 When we begin to talk about actual air, we need to distinguish it from dry air, that ideal gas that we've been analyzing for a couple of months now. When we talk about atmospheric air, that is the combination of the dry ideal air with water vapor. So atmospheric air is actual air. Dry air is ideal air that contains no water vapor. For our purposes, atmospheric air is a combination of just dry air and water vapor. We will be treating both the dry air and the water vapor as ideal gases, and like any other mixture of ideal gases, we can analyze the properties of both of the components of the mixture independently. So first of all, when we talk about dry air, we are going to narrow our analysis down to just the range of temperatures that we commonly encounter with dry air. We notice that the specific heat capacity is very nearly constant from negative 10 to 50 degrees Celsius, which is the range that we'll be considering, and as a result, we can safely assume that the specific heat capacity of the dry air is constant across that entire range. Furthermore, we need to be able to combine our specific enthalpies together. You'll remember that the specific enthalpies for the water in the steam tables is relative to an arbitrary zero point. We can't actually measure enthalpy, what we measure is enthalpy difference, and the zero point we consider for the steam tables is zero degrees Celsius. So all of the enthalpies that we look up in the steam tables are actually relative to zero degrees Celsius. If we see that the specific enthalpy of superheated vapor is 3000 kilojoules per kilogram, that just means it's 3000 kilojoules per kilogram higher than that water was at one atmosphere and zero degrees Celsius. Since we're going to be talking about the mixture of water vapor and dry air, we need the dry air to be relative to the same zero point. So note, when we talk about the specific enthalpy of dry air and we multiply the temperature by specific heat capacity, that temperature is in degrees Celsius. Again, when we calculate the specific enthalpy of dry air by taking the specific heat capacity multiplied by temperature, that temperature is in degrees Celsius when we're talking about the context of atmospheric air. When we analyze the water vapor, again, we are treating the water vapor in the air as being an ideal gas. That's due to the fact that the pressure experienced by the water vapor under Dalton's law is very, very low. You'll remember from our discussion of ideal gases that ideal gases don't really exist. It's just that real gases become more ideal in their behavior under certain conditions. One of those conditions is low pressure. As the pressure of a gas gets lower, its behavior becomes more ideal. For the water vapor in the air as humidity, the pressure experienced by the water vapor is so low that we can treat it as an ideal gas. Therefore, when we describe the properties of atmospheric air, we are describing the properties of the ideal gases dry air and water vapor mixed together. The subscripts we'll be using for dry air and water vapor are A and V respectively. If you see a property without a subscript, it is likely of the mixture. So here, for example, if we're modeling the mixture using Dalton's law, the pressure of the atmospheric air with no subscript is going to be the partial pressure of the dry air plus the partial pressure of the water vapor. Furthermore, the partial pressure of the water vapor is usually referred to as the vapor pressure. Now, like with other mixtures of ideal gases, it is useful for us to refer to the relative proportions of the substances that make up the mixture. When we're talking about atmospheric air, that relative proportion is described as humidity. And we describe it in two ways. Relative humidity, which is expressed as a percentage, and humidity ratio, which is expressed as a proportion of mass to mass. The percentage expressed by relative humidity is the amount of water currently in the air divided by how much water the air can hold. So if I told you the relative humidity outside is 55%, what I'm saying is that the air outside is currently holding 55% of its capacity to hold water. Humidity ratio is a raw proportion. It is mass of water vapor per unit mass of dry air. Generally speaking, relative humidity is more useful when you're describing human comfort, and humidity ratio is more useful for engineering calculations. For example, you as a human feel comfortable when you're able to reject as much heat as you're producing. Assuming you're watching this video sitting down or laying down, you're probably producing around 100 watts. For you to be comfortable, you have to be rejecting 100 watts of heat. If you're rejecting more heat than that, if there's a fan blowing across you, or if there's a cool environment that is dry, and is able to pull heat out of you, you will feel cold. If you're rejecting less heat in that, say there's an insulating layer preventing you from rejecting heat, you will feel warm. Well, a certain amount of the heat that you're rejecting is through what we call sensible heat transfer. That's the direct heat transfer between the temperature of your skin to the temperature of the surrounding air. Regular heat transfer if you will. The rest of heat that you're rejecting is latent heat transfer, or water that is on the surface of your skin that is evaporating. You are pretty much always