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Chalk Talk: Intensive vs. Extensive Variables

Learn the difference between intensive and extensive variables and how they relate to soil water potential vs. soil water content in our new Chalk Talk whiteboard series. In this video series, Dr. Colin S. Campbell teaches basic principles of environmental biophysics and how they relate to measuring different parameters of the soil-plant-atmosphere continuum.

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To learn more about measuring water potential vs. water content read: Why soil moisture sensors can’t tell you everything.

Download the “Researcher’s complete guide to water potential”—>

Download the “Researcher’s complete guide to soil moisture”—>

Video transcript

Hello, my name is Colin Campbell. I’m a senior research scientist here at METER group. And I teach a class on environmental biophysics. Today I wanted to talk about something we teach in the class: the difference between extensive and intensive variables. I’d like to do this with the goal of relating it to the difference between volumetric water content and water potential. 

Here, I have a picture of a ship moving through the ice and some metal that’s been heated in a furnace. I think we would agree the ship has the highest amount of heat in it compared to this very small piece of metal. And if we placed that piece of metal onto the outside of the ship, despite the fact that there is more heat in the metal, we know the heat would not move from the high amount of heat (ship) to the low amount of heat (metal). It would actually move from the highest temperature to the lowest temperature. Why is that?

The reason is that heat moves because of temperature and not because of heat content or the amount of heat in something. Heat content defines an amount or an extent. And we generally term something that defines an extent or an amount as an extensive variable.An extensive variable depends broadly on the size of something or how much of something there is. 

This differs for temperature. Temperature doesn’t depend on size. The temperature could be the same in a very small room or a very large room, but the amount of heat or heat content in those rooms would be quite different. When we describe temperature, we talk about intensity, which is why we call these types of variables intensive variables. This is because they don’t depend on size or amount. 

Let’s talk about another example. Here’s your heating bill. Maybe it’s natural gas. What you’re paying for is the amount of heat you put into the house. But the question is, are you comfortable in the house? And from this bill, we can’t tell. Maybe you put in 200 heat units, whatever those might be. We can’t tell if that’s comfortable because we don’t know the size of the house or the type of insulation. All those things would influence whether you were comfortable. 

Alternatively, if the temperature is 71 F that’s quite comfortable. That’s equivalent to about 22 degrees Celsius. So the intensive variable, temperature, is different than the extensive variable, heat content, that tells us how much heat we put in. And that’s important because at the end of the day, that leads to cost. 

On this side, we don’t know how much we paid to keep it at 22 C because heat content doesn’t tell us anything about that. But the intensive variable temperature does tell us something about comfort. So both of these variables are critical to really understanding something about our comfort in the house. 

Now let’s talk about the natural environment. Specifically, we’re going to talk about soils. We’ll start with the extensive variable. When we talk about water in soil, the extensive variable is, of course, water content. Water content defines the amount of water. Why would we care about water content? Well, for irrigation or a water balance.

The intensive variable is called water potential. What does water potential tell us? It tells us if soil water is available and also predicts water movement. If this soil had a water content of 25% VWC and another soil was at 20% VWC, would the water move from the higher water content to the lower water content? Well, that would be like our example of the ship and the heated piece of metal. We don’t know if it would move. It may move. And if the soil on either side was exactly the same, we might presume that it would move from the higher water content to the lower water content, but we actually don’t know. Because the water content is an extensive variable, it only tells us how much there is. It won’t tell us if it will move. 

Now, if we knew that this soil water potential was -20 kPa and this soil water potential over here was -15 kPa, we would know something about where the water would move, and it would do something different than we might think. It would move from the higher water potential to the lower water potential against the gradient in water content, which is pretty interesting but nonetheless true. Water always moves from the highest water potential to the lowest water potential.

This helps us understand these variables in terms of plant comfort. We talked about the temperature being related to human comfort. We know at what temperatures we are most comfortable. With plants, we know exactly the same thing, and we always turn to the intensive variable, water potential, to define plant comfort.

For example, if we have an absolute scale like water potential for a particular plant, let’s say -15 kPa is the upper level for plant comfort, and -100 kPa is the lower level of comfort, we could keep our water potential in this range. And the plant would be happy all the time. Just like if we kept our temperature between 21 and 23 Celsius, that would be comfortable for humans. But of course, we humans are different. Some people think that temperature is warm, and some think it’s cold. And it’s the same for plants. So this isn’t a hard and fast rule. But we can’t say the same thing with water content. There’s no scale where we can say at 15% water content up to 25% water content you’ll have a happy plant That’s not true.If we know something about the soil, we can infer it. But soil is unique. And we’d have to derive this relationship between the water content and the water potential to know that. 

So why would we ever think about using water content when we measure water in the soil? One reason is it’s the most familiar to people. And it’s the simplest to understand. It’s easy to understand an amount. But more importantly, when we talk about things like how much we’re going to irrigate, we might need to put on 10 millimeters of water to make the plants happy. And we’d need to measure that. Also if we want to know the fate of the water in the system, how much precipitation and irrigation we put on versus how much is moving down through the soil into the groundwater, that also relates to an amount.  

But when we want to understand more about plant happiness or how water moves, it’s going to be this intensive variable, water potential that makes the biggest difference. And so with that, I’ll close. I’d love for you to go check out our website to learn a little bit more about these measurements in our knowledge base. And you’re also welcome to email me about this at colin.campbell@meter

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