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12 votes

Why isn't the free expansion of a gas in an adiabatic container isentropic?

The free expansion isn’t reversible because the gas flows down a pressure gradient (that arises when you remove the piston). Any energy flow down a gradient generates entropy. In contrast, during the (...
7 votes

Why isn't the free expansion of a gas in an adiabatic container isentropic?

If you expand a gas adiabatically using a piston, the process is isoentropic. An adiabatic process is not isentropic unless it is also reversible. To be reversible, it must be carried out quasi ...
  • 58.5k
7 votes
Accepted

Generation of order on the Earth

Not sure what sort of simulation or model you are looking for. Our proximity to the Sun creates a temperature and energy difference across the surface of the the Earth that is essential to almost all ...
  • 36.9k
3 votes

Fundaments of thermodynamics and separating entropy

"Also, from this formalism, we can deduce that entropy production is generated either by work/volume variation or by internal entropy flow in compound system, is this generally true?" No. ...
  • 28.8k
2 votes

Fundaments of thermodynamics and separating entropy

Question 1 If all of this works, why is it never taught in this way? Thermodynamics can be taught and understood in many different ways. If your way makes sense to you, use it. Personally I would not ...
  • 1,361
2 votes
Accepted

Boltzmann Equation Maximum Entropy Production Principle

It might just be a typo, but you did not write out integration over $c$ in the last equation. We should have $${\partial s \over \partial t}+\text{div}(j_s)+k\int{dc\bigg({\partial f \over \partial t}+...
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2 votes

How to derive this $Tds$ relation?

Just follow the literal instructions. What's the $p$ derivative (at constant $T$) of $$T\left(\frac{\partial s}{\partial T}\right)_p=\left(\frac{\partial u}{\partial T}\right)_p+p\left(\frac{\partial \...
2 votes

Why isn't the free expansion of a gas in an adiabatic container isentropic?

There are only two mechanisms by which the entropy of a closed system can change: By heat transfer between the surroundings and the system at the location and temperature of the boundary between the ...
  • 28.8k
2 votes

Fundaments of thermodynamics and separating entropy

we can deduce that entropy production is generated either by work/volume variation or by internal entropy flow in compound system, is this generally true? The following line of thinking could be ...
2 votes

Is the second law of thermodynamics a "no-go" theorem?

I was writing this post for a question that was closed as duplicate before I finished, so I put it here because the answers here do not contain my point. One has to understand what "laws" ...
  • 225k
1 vote

Consequence of entropy increasing with time

I suspect entropy is a trickier concept that someone might think, since it measures way more than just disorder of a system. From the microscopic point of view, it's strongly related to the possible ...
1 vote

Why isn't the free expansion of a gas in an adiabatic container isentropic?

You can also reason from the formula for the entropy change of an ideal gas. \begin{align} \Delta S &= C_V \ln\left(\frac{T}{T_0}\right) + Nk \ln\left(\frac{V}{V_0}\right), \end{align} where $...
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1 vote

Converting from differential form to substantial derivative form (Gibb's Equation)

In the midst of taking a shower (typical), I figured out my mistake! I have not seen this step fully detailed in the textbooks I have looked at, so for anyone that has this question in the future see ...
  • 21
1 vote

Proof of Caratheodory's theorem

Write the conservation of energy in differential form as $\delta Q = dU - \delta W$ and $\delta W = \sum_k y_kdx_k$, where $U$ is the internal energy and $x_k$ are the extensive parameters forming the ...
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1 vote
Accepted

What is the multiplicity of a microstate (not macrostate!)

Almost certainly the multiplicity of a microstate means the number of microstates that are contained within the macrostate that contains the given microstate (and so is the same as the multiplicity of ...
  • 36.9k
1 vote

How to conceptualize the unit Temperature?

Thermodynamics and statistical physics are two equivalent but different approaches to the same types of phenomena. Thermodynamics is a phenomenological/axiomatic approach, in terms of laws, deduced ...
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1 vote

Will a black hole disappear?

We cannot be sure yet if a Black Hole fully evaporates into "nothing" or leaves a stable quantum remnant. Hawking Radiation is hard to observe because it is an incredibly slow process for ...
1 vote

Property Relation on Gibbs free energy

The equation dG=-SdT+VdP applies to the differential change in G between two closely neighboring thermodynamic equilibrium states, one at (T,P) and the other at (T+dT,P+dP) of a single phase constant ...
  • 28.8k
1 vote
Accepted

Property Relation on Gibbs free energy

First I need to correct one of your statements: For general reversible process it is not true that $dG=0$. For $dG$ to be zero the process must be reversible and $T$ and $P$ must be constant. Phase ...
  • 1,361
1 vote

Fundaments of thermodynamics and separating entropy

If all of this works, why is it never taught in this way? ... The three most common paradigms to teach thermodynamics are laws, postulates, and statistical mechanics. They have withstood tests on ...
1 vote

Is the second law of thermodynamics a "no-go" theorem?

There is an argument that can be made that adding the additional but intrinsic to science restriction of limiting physical phenomenon to those that can be empirically attested to renders the obeying ...

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