Latest / Mechanical Engineering Made Simple / (#48) Thermodynamics, Entropy, and Lost Work: The Bedrock of Pollution Control and Mechanical Design

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(#48) Thermodynamics, Entropy, and Lost Work: The Bedrock of Pollution Control and Mechanical Design · Mechanical Engineering Made Simple

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  Welcome back design junkies to Mechanical Engineering made
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  Simle. Our deep dive today is really
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  fundamental. We're talking thermodynamics,
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  material properties, and how they connect to managing energy
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  and importantly, pollution. This is the stuff you absolutely
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  need to know. Sort of the bedrock for talking
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  shop with any engineer. Exactly.
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  That's the mission today. We've looked at the core
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  sources, you know, property tables, the energy laws, even
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  specific pollution control tech. We want to pull it all together
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  and make it clear how these basic physics concepts, Dr.
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  Well, pretty much every design choice, from pumps to scrubbers.
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  OK, let's dive in Thermodynamics.
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  It all started way back with Saudi Karneau trying to figure
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  out the motive power of fire. It's a huge field, but really
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  rests on two key ideas. Let's start with the first law.
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  Right, the first law. It's like the universe's
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  accountant. It's all about conserving
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  energy. Basically it says the change in
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  a system's total energy that's E 2 minus E1 has to equal the heat
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  you add minus the work the system does.
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  Simple balance. So energy itself, that's a
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  property of the system, depends only on its state.
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  Precisely. That's the critical point.
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  Energy is a state property. But heat transfer delta Q and
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  work transfer delta W, Those aren't properties.
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  They depend on how you get from state one to state 2.
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  They're path dependent interactions.
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  OK. And that total energy change E2
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  minus E1. What goes into that?
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  Well, it breaks down into three main parts.
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  The change in internal energy, which is U2 minus U1 plus the
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  change in kinetic energy that's 1/2 M times the difference V 2
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  ^2 -, v one squared. And then plus the change in
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  gravitate in a potential energy MG times Z 2 -, Z one.
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  The first law. Just make sure we track it all.
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  Got it. So the first law says energy is
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  conserved. What about the second law?
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  That one feels different, more restrictive.
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  Yeah, you could say that the second law introduces the
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  concept of irreversibility. It's sort of the universe's tax,
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  the cost of doing anything useful.
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  It tells us we can't ever perfectly convert heat to work
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  or run processes backward without some loss.
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  And we quantify this loss, this irreversibility.
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  We do using entropy generation. We call it estgen.
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  For any real process in a closed system, estgen has to be greater
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  than or equal to 0. Mathematically, SGN equals S 2
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  -, s one minus the integral from one to two of delta Q / t and
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  that whole thing is greater than or equal to 00 means perfectly
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  reversible, which you know, never actually happens.
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  Positive means you've generated some irreversibility, some
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  waste. OK, here's the thing though.
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  Engineers talk about efficiency constantly.
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  How does this abstract entropy generation connect to, well,
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  lost work? Lost money?
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  That's the crucial link. It's formalized by the
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  Goystodola theorem. This is like the ultimate
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  practical consequence of the second law for engineers.
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  It tells you exactly how much useful work potential you've
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  thrown away. OK, break it down.
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  The rate of lost work, let's call it W lost, is directly
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  proportional to the rate of entropy generation S dot Gen.
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  The equation is just W lost equals T 0 * s dot Gen.
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  T0. There is the absolute
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  temperature of the surroundings your environment.
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  Wow, so minimizing that S dot Gen. is literally minimizing the
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  work you could have gotten but didn't.
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  Exactly. Think of entropy generation as
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  the friction or the heat leak in your process.
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  And Goistotela puts a price tag on it in terms of lost work.
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  So if you want the most efficient system, your design
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  goal number one has to be minimizing entropy generation
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  period. OK, that makes sense.
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  So we have these fundamental laws.
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  How do they apply when we're dealing with actual stuff, the
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  working fluids in engines or refrigerators?
