Video: Interpreting Sankey Diagrams

The image shows a Sankey diagram for a fluorescent light. What is the input power of the fluorescent light?


Video Transcript

The image shows a Sankey diagram for a fluorescent light. What is the input power of the fluorescent light?

Okay, so we’ve been given a diagram here that shows a Sankey diagram. What we need to do is to work out what the input power actually is. Now upon closer inspection, the diagram can seem a little bit confusing because of this arrow here says that some of the energy is wasted as heat. And then, we’re told that this is 60 watts. But what is a unit of power not energy? So what exactly is going on?

Well, a power of 60 watts basically means that the energy wasted as heat is 60 joules every second because remember power is defined as energy per unit time. Therefore, if the fluorescent light is wasting 60 watts of power, another way of saying this is that it’s wasting 60 joules of energy every second. So in reality, this is not too problematic. So let’s now try and work out the input power.

Well, a Sankey diagram that shows power has to account for all of the input power turning into some form of output. In other words, we have this amount of input power and some of that turns into energy wasted as heat and the rest turned into light. In other words, the total input power is split into two branches: one branch is the heat and the other is light.

So using that logic, the input power, which we shall call 𝑃 here, must be equal to the 60 watts which is wasted as heat plus the 15 watts which is turned into light. And that’s all it can be. And 60 watts plus 15 watts ends up being 75 watts. Now, the input power can only be 75 watts because if the input is larger than 75 watts — let’s say if the input was 80 watts — right, well then, 60 of those have turned into heat, 15 of those have turned into light.

So what happened to the other five watts? That’s not accounted for on the Sankey diagram. And therefore, this would not be a correct Sankey diagram because it does not completely account for the input power turning into various forms of output. So the input power cannot be more than 75 watts.

Now, let’s assume it was less than 75 watts. Let’s say it was 70 watts. Right, well in this case, 70 watts are being put in and 15 are coming out as light and 60 are wasted as heat. But we’re getting out an excess of five watts. Where are those five watts coming from? We can’t create energy out of nothing. So we can’t create energy divided by time out of nothing.

In other words, we can’t generate power out of nothing. So where are those extra five watts coming from? Well, that’s also not a possibility. And hence, the input power must be 75 watts and that is our final answer.

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