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(#98) Fuel Cells Cheat The Carnot Limit · Mechanical Engineering Made Simple

• 0:00
  Welcome back to Mechanical Engineering Made Simple.
• 0:02
  Today we are going to talk about a device that arguably breaks
• 0:06
  the rules of how we think engines should work.
• 0:09
  That's a bold start. Usually when we talk about
• 0:12
  engines on this show, we're talking about, you know, fire,
• 0:14
  pressure, noise, all sorts of moving parts.
• 0:16
  Exactly. But today we are talking about a
• 0:19
  magic box. Just bear with me on the
• 0:21
  metaphor for a second. Imagine a box where you feed
• 0:24
  fuel in one side, let's say hydrogen.
• 0:26
  But instead of exploding it, right, instead of Pistons
• 0:29
  slamming up and down, or turbines spinning at 10,000 RPM,
• 0:33
  this box just sits there, silent, stationary.
• 0:37
  And yet out the other side comes pure electricity and a little
• 0:41
  bit of water. You're describing the fuel cell
• 0:43
  and you know Wally cringe a little at the word magic.
• 0:46
  You're right that compared to the, well, the violence of
• 0:48
  internal combustion engine, a fuel cell feels impossibly
• 0:52
  clean. It does.
• 0:53
  But as our source material for this deep dive reminds us, it
• 0:55
  isn't magic. It's thermodynamics.
• 0:57
  Specifically, it's a master class in how to, well, cheat the
• 1:02
  limitations of the Steam age. And that is the mission for this
• 1:06
  deep dive. We're walking through a classic
• 1:08
  text on engineering thermodynamics, specifically the
• 1:11
  chapter dedicated to fuel cells. We're going to answer the
• 1:14
  questions that usually stump people online.
• 1:16
  The big ones. Yeah, like, why are steam
• 1:19
  engines and gas engines fundamentally imperfect?
• 1:22
  How do you actually get energy out of fuel without setting it
• 1:26
  on fire? And the big one, what are the
• 1:29
  physics limits of a battery that never ever runs out?
• 1:32
  It's a fascinating area because it really bridges the gap
• 1:35
  between 2 worlds that engineers usually keep separate.
• 1:38
  What's that? The mechanical world of heat
• 1:40
  engines and the chemical world of batteries.
• 1:44
  Our source takes us all the way from the 1880s, when scientists
• 1:47
  first realized we were converting energy all wrong,
• 1:50
  right down to the complex math of electrochemical potential.
• 1:53
  So let's start with the why. We've been building steam
• 1:56
  engines and internal combustion engines for over a century.
• 1:59
  They power the entire world. Why are we trying to fix what
• 2:01
  isn't broken? Well, the source argues that
• 2:03
  they are broken, or at least they're fundamentally flawed.
• 2:06
  The text refers to them as cyclic devices.
• 2:09
  Whether it's a massive steam turbine in a power plant, or you
• 2:13
  know the V6 in your car, the process is the same.
• 2:16
  You take high quality chemical energy.
• 2:18
  The fuel, you degrade it into heat.
• 2:21
  By setting it on fire. By setting it on fire and then
• 2:23
  you try to convert that disordered heat back into
• 2:26
  organized work into motion. And that middle step, the heat,
• 2:30
  that's where the problem is, right?
• 2:31
  Precisely. The second you turn energy into
• 2:33
  heat, you're subject to the second law of thermodynamics.
• 2:37
  You are handcuffed by the carno efficiency limit.
• 2:41
  The carno limit, that's the rule that says you can't just use all
• 2:44
  the heat, you have to throw some of it away you.
• 2:46
  Have to pay a tax to the universe?
• 2:48
  Yeah, to make a heat engine cycle actually work, you must
• 2:51
  dump a significant portion of that heat into a cold Think.
• 2:55
  Like a cooling tower or your car's radiator.
• 2:57
  Exactly. You literally cannot convert
• 2:59
  100% of heat into work. It's just physically.