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  We often use simplified models for these substances, right?
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  We do because real substance behavior can be incredibly
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  complex. The two workhorse models are the
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  ideal gas and the incompressible substance.
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  They represent opposite ends of the spectrum.
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  Let's start with ideal gases. When does that model work well?
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  It's great for gases at high temperatures and relatively low
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  pressures. Think air in an engine cylinder
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  before combustion or hot exhaust gases.
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  The defining relationship is beautifully simple.
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  Pressure P times specific volume V = R * T Well, actually just PV
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  equals R * T Well, actually just PV equals R constant, where R is
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  the ideal gas constant for that specific gas.
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  Right, the ideal gas law, and with ideal gases, specific heats
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  become important. Very important, we use C sub P
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  the specific heat at constant pressure and C sub V specific
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  heat at constant volume. And for an ideal gas, they have
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  a simple relationship C sub P = C sub V + R that same gas
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  constant. Do you have a number for R, say
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  for? Air.
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  Yep. For air R is about 286.8 joules
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  per kilogram per Kelvin. Knowing RCP and CV lets us
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  easily calculate changes in internal energy and enthalpy for
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  ideal gases. OK, what about the other extreme
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  liquids and solids? There we often use the
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  incompressible substance model. Think water in a pump or a block
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  of metal. The key assumption is constant
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  density. This usually holds well at high
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  pressures or low temperatures, basically when the substance
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  isn't easily squished. And how does that simplify
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  things? It simplifies the specific heats
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  dramatically. For an incompressible substance,
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  C sub P&C sub V are essentially the same, so we just talk about
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  the specific heat C So C = C sub V which approximately equals C
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  sub B Makes calculations much easier.
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  Now you mentioned internal energy and enthalpy, and entropy
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  came up with the second law. These aren't always easy to
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  measure directly. How do we relate them back to
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  things we can measure, like pressure and temperature?
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  Good question. We use what are called derived
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  thermodynamic property relations.
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  These are mathematically derived equations that link different
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  properties together. A really important one involves
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  Gibbs free energy, denoted by G. It's change DG can be expressed
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  as DG equals minus SDT plus VDP. OK, unpack that STVP.
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  Right, so SA specific entropy T is temperature, V is specific
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  volume, and P is pressure. What's powerful about this
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  equation is it shows how changes in entropy S and volume V are
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  directly related to changes in measurable things temperature T
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  and pressure P. Relationships like this are
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  actually how thermodynamic property tables, those big books
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  of data, are constructed from experimental measurements.
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  Speaking of measurements units, a classic engineering pitfall.
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  We use SI units mostly, but conversions still bite people.
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  Any key ones to remember? Oh definitely, Pressure is a big
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  11 bar is exactly 10 to the power of 5 pascals.
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  Don't forget that. And if you're dealing with older
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  systems or US customer units, that's roughly 14.504 lbs per
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  square inch absolute size IA mixing those up causes huge
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  errors. Yeah, I can imagine.
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  What about temperature Kelvin versus Celsius?
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  The key thing to remember is that temperature differences are
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  the same in Kelvin and Celsius. So a change delta T of say 10°C
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  is exactly the same as a delta T of 10 Kelvin.
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  Absolute temperatures are different, Kelvin equals Celsius
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  plus 273.15, but the change is identical, critical for heat
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  transfer calcs. Right, OK, so now we have the
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  laws and models for substances. Let's apply them to actual
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  engineering components. Turbines, compressors.
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  These are usually open systems with stuff flowing through
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  right? Exactly.
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  We analyzed them using a control volume approach, looking at what
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  crosses the boundary. Steady flow is a common
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  assumption. Let's take a turbine first.
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  Its job is to produce work. OK, so fluid flows in, expands,
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  spins the turbine flows out. How do we calculate the work?
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  The work rate W die T coming out is simply the mass flow rate N
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  dot times the change in specific enthalpy from inlet to outlet.
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  So M die out times H1 minus H2 enthalpy drops work comes out.
