Before you read this, I suggest you read posts 18.26 and 19.15. In post 18.26, we saw that particles that are free to move in a medium (like molecules in a solution) will spontaneously spread to achieve an even concentration; this process is called diffusion. In post 19.15, we saw that, for diffusion in one… Continue reading 19.16 Solution of the diffusion equation
Before you read this, I suggest you read post 19.14. In post 19.12, we saw how a wave could be represented, in time and space, by the wave equation. The concentration of a diffusing substance also varies in both space and time (post 18.26). Can we represent this dependence by a differential equation too? In… Continue reading 19.15 The diffusion equation
Before you read this, I suggest you read post 18.26. In post 18.26 we saw that molecules (or atoms or ions) move spontaneously from regions of high concentration to regions of low concentration, in order to increase the entropy of the system. Processes that increase entropy occur spontaneously because they lead to a more probable… Continue reading 19.14 Fick’s law of diffusion and the conduction of heat
In post 18.12 I introduced the idea of a standing wave as a vibration that could exist on a string tethered at both its ends. In the picture above, a string of length L is tethered at both ends, A and B. The fundamental wave (shown in red) then has its greatest amplitude of vibration… Continue reading 19.13 More about standing waves: intuition and analysis
Before you read this, I suggest you read posts 19.10 and 19.11. I introduced the idea of a wave in post 18.10 but, if you think about it, you will see that in that post and later posts (18.11, 18.12, 18.13, 18.14, 19.9) on waves, I have never defined exactly what I mean by the… Continue reading 19.12 The wave equation
Before you read this, I suggest that you read posts 17.4 and 18.10. In post 18.10 we saw that a one-dimensional wave could be represented by a wave function, ψ, that is a function (post 19.10) of position, x, and time, t. At a fixed point in space (x is constant), the wave function is… Continue reading 19.11 Partial differentiation
In post 19.2, we saw that the ideal gas equation pV = nRT, provides a good model for the behaviour of most gases except at very high pressures. Here p represents the pressure of the gas, V its volume, n the number of moles and R is the ideal gas constant. In post 18.11, we… Continue reading 19.10 Differential equations
In post 16.25, we saw that an electric charge produces an electric field. If the charge oscillates, relative to an observer, then the field will oscillate. We also saw that a moving electrical charge produces a magnetic field. If this movement is oscillatory, the magnetic field will be oscillatory. The fields can have an influence… Continue reading 19.9 Electromagnetic waves
Before you read this, I suggest you read posts 16.21 and 18.10. The picture shows a sinusoidal water wave (in blue) of amplitude A and wavelength λ (post 18.10) travelling along a straight channel at an instant in time, t. The wave is formed by water in the layer between the lines (that lie in… Continue reading 19.8 Wave energy
Before you read this, I suggest that you read posts 19.5 and 19.6. In post 19.5, we saw that positive charges move spontaneously from hydrogen ions (H+) to zinc atoms because a zinc atom is at a lower electrical potential (post 17.44) than a hydrogen atom. As a result, a zinc atom is converted into… Continue reading 19.7 Redox potentials