• 3:02
  Impossible, and that text is expensive.
• 3:04
  It is huge. The source notes that even our
• 3:07
  most sophisticated rotating machinery, I mean the absolute
• 3:11
  best turbines engineering can produce, are practically limited
• 3:16
  to about 50% efficiency. 50%. So for every unit of fuel you
• 3:20
  buy, half of it is just warming up the atmosphere.
• 3:23
  That brings us to the historical pivot in the text.
• 3:27
  Who was the first person to look at a steam engine, see that 50%
• 3:31
  loss and say this is garbage? That would be Wilhelm Oswalt way
• 3:35
  back in 1880. No way.
• 3:37
  Yeah. He was looking at the steam
• 3:39
  engine and he wrote, and I love this quote because it's so
• 3:41
  understated. He called it an imperfect thing.
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  Imperfect. That is a very polite way of
• 3:46
  saying incredibly wasteful. It is.
• 3:48
  Oswald had this realization. He looked at galvanic cells.
• 3:52
  What? We call batteries too, like.
• 3:53
  Batteries. And he realized they weren't
• 3:55
  heat engines. They don't burn fuel to make
• 3:57
  heat. They convert chemical energy
• 4:00
  directly into electricity. Because they skip the fire step.
• 4:02
  They skip the fire step and because they do that, they skip
• 4:05
  the carnal limit. They don't have to pay that
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  massive heat tax. So if we just strip away those
• 4:10
  heat engine limitations, what kind of efficiency numbers are
• 4:14
  we talking about? If a gas engine is stuck at 50%,
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  what's the ceiling for a fuel cell?
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  The source sites conversion deficiencies for chemical
• 4:22
  processes in fuel cells as high as 60% to 80%.
• 4:27
  That's a massive leap. It is, but there's a nuance here
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  that's even more important for anyone who drives a car.
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  What's that? Think about a standard engine.
• 4:36
  It's most efficient when it's running hard, right?
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  High speed, steady load. But if you're stuck in traffic,
• 4:42
  idling or just creeping along your efficiency tanks, you're
• 4:46
  just burning fuel to keep the engine spinning.
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  Right part load efficiency is usually terrible for combustion.
• 4:52
  Exactly. But a fuel cell it's efficiency
• 4:55
  isn't really reduced by part load operation.
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  In fact, the source points out that it often runs better and
• 5:01
  more efficiently when you aren't demanding maximum power.
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  That's a complete game changer for or, say, urban
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  transportation, where you're always stopping and starting.
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  A total lamp changer. OK, so we've established the
• 5:12
  motivation. Burning things is inefficient.
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  We want to do what a battery does, direct conversion.
• 5:18
  But to understand the fuel cell, the source actually takes a step
• 5:22
  back to the ancestor of all this, the Daniel cell.
• 5:25
  Right, you can't really understand the complex version
• 5:28
  without the simple one. The Daniel cell is It's the
• 5:31
  classic blueprint of an electric cell.
• 5:34
  So paint the picture for us. What does this thing look like?
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  Imagine a vessel. Inside you have two different
• 5:39
  liquid solutions, and they're separated by some kind of
• 5:41
  boundary, maybe a porous pot or a membrane.
• 5:44
  OK. On one side you have a solid
• 5:46
  zinc electrode sitting in a bath of zinc sulfate, on the other a
• 5:50
  copper electrode and copper sulfate.
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  Zinc on the left, copper on the right.
• 5:54
  Simple enough now. If you just threw a piece of
• 5:56
  zinc into copper sulfate, you would react get hot.
• 5:59
  A chemical reaction like a mini combustion.
• 6:01
  Exactly, but here we separate them.
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  The zinc dissolves into the solution, and when a zinc atom
• 6:07
  leaves the metal bar and enters the liquid, it leaves behind 2
• 6:10
  electrons. And those electrons are now just
• 6:13
  stranded on the zinc bar. They want to get to the copper
• 6:16
  side, but they can't swim through the liquid.