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  And efficiency, how good is the turbine in doing that?
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  We use the first law of efficiency, often called
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  isentropic efficiency for turbines ETA T It's the ratio of
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  the actual enthalpy drop H1 minus H2 divided by the ideal
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  enthalpy drop you'd if the process were reversible, meaning
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  isentropic H1 minus H2S. The S means constant entropy.
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  Yes, H2S is the enthalpy at the exit pressure if the entropy
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  stay the same as the inlet entropy S1 it represents the
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  maximum possible work extraction according to the second law.
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  And the second law also tells us directly that the entropy
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  generation rate S dot Gen. which equals M dot dot times S 2 -, s
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  one must be greater than or equal to 0 for the real turbine.
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  OK, now flip it. Compresses or pumps they consume
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  work to increase pressure. Right, the required work rate
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  input W dot C is M dot dot times the enthalpy increase H2 minus
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  H1. And the efficiency definition,
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  it must be different, right? It is.
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  It's flipped upside down compared to the turbine
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  compressor efficiency. A to C is the ideal reversible
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  work required divided by the actual work required.
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  So it's H2S minus H1 divided by H2 minus H1.
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  Why the flip? Why is the ideal the numerator
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  here? Because the ideal reversible
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  process represents the minimum work needed to achieve that
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  pressure rise. Any irreversibility, friction,
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  heat transfer means you have to put more work in to get the same
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  result. OK, so a real compressor always
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  needs more work than the ideal one.
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  Exactly. And again, the second law
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  confirms this. S dot Gen. equals M dot dot
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  times S 2 -, s one, and this must be greater than 0 for any
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  real compressor or pump. That generated entropy is why
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  you need the extra work input compared to the ideal case.
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  It directly connects back to lost work, just like Graisadola
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  said. This is great.
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  It really ties the fundamentals to component performance.
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  Now let's shift gears a bit and connect this to the environment.
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  Pollution control. Combustion is central to so much
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  mechanical engineering, but it's a major source of pollution.
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  Stationary sources like power plants are big contributors,
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  right? Huge, especially for sulfur
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  dioxide, SO2, and oxides of nitrogen NOx.
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  You mentioned the stats like 91% of USSO 2 and half the NOx comes
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  from stationary combustion. So how do we deal with SO2 after
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  it's formed? The main technology is flue gas
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  desulfurization, or FGD scrubbers.
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  Basically the most common type is a wet scrubber.
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  You use a slurry, usually lime or limestone, in water to absorb
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  the SO2 from the flue gas. And they work well.
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  Very well. Efficiencies are typically high,
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  often 90% or even better. But I imagine handling that wet
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  sledge afterwards is a headache. It absolutely is.
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  It adds cost, complexity, disposal issues which leads to
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  the alternative. Dry scrubbers are often called
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  spray dryer absorbers. SDA's here.
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  You spray a finer slurry into the hot gas, the water
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  evaporates quickly. The SO2 reacts and you're left
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  with a dry powder waste product. Easier to handle I assume.
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  Generally yes. Lower capital and operating
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  costs often, but the trade off is usually efficiency.
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  St. As typically run in the 70 to
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  90% removal range. Not quite as good as the best
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  wet scrubbers. So there's that trade off again.
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  Higher efficiency might mean more complex waste handling a
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  higher cost in a different way. It's an optimization problem.
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  Exactly. It's rarely just about
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  maximizing the thermodynamic efficiency of the separation
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  itself. You have to consider the whole
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  system cost and impact, including waste disposal.
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  Sometimes accepting slightly higher entropy generation in the
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  scrubber itself is worth it if it drastically reduces the
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  entropy and cost of dealing with the byproduct.
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  Makes sense. What about NOx control oxides of
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  nitrogen? You said?
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  Prevention is key there. Yeah, because once NO is formed,
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  especially, it's much harder to scrub out chemically than SO2.
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  The main culprit is thermal NOx. This forms when the nitrogen and
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  oxygen that are just naturally present in the combustion air
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  get really hot in the flame. They react.
