6-7-8) is  steam. The Area in the Middle of the Curve is the house the place we’re transitioning from Steam to Water or Vice Versa.

Point 1 is the temperature within the condenser. which represents the outlet and inlet temperature of the cycle as the cycle is a closed loop.  From Point 1-2 the water passes thorugh one degree of Feedwater Heating and the Boiler Feed Pump. From Points 2-3 the water passes via further Feedwater Heaters and the Economizer to the Steam Drum. From 3-4 the water circulates via the Steam Drum / Waterwall System till it converts to steam. During this section all the added calories, 540 Calories in keeping with gram, is going into the Heat of Vaporization and therefore entropy, none of it’s elevating temperature. But there’s a just right reason why for doing this as we’re changing water to stem permitting us to make use of the steam in a turbine to transform the excessive strain to paintings. At level Four all the water has transformed to steam and we now upload warmth in the superheater from issues 4-5. It is apparent from the slope of the 4-Five line that temperature is expanding elevating the plant potency. Thus is the complete level of the Superheater; so as to add warmth at the easiest conceivable temperature in spite of everything of the water has been transformed to steam in order that the  warmth is going into elevating stem temperature and now not changing water to steam thereby developing Entropy.

From 5-6 the steam is increasing via the High-Pressure Turbine giving up calories and doing paintings. It is vital for the temperature at level 6, the exhaust from the HP Turbine be above the level the place the steam would start condensing to water. From 6-7 the steam passes via the reheater including warmth at the easiest conceivable temperature above the temperature the place a few of the warmth would move into changing water to steam. From 7-8 the water passes via the IP and LP Turbines. When the steam reaches the condenser as it’s in a closed gadget it’s less than atmospheric strain, most often at about 2 PSI enabling it to stay as steam at a decrease Temperature.

Finally, from 8-1 the steam converts to water in the condenser giving up its’ hard-earned 540 Calories in keeping with gram Heat of Vaporization to the Cooling Water. As sooner than the whole paintings finished is the house within the curve which additionally displays the building up in house (paintings) because of Superheat and reheat.

We are living in a universe of entropy. In addition to thermodynamics the arithmetic of entropy. have packages in quantum mechanics, pc science, data principle and a number of different fields. And, in the finish, maximum imagine the Universe will die an entropy demise, the whole lot will cool to a temperature close to absolute 0. No paintings will likely be conceivable. However even right here there will likely be some order left in the Universe as molecules could have other states. 

Although we can’t achieve  absolute 0 if we had been in a position to proceed the adventure from the “Entropy Death” Temperature all the way down to absolute Zero we’d in finding that an ideal crystal has just one state at that temperature and therefore has precisely  0 entropy.  This is the Third Law of Thermodynamics.

We have no idea the final temperature of our universe. Some imagine it’s round 40Ok whilst others have other theories.

Spock believes that imagine that because of interactions between the quantum vacuum fluctuations, Dark Energy  and the High Level of Energy present in the Higgs Field in Empty Space (246 GEV) and cosmological consistent concerns the right kind solution to the Heat Death Question  is 420Ok after all offering the final query to head with the already recognized solution to the Ultimate Question – 42.[2]

Spock, glad that you’ve accomplished the Vulcan Second Grade stage, now prepares to beam you again to earth. Knowing you might be newly an expert in entropy and calories conversion; Spock modifies his standard Goodbye announcing, “Live Long and Prosper in the energy conversion business by always adding heat at the highest possible temperature.”

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Authors observe. This paper is open supply. The paper is meant to lend a hand starting Thermodynamics Students perceive entropy sooner than they get into the math and lend a hand other folks in the calories box to expand a greater working out of calories conversion and  energy plant operation and efficeincy. Hopefully it’ll lend a hand satisfy the ones wishes.

I’m an Electrical Engineer (who has hung round energy crops for many of my existence) and absolutely notice that Mechanical Engineering Instructors  can toughen in this paper and that I’ve taken a few shortcuts. So be happy to make use of excerpts, edit the paper on your personal wishes, and so on. without or with attribution.  

Charles E. Bayless   ceb1618@aol.com

­­­Retired President, West Virginia University institute of Technology

Retired CEO of Tucson Electric Power and Illinois Power

Co-Chair of The Climate Institute.


[1] During the smash, the different part used the Food Replicator, and every ate up a Pan Galactic Gargle Blaster. According to the “Hitchhikers Guide to the Galaxy” the results of a Pan Galactic Gargle Blaster are like “having your brains smashed out by a slice of lemon wrapped round a large gold brick.” Other authoritative assets indicate that eating two Pan Galactic Gargle Blasters will reason your Brains to be expelled via your ears. Ford Perfect alternatively is understood to have ate up 3 at a unmarried surroundings which most probably explains numerous Ford Perfect’s conduct.

[2] In “The Hitchhikers Guide to the Galaxy “a Giant Computer “Deep Thought” was once built and instructed to seek for the solution to the Ultimate Question of Life the Universe and Everything. Deep concept calculated for 7.Five million years and then introduced sooner than a Grand Galactic Gathering the Answer – 42. After a number of moments of misunderstanding, clean appears to be like and shocked silence, Deep Thought was once requested, “Err, exactly what is the Ultimate Question.” Whereupon Deep Thought answered, “I don’t know, I wasn’t told to find the question.” A brand new, a lot higher pc, earth, was once then constructed to find what was once the final query. Unfortunately, earth was once destroyed by way of Vogons to make a clearing for a hyperspace throughway ten mins sooner than it arrived at the solution. If Spock is right kind that the final temperature of the universe is 420Ok we might after all have came upon the long-lost query to head with final solution of 42.