• 6:18
  Correct. The liquid blocks them.
• 6:21
  So if you connect a wire from the zinc to the copper, the
• 6:26
  electrons finally have a path. And they rush.
• 6:28
  Through it they rush. Through that wire, that flow,
• 6:30
  that is your electricity. They travel over to the copper
• 6:34
  side, where copper ions in the solution grab them and turn into
• 6:38
  solid copper plating on the electrode.
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  So it's a cold burn. You're getting the energy of the
• 6:42
  reaction, but instead of heat you get work moving through the
• 6:45
  wire. That is the perfect way to
• 6:47
  visualize it. The source explains this using
• 6:50
  the first law of thermodynamics. In an open circuit, you have
• 6:53
  this chemical energy just waiting to be released.
• 6:56
  We call that the Gibbs energy. And there's some specific math
• 6:59
  the source uses to calculate exactly how much power we get,
• 7:02
  right? It's not just a guess.
• 7:04
  Oh, it's very precise. The text uses Faraday's laws of
• 7:07
  electrolysis. It establishes a clear
• 7:09
  relationship between the amount of stuff reacting and the
• 7:12
  electricity you get out. Walk us through that equation.
• 7:15
  I see it here Delta W = Z * F times E What are we looking at?
• 7:20
  It's simpler than it looks. Delta W is the work the
• 7:23
  electrical energy you get. Z is the valency.
• 7:26
  That's just how many electrons an atom gives up.
• 7:29
  For zinc, that would be two. 2F is Faraday's constant.
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  You can think of that as the total electric charge in a big
• 7:35
  bucket of electrons, a mole of them and E is the voltage.
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  So work is the number of electrons times the charge of
• 7:43
  those electrons times the voltage that's pushing them.
• 7:46
  Spot on, and for this specific Daniel cell at about 25°C, the
• 7:51
  text gives the the electromotive force the EMF as roughly 1.107
• 7:57
  volts. 1.1 volts, so it's small. It's essentially a AA battery
• 8:01
  very much, but it proves the concept direct conversion.
• 8:05
  However, there is a problem with the Daniel cell and really with
• 8:08
  all batteries. They die.
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  The zinc eventually dissolves completely.
• 8:11
  The fuel is trapped inside the casing.
• 8:13
  Once it's gone, the party is over.
• 8:15
  And that is the transition to the fuel cell.
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  I think a lot of people get confused here.
• 8:19
  Is a fuel cell just a fancy battery?
• 8:21
  Structurally, yes. Functionally no.
• 8:24
  A battery is a storage device. It contains all its fuel.
• 8:27
  Inside a fuel cell is an engine. It's an electric cell where the
• 8:32
  electrodes the fuel are continuously supplied from the
• 8:35
  outside. So it's a battery that never
• 8:36
  dies as long as you keep seeding it.
• 8:39
  Precisely. Let's look at the hydrogen
• 8:41
  oxygen fuel cell. That's the standard model
• 8:43
  discussed in the source. How is the setup different from
• 8:46
  the zinc and copper one? We aren't dissolving metal bars
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  anymore. No, here the electrodes usually
• 8:52
  made of platinum. They aren't the fuel, they're
• 8:54
  just the stage where the action happens.
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  The platinum acts as a catalyst. You pump hydrogen gas to the
• 8:59
  anode, the negative side, and oxygen to the cathode.
• 9:03
  And the electrolyte in the metal.
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  It could be a few things, but the source describes using
• 9:08
  something like dilute hydrochloric acid or potassium
• 9:11
  hydroxide. The magic happens right at the
• 9:13
  surface of that platinum. How does it work?
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  Hydrogen flows in, hits the platinum and the bond breaks the
• 9:18
  protons, the H plus ions. They swim through the liquid
• 9:22
  with the electrons. They get forced to take the long
• 9:25
  way around through the wire. Powering your motor, your
• 9:28
  lights, whatever you have connected.