sweating a little bit. If you're sitting or laying down about a third of the heat that you're rejecting is through latent heat rejection, the other two thirds is sensible heat rejection. If all of a sudden you started producing a lot more heat, say you started playing a sport, all of a sudden your body needs to be able to reject a lot more heat for you to feel comfortable. It can ramp up both modes. It can increase the surface temperature of your skin by pushing blood a little closer to the surface, at which point you reject a little bit more sensible heat rejection due to the fact that there's a greater temperature difference between your skin and the surrounding air. But your body can't increase how much sensible heat rejection it produces nearly as much as the latent heat rejection. If you're in a situation where you need to reject hundreds of watts of heat, most of that is going to be done with latent heat rejection as a result of your body producing a lot more sweat. Well, how much heat you can reject as latent heat rejection is a function of how much sweat can evaporate, and how much sweat can evaporate is a function of how much water is in the air. If the relative humidity of the air is 50%, that means that it can hold 50% more water, and as a result it will be pulling water off of your skin faster than if the relative humidity were 90% under the same conditions. 90% relative humidity means that there's less capacity left, meaning not as much sweat is going to be evaporated. So relative humidity has a huge effect on how much sweat can be evaporated, which has a huge effect on how much latent heat rejection your body is able to produce, which has a big effect on if you feel comfortable or not. But on the other hand, relative humidity is a little bit annoying when it comes to handling the math associated with energy balances. The reason for that is the amount of water that the air can hold changes. If you imagine a box full of atmospheric air initially at let's say 50% relative humidity and a temperature of 71 degrees, if I added heat to that box and increased the temperature of the air, the air is able to hold more water as it increases in temperature. Therefore, the same amount of water in the air divided by a larger capacity to hold water means that the relative humidity of the air in the box will be decreasing as it heats up. But the humidity ratio will be unaffected. The mass of water in the air and the mass of air in the atmospheric air are unaffected by the change in temperature. So in that example, heating up a sealed rigid box of atmospheric air will drop the relative humidity and not affect the humidity ratio. If we cool the box down, the air's ability to hold water decreases and the relative humidity would increase. It would continue to increase until it reached a point where it could not hold any more water. That is, the air's capacity to hold water reaches how much water is in the air, meaning a relative humidity of 100%. Cooling past that point would result in condensation occurring. But again, the humidity ratio is unaffected. Or rather, is unaffected until the condensation starts occurring, because at that point, the water that is now condensed is no longer water vapor. Therefore, the humidity ratio would decrease. Here, let's try describing these properties with a little bit more math. Again, the analysis of water vapor in dry air is called psychrometry. So these are psychrometric properties. We abbreviate relative humidity with the Greek letter phi, and phi represents the mass of water vapor in the air divided by how much water vapor the air can hold. Or rather, the mass of water vapor that would be in the air if it was saturated with water. If it was saturated, so we're calling that a G, just like in the steam tables. Then, because I'm describing the behavior of the atmospheric air as an ideal gas and all of the individual species that make up the atmospheric air as ideal gases, I can describe this proportion as a proportion of ideal gases. So I'm taking PV is equal to MRT, solving for m, at which point I have PV over R times T. The mass of the water vapor can be represented as the partial pressure of the water vapor times the volume occupied by the water vapor divided by the specific gas constant of the water vapor times the temperature of the water vapor. The mass of the water at saturation can be represented as the partial pressure of the water at saturation times the volume of the water at saturation divided by the specific gas constant of the water at saturation times the temperature of the water at saturation. In this proportion, the volume occupied by the water is unaffected regardless of how much there is because we're describing the behavior using Dalton's law. Similarly the water is still water both at saturation and not and the temperature is the same because we're considering if the air were to become fully saturated at that temperature. So the relative humidity simplifies down to just the partial pressure of the water vapor or vapor pressure divided by the partial pressure of the water vapor at saturation and PG we can look up for a given temperature in our steam tables and it's just going to be PSAD at T. So relative humidity is the vapor pressure divided by the pressure at saturation corresponding to that temperature. The humidity ratio we abbreviate with an omega and that's the proportion of mass of the