热力学代写 Thermodynamics代考2023

热力学代写Thermodynamics

统计力学Statistical mechanics代写

• Chemical thermodynamics化学热力学
• Equilibrium thermodynamics平衡热力学

热力学的历史

Thermodynamics is a branch of classical physics and chemistry that studies and describes the thermodynamic transformations induced from heat to work in a thermodynamic system in processes involving changes in the state variables temperature and energy.

Classical thermodynamics is based on the concept of a macroscopic system, i.e. a part of the mass physically or conceptually separated from the external environment, which for convenience is usually assumed not to be disturbed by the exchange of energy with the system (isolated system): the state of a macroscopic system in equilibrium is specified by quantities called thermodynamic variables or state functions, such as temperature, pressure, volume and chemical composition. The main notations of chemical thermodynamics have been established by IUPAC.

热力学相关课后作业代写

A state function for a Van der Waals gas is given by an equation between thermodynamic variables that depend on model parameters $A, B$, and a physical constant $R$ :
$$\left(P+\frac{A N^2}{V^2}\right)(V-N B)=N R T$$
where $A N^2 / V^2$ is referred to as the internal pressure due to the attraction between molecules and $N B$ is an extra volume, sometimes associated with the the volume per molecule.

Write out a differential expression for $d N$ in terms of differentials of the thermodynamic variables.

A state function for a Van der Waals gas is given by an equation between thermodynamic variables that depend on model parameters $A, B$, and a physical constant $R$ :
$$\left(P+\frac{A N^2}{V^2}\right)(V-N B)=N R T$$
where $A N^2 / V^2$ is referred to as the internal pressure due to the attraction between molecules and $N B$ is an extra volume, sometimes associated with the volume per molecule.

Write out a differential expression for $d N$ in terms of differentials of the thermodynamic variables.

The solution is pretty straightforward. One way is to differentiate the entire expression and group the terms corresponding to $d N, d P, d T$, and $d V$. Another way to do is by implicit differentiation. The real gas equation can be rewritten such that,
\begin{aligned} N & =N(T, V, P) \ d N & =\left(\frac{\partial N}{\partial P}\right){T, V} d P+\left(\frac{\partial N}{\partial V}\right){T, P} d V+\left(\frac{\partial N}{\partial T}\right){P, V} d T \end{aligned} In an equivalent way, you could have written the function $P=P(V, T, N)$ and extract $d N$ from the following. $$d P=\left(\frac{\partial P}{\partial N}\right){T, V} d N+\left(\frac{\partial P}{\partial V}\right){T, N} d V+\left(\frac{\partial P}{\partial T}\right){N, V} d T$$
For instance, the first term $\left(\frac{\partial P}{\partial N}\right){T, V}$ can be evaluated as $$\left(\frac{\partial P}{\partial T}\right){P, V}=\frac{N R}{V-N B}$$
Using any one of the methods you would get
$$d N=\frac{(V-B N) d P+\left(P-\left(A N^2 / V^2\right)+\left(2 A B N^3 / V^3\right)\right) d V-R N d T}{B P+R T+\left(3 A B N^2 / V^2\right)-(2 A N / V)}$$