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  Then they meet up with the oxygen and the protons on the
• 9:32
  other side. And the only thing coming up the
• 9:34
  tailpipe is? Water.
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  Just water. H2O.
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  It's remarkably elegant. Hydrogen plus oxygen equals
• 9:42
  water plus electricity. Now the source actually throws A
• 9:45
  curveball here. It shows a diagram of a proposal
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  for a vehicle, but it doesn't carry hydrogen tanks, it carries
• 9:53
  methanol. Why complicate things with
• 9:56
  methanol? This is a nod to the real world
• 9:58
  logistics of engineering. Hydrogen gas is well, it's
• 10:02
  fluffy, it's low density. Even when you compress it, it
• 10:04
  takes up a lot of space. Methanol is a liquid at room
• 10:07
  temperature. It's easy to pump, easy to
• 10:09
  store. And we already have gas stations
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  designed for liquids. Exactly.
• 10:12
  But you can't just feed methanol directly into a hydrogen fuel
• 10:16
  cell, can you? No, not directly.
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  So the vehicle uses a chemical trick called the water gas
• 10:20
  reaction. The car basically has a device
• 10:23
  called a reformer on board. It takes the liquid methanol,
• 10:26
  reacts it with water, and it cracks it open to release the
• 10:28
  hydrogen gas right there on the spot just before it enters the
• 10:32
  fuel cell. That's very clever.
• 10:34
  It's like carrying a dehydrated meal and adding water right when
• 10:37
  you want to eat instead of carrying a heavy soup around all
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  day. It's a bridge technology.
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  The text mentions that while commercial fuel cells are still
• 10:43
  maturing, we've seen them in spacecraft and some large scale
• 10:47
  applications, like a one MW plant built by Tokyo Gas in
• 10:50
  Japan. OK, so we've covered the what
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  and the how. Now I want to get into the
• 10:55
  physics because I think the most common misconception is that
• 10:58
  this electricity just happens. But there's a force pushing
• 11:02
  these electrons, right? It's not magic, it's something
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  the text calls electrochemical potential.
• 11:08
  The source uses a symbol for this, a Greek mew with a little
• 11:11
  tilt over it. It looks complicated, but what
• 11:13
  does it actually represent? Think of it as chemical pressure
• 11:17
  combined with electrical pressure.
• 11:19
  Chemical potential is the desire of the chemicals to react like a
• 11:22
  rock wanting to roll downhill. Electrical potential is the
• 11:26
  attraction of the positive and negative charges.
• 11:29
  Electrochemical potential combines those two into one
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  single value that tells you how badly the system wants to reach
• 11:36
  equilibrium. And equilibrium means the
• 11:38
  battery is dead, so we want to stay as far away from
• 11:42
  equilibrium as possible to get power.
• 11:44
  Exactly. As long as there's a difference
• 11:46
  in this potential between the anode and the cathode, current
• 11:50
  will flow. The source introduces the Nernst
• 11:53
  equation to quantify all this. And this relates back to that
• 11:56
  Gibbs function we mentioned earlier.
• 11:58
  Right, the maximum electrical work you can possibly get is
• 12:00
  determined by the change in the Gibbs function delta G and the
• 12:04
  critical rule to remember from the text is this.
• 12:08
  If delta G is negative, the reaction is spontaneous.
• 12:12
  It wants to happen. It produces power.
• 12:14
  Yes, and the Nernst equation links that chemical desire to
• 12:18
  the voltage you actually see on the meter.
• 12:20
  So the standard EMFE 0 is derived from that Gibbs energy.
• 12:25
  It is. It's basically here's the total
• 12:27
  chemical energy available divided by the number of
• 12:29
  electrons. Gives you the voltage per
• 12:30
  electron. It's a direct conversion.
• 12:32
  Now here's where the thermodynamics it's really
• 12:34
  counterintuitive for me. I think most people assume that
• 12:37
  if you want a chemical reaction to go faster or work better, you
• 12:40
  heat it up. Sure, fire burns hotter.