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  And the reaction depends heavily on temperature.
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  Exponentially higher peak flame temperature means much, much
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  more thermal NOx. So the solution is cooler
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  flames. Essentially yes.
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  That's the principle behind low NOx burners, or L and BS.
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  They're designed to carefully control how the fuel and air
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  mix. They stage the combustion,
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  create fuel Rick zones initially, and manage airflow to
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  reduce those peak flame temperatures.
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  They also limit how much oxygen is available right in the
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  hottest zones. It's clever fluid dynamics and
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  reaction control. OK.
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  So we've covered air pollution from combustion.
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  What about water pollution? Similar principles of play.
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  Absolutely. Separation processes are key for
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  municipal wastewater treatment. The basic goals are usually set
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  by regulations. Typically they need to reduce
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  BOD biochemical oxygen demand. Basically how much oxygen
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  microbes will consume to breakdown the waste and
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  suspended solids. S S by at least 85% or meet
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  specific effluent limits, often around 30 milligrams per liter
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  for both BOD and S S. And beyond standard biological
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  treatment, what advanced methods use these thermodynamic or
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  preparation principles? Well activated carbon absorption
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  is a big one. It's used to remove dissolved
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  organic compounds, things like benzene, solvents that
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  biological treatment might miss. You pass the water through
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  columns packed with granular activated carbon.
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  The organic stick to the surface of the carbon.
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  How do you know how much carbon you need?
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  How much you can hold? We model the capacity using
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  absorption isotherms. A common one is the Fringlich
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  isotherm. It relates the amount absorbed
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  per unit mass of carbon Q to the concentration of the salute in
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  the water C The equation looks like Q = K one times C to the of
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  one over. NK1 and N are constants
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  determined experimentally for a specific pollutant and carbon
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  type. The key thing is it's nonlinear.
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  Capacity doesn't just scale directly with concentration.
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  Interesting. So you need data to design it
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  properly? What about removing salts?
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  Inorganic ions. For that membrane technologies
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  are dominant. Reverse osmosis or RO is
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  probably the most widespread for desalina tion.
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  In high purity water you use very high pressure, sometimes
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  hundreds of Sios to literally force water molecules through a
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  semi permeable membrane, leaving salts and other salutes behind.
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  That high pressure sounds like a lot of work input back to
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  thermodynamics. Directly, you're expending work
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  via the pump to overcome the osmotic pressure, which is
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  related to the chemical potential difference between the
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  freshwater and the salty water. It's the energy cost of
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  separation. Is there an alternative to RO
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  for ion removal? Yes, electrodialysis or Ed.
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  It also uses membranes, but specialized ones that allow ions
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  to pass, not water. You apply a direct electric
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  current across the stack cations.
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  Positive ions move towards the cathode anions negative ions
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  towards the anode, passing through their respective
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  membranes, leaving purified water in the central channel.
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  So instead of pressure work, you're using electrical work to
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  achieve the separation. Different driving force.
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  Same from thermodynamic principle of needing energy
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  input to create order separation.
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  Wow. OK.
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  So from Carno's original questions about fire all the way
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  to designing membrane systems for pure water, it really all
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  comes back to these core thermodynamic laws?
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  It absolutely does. The first law tracks the energy,
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  but the second law, through entropy generation and lost
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  work, dictates the efficiency, the cost, the feasibility of
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  everything from how much work a turbine produces to how much
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  energy a desalina tion plant consumes, to the trade-offs in
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  designing A pollution scrubber. The constant challenge is
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  minimizing that irreversible entropy generation within the
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  economic and practical constraints.
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  So the challenge for you design junkies listening is this.
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  Next time you look at any piece of engineering equipment, any
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  process, ask yourself where is the available work being lost?
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  What part of the system, what material property, what
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  interaction is generating the most entropy?
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  Finding that is the first step to making it better.
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  Until the next equation designed junkies, we are mechanical
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  engineering made simle.