body surface area calculator

The behaviour of liquid surfaces and the phenomenon of surface tension can be explained by considering the forces of attraction between the molecules of a liquid.Intermolecular forces of attraction are of two types : (i) Attraction between two molecules of the same substance is called cohesion and the force of attraction is called the cohesive force, (ii) Attraction between two molecules of different substances is called adhesion and the corresponding force of attraction is called the adhesive force.These intermolecular forces, both cohesive and adhesive, are short range forces, i.e. they are effective over a very short distance, beyond which they are negligible. The maximum distance between two molecules upto which the intermolecular forces are effective is called the range of molecular attraction (R). An imaginary sphere drawn round a molecule as centre, with a radius equal to the range of molecular attraction, is called the sphere of influence of that molecule. The molecule is attracted only by the other molecules inside this sphere since the forces exerted by molecules outside the sphere are negligible.Three molecules. A, B and C of a liquid, with their spheres of influence, are shown in Fig. 6.3. The molecule A is well within the liquid, molecule B is just inside the liquid surface and molecule C is on the liquid surface.The sphere of influence of the molecule A is completely inside the liquid, so that the other liquid molecules are symmetrically distributed around the molecule A. The molecule is therefore attracted equally in all directions, so that the resultant intermolecular force acting on this molecule is zero.The molecule B is just inside the liquid surface. Its distance from the liquid surface is less than the range of molecular attraction. Therefore a part of its sphere of influence lies outside the liquid surface. This part contains molecules of air, but their number is very small and the forces of attraction exerted by them on molecule B are negligible compared to those exerted by the liquid molecules, inside the sphere of influence. It is clear from the consideration of symmetry, that a resultant downward force acts on the molecule B, trying to pull it inside the liquid.For the molecule C, which is on the liquid surface, half of the sphere of influence lies outside the liquid. This half contains air molecules whose number is extremely small compared to the number of liquid molecules in the lower half of the sphere. Therefore the molecule C experiences maximum downward force, trying to pull it into the liquid.Thus all molecules in a layer of thickness R, below the free surface of the liquid, experience an inward pull. The pull is greater if the molecule is nearer to the surface and it is maximum for a molecule on the surface.In order to increase the surface area, molecules from inside the liquid must be brought to the surface. For this purpose, work must be performed against the in ward pull exerted by the liquid. This work is stored in the surface in the form of potential energy. Thus potential energy of the liquid increases due to increase in its surface area. Conversely, the potential energy of a liquid decreases with decrease in its surface area. Now the natural tendency of a body is to attain the condition of minimum potential energy. Therefore the free surface of a liquid has a tendency to contract and minimise its area, so that the potential energy of the liquid is minimum. This tendency to minimise the surface area gives rise to the phenomenon of surface tension. In order to minimise the surface area, the forces due to surface tension always act tangentially to the liquid surface.The free surface of a liquid is ordinarily plane and horizontal. Sometimes, however, we find the liquid surface to be concave or convex. For example, the surface of water in a capillary tube is concave, while the surface of mercury in a capillary tube is convex. We shall consider the explanation of curved surfaces in Art. 6.4