• 12:42
  Engines run better when they're warm.
• 12:43
  Exactly. But the text raises the
• 12:45
  question, does it work better if it's hotter?
• 12:48
  And the answer is no. In this specific case,
• 12:52
  surprisingly no. You have to look at the type of
• 12:54
  reaction. The hydrogen oxygen reaction is
• 12:57
  exothermic. Meaning it releases heat as a
• 13:00
  byproduct. It gives off heat.
• 13:02
  Right now, there's a principle in chemistry, Le Chatelier's
• 13:05
  principle, that basically says if you add more of what a
• 13:09
  reaction produces, you actually choke the reaction.
• 13:12
  Since the reaction already produces heat, if you add more
• 13:15
  external heat, you're fighting against the process.
• 13:17
  That is fascinating. So a hotter fuel cell
• 13:19
  theoretically produces less voltage.
• 13:22
  The source references the Van Hoff equation to prove this.
• 13:25
  It shows that as temperature T goes up the EMF, the voltage
• 13:29
  actually goes down. It's a fascinating balance,
• 13:32
  because in practice engineers might need some heat to keep the
• 13:35
  catalyst happy or to keep the water from freezing.
• 13:37
  But thermodynamically, heat is the enemy of voltage here.
• 13:40
  What about pressure and a piston engine?
• 13:43
  Compression is everything. If I squeeze the gas in a fuel
• 13:45
  cell, does that help? Yes, pressure helps.
• 13:48
  The source gives a specific calculation for this.
• 13:52
  If you raise the pressure from 40 bar to 80 bar, so you double
• 13:55
  the pressure, the voltage does increase by a lot.
• 13:58
  Not really. The calculation shows an
• 14:00
  increase of about 0.0075 volts. That seems negligible.
• 14:05
  It's small per cell, but if you have a stack of hundreds of
• 14:08
  these cells, it starts to add up.
• 14:11
  Still, the take away is that the chemical drive, the bond energy,
• 14:14
  is much, much stronger than the mechanical pressure drive.
• 14:17
  You can't just squeeze more power out of it easily.
• 14:19
  So let's look at the balance sheet.
• 14:21
  We have this silent engine. It bypasses the Carnot limit.
• 14:24
  It has no explosions. Why isn't it 100% efficient?
• 14:28
  The source mentions an efficiency paradox.
• 14:30
  This is the So what of the physics?
• 14:33
  Even though it's not a heat engine, the fuel cell cannot
• 14:36
  escape the laws of entropy. Entropy, the measure of disorder
• 14:40
  in the universe, right? Think about the reactants.
• 14:42
  You have hydrogen gas and oxygen gas.
• 14:44
  They're chaotic, flying around, bouncing off walls.
• 14:47
  That's high entropy. When you combine them into
• 14:49
  liquid water, you're constraining them.
• 14:51
  You're creating order. And nature doesn't like it when
• 14:54
  you create order for free. Exactly.
• 14:56
  You have to pay for it to pay for that creation of order.
• 14:59
  This is the must dump energy. The term in the equation is T
• 15:02
  times delta S Because the entropy change is negative,
• 15:05
  we're becoming more ordered. The cell must give off some heat
• 15:09
  to the surroundings just to stay at a constant temperature.
• 15:12
  So that heat is lost energy. It's not friction, it's not bad
• 15:16
  design. It's just.
• 15:18
  Physics. It's fundamental.
• 15:20
  It's energy that cannot be turned into electricity because
• 15:23
  it must be paid to the universe to satisfy that entropy change.
• 15:27
  The source calculates that for a hydrogen oxygen cell at 25°C,
• 15:31
  this entropy penalty reduces the theoretical maximum efficiency
• 15:35
  to about 94.5%. Still, 94.5% is incredible
• 15:40
  compared to the 50% of a steam turbine.
• 15:42
  It is, but that is the theoretical limit.
