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# 物理代写|热力学代写Thermodynamics代考|EGM-321 Entropy & Reversible Change

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## 物理代写|热力学代写Thermodynamics代考|Entropy & Reversible Change

The Second Law tells us what happens to $S_{\text {tot }}$ under a spontaneous irreversible change. What happens to $S_{\text {tot }}$ under a reversible change? Recall that all thermodynamic changes are “reversible” for the surroundings; therefore, a reversible change for the system must also be reversible for the total system.
Consequently, under a reversible change:

$\Delta S_{\text {tot }}$ cannot be greater than zero, or the process would be spontaneous irreversible.

$\Delta S_{\text {tot }}$ cannot be less than zero, or the process would be forbidden by the Second Law.

$\therefore \Delta S_{\text {tot }}=\Delta S+\Delta S_{\text {sur }}=0 . \quad[$ reversible $]$

Thus, the information about the total system is conserved under a reversible change; whatever information is gained about the system is lost about the surroundings, or vice-versa. This situation is reminiscent of the balance between volume and temperature information that characterizes the system under reversible adiabatic expansions, resulting in $\Delta S=0$. We now see that reversible adiabatic changes also satisfy $\Delta S_{\text {sur }}=\Delta S_{\text {tot }}=0$. Expansions of this kind form a key part of the Carnot cycle (Section 13.2), and will therefore be reviewed here.

Reversible adiabatic expansion of ideal gas: Recall from Sections $8.5$ and $9.1$ that a reversible isothermal expansion can be achieved by placing a piston-cylinder apparatus in a heat bath, and then slowly easing up on $P_{\text {sur }}$. The resultant reversible path is an isotherm, given for the ideal gas by $P(V) \propto V^{-1}$.

To achieve reversible adiabatic expansion, we surround the apparatus in some thermally insulating material, rather than a heat bath – but otherwise we proceed similarly. Because work is done but no heat is absorbed, $U$ and $T$ both decrease. The resultant reversible adiabatic path, or “adiabat,” is thus different from the corresponding isotherm-although both paths lie on the equation of state, as indicated in Figure 13.1.

## 物理代写|热力学代写Thermodynamics代考|Carnot Cycle & Absolute Zero Temperature

The Carnot cycle is the quintessential thermodynamic cycle, covered in every thermodynamics textbook. It provides a useful and quantitative understanding of the operation of heat engines (Section 12.1), whereas the reverse Carnot cycle does the same for heat pumps (e.g., air conditioners). It is also an excellent example for analyzing how entropy behaves under reversible change – in which context, it relates to the Third Law of Thermodynamics.

In a Carnot cycle, the “loop” is a precise set of four consecutive but reversible stages, as indicated in Figure 13.2. Two of these stages are expansions, and two are compressions. Also, two are isothermal, and two are adiabatic. Being a cycle, for all state functions $X, \Delta X$ is zero around the entire cycle-but not necessarily zero over each individual stage. Finally, $W=-Q \neq 0$ around the entire cycle-with $(W<0, Q>0)$ corresponding to a clockwise traversal (heat engine), and $(W>0, Q<0)$ to the reverse or counterclockwise traversal (heat pump).

In practice, care must be taken to ensure that every stage is as reversible as possible. For example, heat flow must be avoided when the apparatus is inserted into the hot bath at state A (or cold bath at state $\mathrm{C}$ ), by ensuring that $T$ is equal to $T_h$ (or $T_c$ ), at the end of the preceding adiabatic stage 4 (or 2 ).

Note that $Q_h$ is the absorbed heat, and $-Q_c=\left|Q_c\right|$ the released or “wasted” heat, as per Section 12.2. Their difference is the work performed by the system, $-W=Q_h-\left|Q_c\right|$. That $W<0$ follows from the fact that more heat is absorbed than released $\left.\left(Q_h\right\rangle\left|Q_c\right|\right)$. This in turn follows from $\Delta S=Q_h / T_h+Q_c / T_c=0$, together with the fact that $T_h>T_c$.

## 物理代写|热力学代写Thermodynamics代考|Entropy \& Reversible Change

$\Delta S_{\text {tot }}$ 不能大于零，否则该程将是自发的不可逆的。
$\Delta S_{\text {tot }}$ 不能小于零，否则第二定律将禁止该过程。
$\therefore \Delta S_{\text {tot }}=\Delta S+\Delta S_{\text {sur }}=0$
[可逆的]

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