Please show all woking neatly, thanks! A spherical vessel of diameter 1 m is fir

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Please show all woking neatly, thanks!

A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough estimate of how long one must wait before a uniform mixture has formed (use the result for the time dependence of the root mean square travel distance in a random walk in ID.) Suggest a better way to make a uniform mixture.

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The field of information security has grown and evolved significantly in recent years. There are many ways of gaining entry into the field as a career. It offers many areas for specialization including: securing network(s) and allied infrastructure, securing applications and databases, security testing, Each model of diffusion expresses the diffusion flux through concentrations, densities and their derivatives. Flux is a vector mathbf{J}. The transfer of a physical quantity N through a small area Delta S with normal u per time Delta t is Delta N = (mathbf{J}, u) Delta S Delta t +o(Delta S Delta t), , where (mathbf{J}, u) is the inner product and o(...) is the little-o notation. If we use the notation of vector area Delta mathbf{S}= u Delta S then Delta N = (mathbf{J}, Delta mathbf{S}) Delta t +o(Delta mathbf{S} Delta t), . The dimension of the diffusion flux is [flux]=[quantity]/([time]·[area]). The diffusing physical quantity N may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity. For its density, n, the diffusion equation has the form rac{partial n}{partial t}= - abla cdot mathbf{J} +W , , where W is intensity of any local source of this quantity (the rate of a chemical reaction, for example). For the diffusion equation, the no-flux boundary conditions can be formulated as (mathbf{J}(x), u(x))=0 on the boundary, where u is the normal to the boundary at point x. Fick's law and equations Main article: Fick's laws of diffusion Fick's first law: the diffusion flux is proportional to the negative of the concentration gradient: mathbf{J}=-D abla n , ;; J_i=-D rac{partial n}{partial x_i} . The corresponding diffusion equation (Fick's second law) is rac{partial n(x,t)}{partial t}= ablacdot( D abla n(x,t))=D Delta n(x,t) , where Delta is the Laplace operator, Delta n(x,t) = sum_i rac{partial^2 n(x,t)}{partial x_i^2} . Onsager's equations for multicomponent diffusion and thermodiffusion Fick's law describes diffusion of an admixture in a media. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law is the antigradient of concentration, - abla n. In 1931, Lars Onsager[10] included the multicomponent transport processes in the general context of linear non-equilibrium thermodynamics. For multi-component transport, mathbf{J}_i=sum_j L_{ij} X_j , , where mathbf{J}_i is the flux of the ith physical quantity (component) and X_j is the jth thermodynamic force. The thermodynamic forces for the transport processes were introduced by Onsager as the space gradients of the derivatives of the entropy density s (he used the term "force" in quotation marks or "driving force"): X_i= { m grad} rac {partial s(n)}{partial n_i} , where n_i are the "thermodynamic coordinates". For the heat and mass transfer one can take n_0=u (the density of internal energy) and n_i is the concentration of the ith component. The corresponding driving forces are the space vectors X_0= { m grad} rac{1}{T} , ;;; X_i= - { m grad} rac{mu_i}{T}; (i >0) , because { m d}s=rac{1}{T}{ m d}u-sum_{i geq 1}rac{mu_i}{T} { m d} n_i where T is the absolute temperature and mu_i is the chemical potential of the ith component. It should be stressed that the separate diffusion equations describe the mixing or mass transport without bulk motion. Therefore, the terms with variation of the total pressure are neglected. It is possible for diffusion of small admixtures and for small gradients. For the linear Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium: X_i= sum_{k geq 0} left.rac{partial^2 s(n)}{partial n_i partial n_k} ight|_{n=n^*} { m grad} n_k ,

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