# Tagged Questions

A important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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### Why can we say that $\bar{d}Q=TdS$?

When we introduce entropy we do this by saying that: $$\bar{d}Q=TdS.$$ Now I was wondering why this should be true? I know that by looking at a Carnot cycle, we do get this relation for reversible ...
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### entropy of a long molecule chain with respect to its length

Consider a (very long) one-dimensional chain of $N$ moleculs, which can be in either of the energy states $\alpha$ or $\beta$. The configurations have length $a$ or $b$ respectively. Show ...
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### What is the conceptual difference between Gibbs and Boltzmann entropies?

In simple words what is the conceptual difference between Gibbs and Boltzmann entropies? Gibbs entropy: $S=-k_B\sum p_i\ln p_i$ Boltzmann entropy: $S=-k_B\ln \Omega$
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### Calculating entropy [duplicate]

Suppose 30 gram of metal Gallium melts at 36 °C. The specific heat of fusion is 80.3 kJ/kg and the melting temperature is 29.9 °C. Explain if the melting of the Gallium in this process is ...
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### Isentropic and Isothermal Compressibility

Why isentropic compressibility is greater than isothermal compressibility ? While deriving $C_p$ and $C_v$ relation, I got $\frac{Cp}{Cv}$ as $\frac{ke}{Kt}$. Which tells us that $Ke > Kt$. But ...
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### Isentropic process and reversibility [duplicate]

I know that every adiabatic reversible process is an isentropic process. Can a process be isentropic but still not reversible adiabatic? Please provide me some examples.
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### Unmixing of gases: What is the relevant temperature for my Entropy?

This answer to a question about unmixing gases states: However, let us now assume we have to hand a source of mechanical work, and a large heat reservoir at temperature $T$. I'll assume that ...
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### Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
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### Is the second law of thermodynamics a real law? [duplicate]

Everytime I ask people why the second law of thermodynamics is true, they say because the probability of entropy increasing is very large. This for some reason doesn't seem right for me. Just because ...
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### What is the difference between a low vs. high entropy plasma just after and before a singularity occurs?

Although it appears that the universe is not closed (since it is accelerating) I have been reading different websites on how the universe would look like if it was closed and the big crunch did occur. ...