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Imagine that here, in front of me, is a box. But this is no ordinary box.

It’s indestructible, could be any size, and anything could be happening inside it. Maybe it’s making steel from iron. Or maybe it’s burning coal to generate electricity, or creating compounds to be used in medicines.

No matter what’s going on inside this magical box, it’s our job as engineers to make it the best most efficient box it can be. And to do that, we’ll need to rely on an incredibly basic rule. A law, if you will.

It’s called the Law of Conservation, and it says that matter and energy can neither be created nor destroyed. And we can use this law to figure out both, where our box isn’t operating as efficiently as it can be, and how to fix it. [Theme Music] Whatever it’s doing, our box is what engineers call a system, and what’s happening inside it is a process. Everything beyond the box is known as the surroundings.

Let’s say you have an entire steel mill inside this particular box, so the process is converting iron to steel. Now, iron is expensive. Running steel mills is expensive.

So if there’s something inefficient about the way your box works, you’re going to want to know about it – and fix it. Ideally, whatever you feed into the system at the beginning, is what you get at the end. Input equals output.

If your box is perfectly efficient, the law of conservation tells you that the amount of steel you get at the end, should weigh exactly as much as the ingredients you put in. So if you have 100 kilograms of iron and other ingredients going into your box every hour, you’d also have 100 kilograms of steel coming out. You know you’re not going to get 105 kilograms of steel, because you can’t create 5 kilograms of matter from nowhere.

And you can’t have 95 kilograms at the end, either, because everything you put into this perfect version of the box is being turned into steel, and 5 kilograms of matter just can’t disappear. If you’re running this system continuously, with ingredients always flowing in and an equal amount of steel always coming out, you have what’s called steady-state. When a system is steady-state, that means the variables at the input and output remain constant, despite what’s happening inside the system.

It’s like water flowing through a full tank: if the system is steady-state, water comes out at the same rate it flows in, and the tank stays full. Of course, we’re just talking about what would happen in an ideal situation – if the box is perfectly efficient at steel-making. The thing is, the real world doesn’t usually work that way.

Engineers deal with systems that are way more complex, and they’re not going to be perfectly efficient. But you can use the law of conservation to get a system as close to perfect as possible – in other words, to get as much output from your input, as you can. Before we go back to our steel mill, though, let’s bake a cake.

The pan will be our system, the oven will be our surroundings, and the cake batter will be our raw materials, or input. The cake itself will be our delicious output. Like most processes, we’re using this one to make something we want – the cake.

But, again like other processes, it’s probably gonna produce some byproducts. When you burn coal to get electricity, for example, you also get ash, sulfur oxides, and nitrogen oxides. Steelmaking creates dust from zinc and other metals, which is considered abrasive, hazardous waste.

And don’t even get me started on chemical waste from manufacturing pharmaceuticals. Our cake will probably have some byproducts, too, like if we burn some of the batter on the pan, creating some charred bits that we wouldn’t want to eat. Look, not everyone’s a master chef.

There are lots of other ways to end up with leftovers, too. Sometimes you can’t get all of your raw materials to react or turn into what you want – like if there’s some batter in the pan that doesn’t get cooked. Some of the final product can also get stuck in the system.

Maybe some of the batter spilled onto the oven racks. Any of these examples could be waste since you couldn’t simply separate them back into their initial parts to use them as input next time. There’s also the possibility our raw materials were contaminated, which could easily end up in our final product.

When we cracked open the eggs, for example, some small pieces of shell might have fallen into the batter, which means we’ll probably still find them when we try a slice of finished cake. You know, on second thought, maybe I’ll pass. So, clearly our cake-baking process has a lot of room for improvement.

Engineers define problems like these in terms of conversion and yield. Conversion describes how much of our initial input was used in the process. If our system has a conversion rate of less than 100%, it means you’ll have some leftover or waste.

Now that our cake is done, let’s go back to the steel mill in a box. If you had 100 kilograms of iron and other ingredients going in, and a 60% conversion rate, that means you’d have 40 kilograms of iron left over at the end of the process. That’s a lot of wasted iron!

Yield, meanwhile, describes how much of the final product you were able to get from your initial input. So if your box has a 30% yield, 100 kilograms of raw materials would get you 30 kilograms of steel, and 70 kilograms of waste. The most basic way to think about a system is in terms of “balance”.

Engineers measure the values that go in and the values that come out, and if there’s a difference, they’ll try to figure out what’s causing it. But conversion and yield only cover the beginning and end of the process. Engineering, like life, is usually not that simple.

If you have a system that’s not in steady-state, then you probably don’t have the same amount of mass coming in and out. Real-life processes are messy, and stuff gets stuck along the way. That’s accumulation, and as engineers, we can use it to keep track of the differences between what’s coming in and what’s going out.

The basic idea is pretty simple: if you subtract your output from your input, you get your accumulation. If you’re measuring all this in terms of mass, that simple equation is probably all you need. Mass goes in, and whatever mass doesn’t come out at the end, is stuck inside the system.

But when there are chemical reactions happening inside the system – which there often are – it can be more useful to think about accumulation in terms of molecules. During a process, your raw materials might go through a chemical reaction that generates some molecules that don’t end up in your product. Or a reaction might consume some molecules that are hanging around inside the system and weren’t part of the input.

To keep track of where all your molecules are, and which of them are accumulating inside the system, you need two more terms: generation and consumption. To calculate accumulation, you’d take your input and subtract the output like usual. But then you’d also add the molecules being generated within the system by chemical reactions, and subtract any molecules being consumed.

Whatever’s left over is what’s accumulated inside the system. This equation is essential to engineering. Even in its simplest form, engineers can use this equation to figure out how to improve a system.

So let’s see how we can improve ours! The steel mill in our box has some raw materials flowing in and steel flowing out. As engineers, our goal is to make as much steel as possible at the end of the process.

Let’s say we begin with 100 kilograms of raw materials with a 70% conversion rate, which means we’re only making 70% of what’s possible, or 70 kilograms of steel. Not bad, but not great. We’d be losing out on 30 kilograms of raw materials, and probably a good bit of money!

This is where we’ll need to problem-solve as an engineer and figure out how to make the process better. How about a recycling system? We can introduce a separator at the end of our system to sort out any leftovers.

Then we can run that stream of unused raw materials back into the beginning of our process. We already have 70 kilograms of steel and 30 kilograms of iron and other ingredients that weren’t used. Let’s send those 30 kilograms back.

Now, instead of 100 kilograms being fed into the system, we have 100 kilograms plus the leftovers from the previous cycle. So, even though we still have a 70% conversion rate, we’re still getting more steel from the same amount of raw material, than we were before. But what if our raw materials aren’t perfectly clean?

What if we have contaminants? Sometimes contaminants can lead to big problems, literally ruining machines and halting production. It can be very serious and costly.

For example, soda bottling plants have had to shut down production because of possible chlorine contamination. With our steelmaking example, let’s assume the contaminants are relatively harmless and won’t react with anything. We’ll keep using our recycling system from before, but now we’ll also need a ‘purge system’ to filter out the contaminants.

If we don’t get rid of them, we’ll be passing them back while adding new contaminants during the next cycle. As the contaminants build up, we’d run into more and more problems with our machines and tools. Remember, just because we’re following the Law of Conservation, or any other principles of engineering for that matter, it doesn’t mean everything is working out the way we want it to.

As engineers, we’ll encounter limitations like these and many others. But with clever designs, we can work around them. Engineering is all about testing our limits and pushing them as far as we can until we reach something truly extraordinary.

So today we learned all about the law of conservation, beginning with simple, steady-state systems. We then introduced the terms conversion and yield, showing how they apply to a system. We ended with accumulation and covered how generation and consumption can affect how much accumulation there is in a system.

I’ll see you next time, when we’ll learn all about reversibility and irreversibility and how they affect engineering. Thank you to CuriosityStream for supporting PBS Digital Studios. CuriosityStream is a subscription streaming service that offers documentaries and non-fiction titles from a variety of filmmakers, including CuriosityStream originals.

For instance, CuriosityStream has “Stephen Hawking's Favorite Places” a series where renowned physicist Stephen Hawking takes a flight of epic proportions to visit his favorite places in the Universe. You can learn more at curiositystream.com/crashcourse and use the code crashcourse during the sign-up process. Crash Course Engineering is produced in association with PBS Digital Studios.

You can head over to their channel to check out a playlist of their latest amazing shows, like The Origin of Everything, Deep Look, and Eons. Crash Course is a Complexly production and this episode was filmed in the Doctor Cheryl C. Kinney Studio with the help of these wonderful people.

And our amazing graphics team is Thought Cafe.