物理代写|热力学代写thermodynamics代考|Simple Electrolyte Solution Systems

Many science and engineering processes involve electrolytes. An electrolyte system may be viewed as a solution having a lot of particles with electric charge (e.g., ions). We are interested in the equilibrium conditions of such an electrolyte system under the influence of an external electrical field.

For a simple electrolyte solution system, the fundamental equation in energy form is given by:
$$d \bar{U}=d U+d U_e$$
where $\bar{U}$ is the total internal energy of the electrolyte solution; $U=U\left(S, V, N_l\right.$, $\ldots . N_r$ ) is the internal energy of the electrolyte solution without considering the electric field effects; and $U_e$ is the electrical part of the total internal energy, due to the interaction of the charged particles with the applied electrical field. It can be shown that
$$d U_e=\psi d Q$$
where $\psi$ is the electrical potential of the electrical field, and $Q$ is the total charge of ions.
$$Q=F \sum Z_i N_i$$
where $F$ is the Faraday constant; $\mathrm{Z}{\mathrm{i}}$ is the electro-valence of the ith ionic species; and $\mathrm{N}{\mathrm{i}}$ is the mole number of the ith ionic species. Thus,
$$d U_e=F \psi \sum Z_i d N_i$$
Recall
$$d U=T d S-P d V+\sum \mu_i d N_i$$

物理代写|热力学代写thermodynamics代考|Systems in Gravitational Field and in Centrifugal Field

Let us consider a moving system subject to a gravitational field and a centrifugal field. For example, a cylinder filled with a solution is spinning around a vertical shaft, as illustrated in the figure below. Such a centrifugal device is often used in industrial separation processes.

Because the presence of external fields (the gravitational field and the centrifugal field in this case), the properties of the solution are no longer uniform. For example, the pressure and the density of the solution are functions of position, i.e.,
$$P=P(r, z) \quad \text { and } \quad \rho_i=\rho_i(r, z)$$
Obviously, such a system is not a simple system; therefore, we cannot use the fundamental equation for a simple system such as
$$\mathrm{U}=\mathrm{U}\left(\mathrm{S}, \mathrm{V}, \mathrm{N}1, \ldots \mathrm{N}{\mathrm{r}}\right)$$
to model such a system.

热力学代考

物理代写|热力学代写thermodynamics代考|Simple Electrolyte Solution Systems

$$d \bar{U}=d U+d U_e$$

$$d U_e=\psi d Q$$

$$Q=F \sum Z_i N_i$$

$$d U_e=F \psi \sum Z_i d N_i$$

$$d U=T d S-P d V+\sum \mu_i d N_i$$

物理代写|热力学代写thermodynamics代考|Systems in Gravitational Field and in Centrifugal Field

$$P=P(r, z) \quad \text { and } \quad \rho_i=\rho_i(r, z)$$

$$\mathrm{U}=\mathrm{U}(\mathrm{S}, \mathrm{V}, \mathrm{N} 1, \ldots \mathrm{Nr})$$

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