water vapor to massive dry air and if we plug in our ideal gas law substitution and then again Dalton's law means that the volume occupied is unaffected by which species we are looking at the volume of the water vapor is the same as the volume of the dry air. The temperature experienced by both of these substances in the mixture is the same. The gas constant doesn't cancel this time because it's now water and air so I write this as PV over PA times RA over RV and then because the specific gas constants are constants the proportion of RA over RV is also a constant and for convenience I can calculate that a single time and then plug it into my equation every time. The specific gas constant for dry air would be the universal gas constant divided by the molar mass of dry air and the specific gas constant for water vapor would be the universal gas constant divided by the molar mass of water vapor therefore the proportion of the specific gases of dry air and water vapor is going to be the universal gas constant divided by the molar mass of dry air divided by the universal gas constant divided by the molar mass of water vapor The universal gas constants are the same, so they cancel, so I'm left with just MV over MA. Both of those quantities come from table A1. The molar mass of dry air is 28.97. The molar mass of water vapor is 18.02. Both of them are in kilograms per kilomole, which means that the units will cancel, so I have 0.622-023. So for convenience, I can write humidity ratio is equal to about 0.622 times the partial pressure of water vapor divided by the partial pressure of dry air. And depending on the circumstances, it might be more or less useful to rewrite PA as total pressure minus the vapor pressure, or it might be more useful to write PV as phi times PG, or it might even be useful to write PV up here as PA times the humidity ratio divided by 0.622. Depending on the circumstances, different forms of the same relationship are more or less useful. Next up on my list of psychrometric properties, I have specific enthalpy. Specific enthalpy is expressed per unit mass of dry air, and that's just a matter of convenience. We define the specific enthalpy of atmospheric air per unit mass of dry air because the mass of the dry air is often constant in our analyses. I mean if you have a cooling process that involves dehumidification, or if you are adding water vapor to a stream of dry air to humidify it, in both cases the mass flow rate of dry air is the same, so it is convenient to express enthalpy per unit mass of dry air instead of per unit mass of atmospheric air. We do that with essentially all of these specific quantities within atmospheric air. We define them per unit mass of dry air for again the same reasons. So I can jump back into my list of psychrometric properties. The specific enthalpy of atmospheric air is defined as the total enthalpy of atmospheric air divided by the mass of the dry air. The total enthalpy of the atmospheric air is going to be the mass of dry air times the specific enthalpy of dry air plus the mass of the water vapor times the specific enthalpy of the water vapor all divided by the mass of the dry air. If So I split the denominator, I can write that as HA plus MV over MA times HV, and HA can be expressed as the Cp of air times the temperature in Celsius, remember, MV over MA is our definition of the humidity ratio, and HV we can technically determine because it's going to be a superheated vapor at some pressure and temperature, but within the scope of HVAC analysis, we can get away with approximating it. So we say HV is pretty close to HG at T. We are treating the water vapor in the air as a saturated vapor, therefore we can write the specific enthalpy of the atmospheric air as Cp of air times temperature in degrees Celsius plus the humidity ratio of the air times the specific enthalpy of the saturated vapor that we are approximating the superheated vapor in the air as at temperature. Next up on our list of psychrometric properties, we have temperatures. Our first two temperatures are the dry bulb temperature and the dew point temperature. The dry bulb temperature is just the regular temperature, that temperature that you've been using for forever. If you have a thermometer sitting without any water on it and no water actively evaporating, you have a regular thermometer also known as a dry bulb thermometer. The dry bulb temperature is the regular temperature. The dew point temperature is the temperature at which condensation will start to occur if you cool the air at a constant pressure. Do you remember that box full of atmospheric air example from earlier? If we cool the atmospheric air, the capacity of the air to hold water drops, eventually it will hit 100% after which water will be condensing out of the air. The temperature at which you hit 100% relative humidity is the dew point temperature. We can look up the temperature at which saturation will occur by using the fact that the relative humidity will hit 100%, at which PV will equal PG, which is the saturation pressure at our temperature, therefore the dew point temperature will be T sat at PV. There will be one more temperature that we'll introduce as a psychrometric property, which is called the wet bulb temperature, or the adiabatic saturation temperature, but that one deserves its own video. Let's try an example to get the hang of these calculations.