# Tagged Questions

Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].

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### How is it possible to equate the internal energy at constant volume with the internal energy of an adiabatic process?

I hope my question makes sense. My problem is that, I have read through numerous textbooks that $$nCdT = -PdV$$ (where $NC$ is constant volume) when deriving the relationship between $T$ and $V$ for ...
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### Integrating factor $1/T$ in 2nd Law of Thermodynamics

How would you prove that $1/T$ is the most suitable integrating factor to transform $\delta Q$ to an exact differential in the second law of thermodynamics: $$dS = \frac{\delta Q}{T}$$ Where $dS$ is ...
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### The notion of an adiabatic process in thermodynamics -vs- quantum mechanics

I'm confused about the terminology in the two contexts since I can't figure out if they have a similar motivation. Afaik, the definitions state that quantum processes should be very slow to be called ...
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### Time constant of ice melt

I'm familiar with problems of "how much ice can you melt given some amount of energy", but I'm writing to get some clarification on the time constant of this event. This question might be somewhat ...
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### Perfect fluids in cosmology?

In cosmology, it is often assumed that the equation of state of a cosmological fluid is of the form $p=w\rho$. Why is this? Is it the equation of a perfect fluid? Why does $w=0$ for matter $1/3$ for ...
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### Why does Hydrogen molar heat capacity reach 7/2 R?

If a diatomic gas like Hydrogen has 6 maximum degrees of freedom why its molar heat capacity reaches at high temperatures $C_V = \frac{7}{2} R$ and not $C_V = \frac{6}{2} R= 3R$? molar heat capacity ...
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### Gas transformation for different molar number

When a gas at normal conditions (1atm, 273K, 22.4L) we say like the $$\frac{PV}{T} = 0.0820...$$ And by the know equation: $$PV = nRT$$ Where R is equals to $0.08205...$ and $n$ is the number of mols ...
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### Which form of the first law of thermodynamics should I use?

I usually wonder which thermodynamics first law is better to use ? The one given by physics : $\Delta U=Q-\Delta W$ or the one by chemistry : $\Delta U=Q+\Delta W$ In other words, should I take ...
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### How does a thermal temperature gun work?

I once worked as a kitchen porter over a winter season. We had fun with thermal temperature guns (like these) which I learned can be used for measuring the temperature of something a reasonable ...
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### How hot is the water in the pot?

Question: How hot is the water in the pot? More precisely speaking, how can I get a temperature of the water as a function of time a priori? Background & My attempt: Recently I started spend ...
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### Why does $U = T S - P V + \sum_i \mu_i N_i$?

From the first law of thermodynamics: $$dU = TdS - PdV + \sum_i\mu_i dN_i.$$ Quoting Wikipedia: As conjugate variables to the composition $N_{i}$ the chemical potentials are intensive ...