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Suppose Fluid (say, water) occupies a domain D and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let be the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.
Fick's law for diffusion states that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that .
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.
Determine the causality principle for the Klein- Gordon equation in one dimension. Deduce that the speed of propagation is at most c.
The molar heat capacity of a gas at constant pressure is 18.7 J mol -1 K -1 . What is the heat capacity of 9.4 moles of this gas at constant volume ?
Calculate how much heat energy is required to raise the temperature of a cube of copper of side 2cm. from 300 to 320k. given: density=8933kg/m cube , atomic weight=63.55, cp=24j/k/
tell me about the terms of temporal coharence
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A diffraction grating used at normal incidence provides a spectral line of certain order with wavelength 6000A 0 superimpose on another spectral line of wave length 5000A 0 of th
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two blocks of mass 2kg and 4 kg are held together by a string force of 10N is applied on 2kg and 20N on 4kg find the tension in the string connected between two blocks
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