# 物理代写|热力学代写thermodynamics代考|MECH3720

## 物理代写|热力学代写thermodynamics代考|PATH INDEPENDENCE

That entropy is independent of the path is shown by considering two states of a system of an ideal gas, namely, $p_1, V_1, T_1$ and $p_2, V_2, T_2$ with $T_1=T_2=T$. Thus, the two states lie on an isotherm $p V=n R_0 T=$ constant and is shown in Figure 5.1. The environment is also considered to be at the same temperature $\left(T_0=T\right)$. The isothermal path is reversible and is chosen to determine the entropy change $\Delta S=S_2-S_1$. Since the internal energy of an ideal gas depends only on the temperature, we have for the isothermal path $d U=0$ and therefore the first law becomes $\delta Q_{r e v}=p d V$. Thus,
$$\Delta S=\int \frac{\delta Q_{\mathrm{rev}}}{T}=\int_{V_1}^{V_2} \frac{p}{T} d V=n R_0 \ln \frac{V_2}{V_1}$$

We have assumed that the system exchanges heat with the environment at temperature $T_0$ and $T_0=T$. If $T_0 \neq T$, then a reversible heat pump is used to effect the reversible heat transfer as shown in Figure 5.2. Denoting $\delta Q_0$ as the reversible heat transfer during an infinitesimal part of the isothermal path from the environment at temperature $T_0$, we have from the second law
$$\frac{\delta Q_0}{T_0}=\frac{\delta Q}{T}=\frac{p d V}{T}$$
The entropy change in the environment is therefore
$$\Delta S_{\mathrm{env}}=-\int \frac{\delta Q_0}{T_0}=-n R_0 \ln \frac{V_2}{V_1}$$
But
$$\Delta S_{\mathrm{sys}}+\Delta S_{\mathrm{cur}}=0$$
in accord with the second law. This gives the entropy change between states 1 and 2 as
$$\Delta S_{\mathrm{sys}}=n R_0 \ln \frac{V_2}{V_1}$$
which is the same as Eq. $5.1$ derived earlier.

## 物理代写|热力学代写thermodynamics代考|REVERSIBLE WORK

It can be shown from Clausius inequality that the reversible work between two equilibrium states is the same for all reversible paths linking the two states. It also follows that the reversible work is the maximum work.

To prove the above, consider a real path $X$ linking two equilibrium states. The system exchanges heat with the environment at a temperature $T_0$. For the real path $X$ linking states 1 and 2, as shown in Figure 6.1, the first law can be written as
$$\Delta U=Q_X-W_X$$
where $Q_X$ and $W_X$ are the heat transfer to and work done by the system for path $X$. Similarly for a reversible path $R$ linking the two states (Figure 6.1), we write
$$\Delta U=Q_R-W_R$$
We can form a cycle by going from state 1 to state 2 via a path $X$ and return to state 1 by reversing along a reversible path $R$. For the cycle, we write
$$\Delta U=0=\left(Q_X-W_X\right)-\left(Q_R-W_R\right)$$

Thus, $Q_X-Q_R=W_X-W_R$. From Clausius inequality
$$\sum_{\text {cycle }} \frac{Q}{T} \leq 0, \frac{Q_x}{T_0}-\frac{Q_R}{T_0} \leq 0$$
or
$$Q_X-Q_R \leq 0$$
The equality sign applies if $X$ is also a reversible path. Hence, we obtain the result
$$Q_R \geq Q_X$$
that is, the heat transfer for the reversible path is greater than that for a real path. It follows that
$$W_X-W_R \leq 0$$
and
$$W_R \geq W_X$$

# 热力学代考

## 物理代写|热力学代写thermodynamics代考|PATH INDEPENDENCE

$T_1=T_2=T$. 因此，这两个状态位于等温线上 $p V=n R_0 T=$ 常量，如图 $5.1$ 所示。环境也被

$$\Delta S=\int \frac{\delta Q_{\mathrm{rev}}}{T}=\int_{V_1}^{V_2} \frac{p}{T} d V=n R_0 \ln \frac{V_2}{V_1}$$

$$\frac{\delta Q_0}{T_0}=\frac{\delta Q}{T}=\frac{p d V}{T}$$

$$\Delta S_{\text {env }}=-\int \frac{\delta Q_0}{T_0}=-n R_0 \ln \frac{V_2}{V_1}$$

$$\Delta S_{\mathrm{sys}}+\Delta S_{\mathrm{cur}}=0$$

$$\Delta S_{\mathrm{sys}}=n R_0 \ln \frac{V_2}{V_1}$$

## 物理代写|热力学代写thermodynamics代考|REVERSIBLE WORK

$$\Delta U=Q_X-W_X$$

$$\Delta U=Q_R-W_R$$

$$\Delta U=0=\left(Q_X-W_X\right)-\left(Q_R-W_R\right)$$

$$\sum_{\text {cycle }} \frac{Q}{T} \leq 0, \frac{Q_x}{T_0}-\frac{Q_R}{T_0} \leq 0$$

$$Q_X-Q_R \leq 0$$

$$Q_R \geq Q_X$$

$$W_X-W_R \leq 0$$

$$W_R \geq W_X$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: