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The entropy increases always. There is nothing unusual about the example of planet formation. Either one of two things has to happen when the dust contracts into a planet: The planet heats up as the dust contracts, increasing entropy. Heat is radiated into empty space, decreasing the entropy of the collection of dust but increasing the entropy of the rest ...

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Mirrors and lenses cannot do what you ask. Light has a specific intensity, meaning a power per unit area per unit solid angle per unit wavelength. Mirrors and lenses can never increase the specific intensity. As an example, consider using a lens to focus sunlight onto a target. The specific intensity of the sunlight is the same with or without the lens. ...

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A somewhat longer answer, since I'm afraid my comment may have seemed a bit abrupt... Lets look at a fairly simple thermodynamic system, the Ag-Ge binary phase diagram. This consists of 3 phases only, fcc Ag, diamond cubic Ge, and the liquid. Taking the published thermodynamic model from J. Wang et al. in Thermochimica Acta 512 240-246 (2011), one can ...

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I am not familiar with the textbook you mentioned but there is a conventional "proof" of the equality $\oint _{rev}\frac{\delta Q}{T}=0$ for states that can be described by a thermal parameter, usually temperature $T$ and by a mechanical parameter, such as $V$. The "proof" goes by approximating the area enclosed by the $T,V$ cycle with Carnot cycles, that is ...

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In the limit that $T\rightarrow\infty$, the partition function and the multiplicity of states are equal. Why? Well, we have that $Q=\sum_{i} e^{-E_i/kT}$, where $i$ indexes all possible microstates. If $T\rightarrow\infty$, these Boltzman factors all approach one, and we have $Q=\sum_i 1=\Omega$. You might think that in the limit $T\rightarrow\infty$ the ...

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They look like they could be related. What is the relationship? From your two equations, we have $$k\ln \Omega = k \ln Q + kT\frac{\partial}{\partial T} \ln Q = k \ln Q + \frac{kT}{Q}\frac{\partial}{\partial T}Q$$ but $$Q = \sum_ie^{-\frac{E_i}{kT}}$$ and so $$k\ln \Omega = k \ln Q + \frac{kT}{Q}\frac{1}{kT^2}\sum_i E_ie^{-\frac{E_i}{kT}} = ... 1 When energy flows from a hotter subsystem to a colder subsystem the entropy of the combined system increases.$$\frac{dS_1}{dE_1}=\frac{1}{k_BT_1}<\frac{1}{k_BT_2}=\frac{dS_2}{dE_2}. So if they exchange energy in a way that conserves energy then we get $-\Delta S_1<\Delta S_2$ and the total entropy increases. This does require that the systems ...

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Introduction: Entropy Defined The popular literature is littered with articles, papers, books, and various & sundry other sources, filled to overflowing with prosaic explanations of entropy. But it should be remembered that entropy, an idea born from classical thermodynamics, is a quantitative entity, and not a qualitative one. That means that entropy ...

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The connection of heat to entropy in thermodynamics is through: where S is entropy Q is heat T is temperature, and it is through differential changes. This in no way means that heat is entropy . The easiest way to acquire an intuition of entropy is to read up on the statistical definition which can be proven to be the same as the thermodynamic ...

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To start with the law of increasing entropy applies to isolated systems. The system you describe is isolated if one considers the total entropy of both the paramagnetic material and the permanent magnet, including any radiation. The order introduced in the paramagnetic material is balanced by a disorder in the permanent magnet plus any radiation from ...

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Issues with that derivation: You're missing the extra term $\frac 52 k N,$ which may matter if you have to do any work with chemical potentials. Your students will not necessarily know why to parcel the space into volumes of size $\lambda^3$. Starting from the definition of entropy and deriving that the thermal volume $\lambda^3$ is important seems ...

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