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Video 1
Hello all, we have been discussing the concept of vapor pressure lowering which can be well understood using Kelvin’s equation. So, Kelvin’s equation a which states that the vapor pressure on a curved surface equals to the saturated vapor pressure times exponential of partial molar volume of water times change in the pressure across the interface divide by RT. So, the implication of Kelvin’s equations is that above a curved surface the vapor pressure is larger than in the fluid. So if you consider a capillary tube immersed in a beaker of water, the water rises in order to balance the chemical potential and it assumes a meniscus or curved surface like this depending on the interaction between the capillary tube and the fluid. So, this is a typical example of water in a glass beaker or glass capillary so you have a meniscus like this. So, the vapor pressure above a curved surface is u v which will be less than the saturated vapor pressure which will be above the flat surface, so this is the implication of Kelvin’s equation. More than that the vapor pressure even though this is less than the saturated vapor pressure water vapor condenses into water and it accumulates in a capillary tube which we will understand. As there is a pressure drop across the interface, so this is ua atmospheric pressure and this is water pressure. So, there is a pressure drop across the interface because of which there is a change in the vapor pressure. Similarly, when there is a capillary tube which causes a lowering of the vapor pressure. So, you have, say for example, here you are maintaining RH equals 100 percent. So, thenyou have u v sat here in the ambiance, so here the vapor pressure is lower than the saturated vapor pressure u v inside the capillary tube. Even though the vapor pressure inside a capillary tube is lower than saturated vapor pressure, you see that the water accumulates into the capillary tube with time and you see that there is a filling of water within the tube. So, which fills because, a number of water molecules that get trapped in this small cavity, so slowly the water level increases within the capillary tube in order to which is nothing but condensation. So, condensation takes place at a vapor pressurewhich is less than saturated vapor pressure that is the implication of Kelvin’s equation, this has a very important application, important correspondence to our soil mechanics. Because, when you take a soil sample which is kept outside this is initially dry which is the oven-dried, initially at the oven-dried state you take a clay powder, say any clay powder or even soil at oven-dry state if you take and then place it in the cup and in an atmosphere when you leave it the relative humidity of the atmosphere maybe 80 percent or it could be anything, it may vary usually between 60 to 90 are closed to 100 percent depending on the location. So, when you have some particular RH and temperature of the ambiance, then you would see that there is an accumulation of water at the surface of the soil due to condensation. Because, if you consider the force of soil grains hasindividual capillaries you have a number of capillaries attached here which lowers thevapor pressure above this and eventually there is a condensation that takes place at lower vapor pressure which causes accumulation of water at the surface, because of the potential difference from the top surface and the bottom surface there is a diffusion that takes place and water slowly penetrates into the deeper layer of the soil.So, this happens in any type of soil but clays generally the pore size is very small, so therefore easily the condensation takes place and more water will get accumulated. So,the vapor pressure lowering depends on the capillary size, so here in this particular case Kelvin’s equation a simple capillary tube is assumed. Therefore, the pressure drop across the water interface is 2 T s by r surface tension times 2 by the radius of the capillary tube. So, capillary tube diameter or the radius is very important in controlling the vapor pressure and condensation so this is called capillary condensation. This is a very important concept in soil mechanics because this concept is also utilized in the estimation of the specific surface area of fine-grained soil such as Carnuts and other clays not expensive clays like Bentonite etcetera. Because Bentonite generally they have dual porosity system and you have smaller pore fractions that exist this generally used for only for Carnot clays using adsorption isotherms. So, you take a soil sample and you expose the soil sample to a particular temperature and then relative humidity and absorption of. So you would expect that there is an absorption of water molecules around the clay surface and the exchangeable Cations because of the hydration there is waterthat accumulates. So, you would see that the adsorption increases with time for a given RH, and also it increases the adsorption amount of adsorption also increases with an increase in the RH, so using this concept the specific surface area is estimated.
Video 2