• 15:45
  The source then drags us back to reality with a section on
• 15:48
  irreversible thermodynamics, because, as we know, theory is
• 15:52
  nice. But reality is messy.
• 15:54
  Very messy. Right, Nothing is perfect.
• 15:56
  What slows us down in the real world?
• 15:58
  Detect lists a few big losses. First.
• 16:02
  Unlike losses, the electrolyte itself has resistance.
• 16:05
  Just like a wire heats up, the liquid heats up as ions move
• 16:08
  through it. That's lost voltage.
• 16:10
  It's basically chemical friction.
• 16:12
  You could call it that. Then you have concentration
• 16:14
  gradients. Imagine the ions trying to get
• 16:17
  to the electrode. If you demand a lot of current,
• 16:19
  if you floor the gas pedal, the ions start to crowd up at the
• 16:22
  electrode. They just can't diffuse fast
• 16:24
  enough. We call that polarization.
• 16:26
  So as you ask for more power, more current, the actual voltage
• 16:30
  drops, yes. The source defines this with
• 16:32
  current density J. As J increases, the voltage
• 16:36
  drops further and further away from that perfect 1.1 or 1.2
• 16:41
  volts. It sounds like a traffic jam.
• 16:42
  That is a perfect analogy. At low traffic, everyone moves
• 16:45
  at the speed limit. That's maximum voltage.
• 16:48
  But as you pack more cars, more current onto the road,
• 16:50
  everything slows down. Congestion builds and you lose
• 16:54
  potential, You lose efficiency. It's interesting because this
• 16:56
  brings us full circle back to that Magic Box idea.
• 16:59
  We want it to be infinite power, but it's still subject to
• 17:03
  resistance and crowding. Exactly.
• 17:05
  But even with those real world losses, it operates on a
• 17:08
  completely different plane than the combustion engine.
• 17:10
  So let's zoom out and look at the big picture here.
• 17:13
  We started with the steam engine, a loud, hot, messy
• 17:18
  device that relies on the chaos of fire and throws away half its
• 17:22
  fuel just to follow the. And we ended up with the fuel
• 17:24
  cell, a device that is all about control.
• 17:28
  It really is a different philosophy of energy, isn't it?
• 17:30
  Completely. The steam engine tries to
• 17:32
  harness chaos. It creates a fire, pure chaos,
• 17:35
  and then tries to force it into mechanical motion.
• 17:38
  The fuel cell is about precision, it takes the chemical
• 17:41
  bond energy and it guides the electrons specifically where we
• 17:45
  want it to go. It's interesting that the source
• 17:47
  reinforces that while fuel cells are constrained by the first
• 17:50
  law, you can't create energy. They dodge that heavy tax of the
• 17:53
  second law that limits all combustion engines.
• 17:56
  They do. They are the closest we get to
• 17:58
  pure energy conversion. We aren't limited by the
• 18:02
  temperature of the fire or the coldness of the radiator.
• 18:04
  We're only limited by the chemistry itself and the speed
• 18:09
  at which we can move ions through a fluid.
• 18:11
  It really makes you rethink how we use energy.
• 18:14
  We usually burn hydrogen to get heat.
• 18:16
  Accepting all that chaotic waste of energy, the fuel cell asks,
• 18:20
  what if we simply guided the electrons to their destination
• 18:23
  instead? It's a fundamental shift from
• 18:25
  brute force to precision, and in engineering, precision usually
• 18:30
  wins in the long run. That is a fantastic thought to
• 18:32
  end on. From the clunky steam engines of
• 18:34
  1880 to the electrochemical potential of the future, it's
• 18:38
  all about finding a better way to move energy.
• 18:40
  And understanding the thermal dynamics behind it all.
• 18:42
  Absolutely. Well, that wraps up our deep
• 18:45
  dive into the Xylan engine. If you haven't already, get over
• 18:48
  to our YouTube channel Mechanical Engineering Made
• 18:50
  Simple, where we post hands on how to videos, visual
• 18:53
  breakdowns, and practical engineering walkthroughs.
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