All Questions
17,220 questions
4
votes
2
answers
212
views
What is the upper bound for black hole entropy derived from in the Bekenstein bound?
From several unrelated sources (such as Scott Aaronson's discussion of hypercomputation or this article about a bound on the number of degrees of freedom of any theory with a positive cosmological ...
- 428
1
vote
1
answer
45
views
Is a non-cyclic device (i.e. a process) which transfers heat from low to high temperature without work input possible?
The Clausius Statement: "It is impossible to construct a device that OPERATES IN A CYCLE and produces no effect other than the transfer of heat from a heat source to sink". So, is a non-...
- 19
3
votes
1
answer
68
views
Why are metastable crossover times equal to the exponential of the free energy barrier?
Many different models in stastical mechanics (for example, Curie-Weiss models) share the property that the (expected value of the) time it takes the system to move from one local minimum of the free ...
- 1,911
0
votes
0
answers
30
views
Why thermodynamic equilibrium and pressure balance is considered for having a reversible process? [duplicate]
When we compare the rapid expansion of an ideal gas to a very slow expansion from an initial state to a final state, we categorize one as irreversible and the other as reversible. This distinction ...
0
votes
0
answers
15
views
Simplified scenario: evaporative cooling vs convective heating between water and air
While thinking through this question I thought of a simplified scenario that would model one of the extremes:
A body of water with mass $M_W$, temperature $T_W$, and surface area $S_W$ is surrounded ...
- 924
0
votes
1
answer
36
views
Carnot efficiency for IC engine
Consider
$$e= \frac{T_h-T_c}{T_h}.$$
What is $T_c$ in Carnot efficiency for internal combustion engine, atmosphere or exhaust temperature?
If $T_c$ is atmosphere temperature, does that mean engine is ...
- 730
1
vote
2
answers
80
views
Is $T(V, P)$ a valid state equation for an ideal gas?
If I consider an ideal gas with constant number of particles, I can easily think an experiment where I can control $(V, T)$ or $(P, T)$ independently (state variables). But I cannot imagine an ...
- 167
0
votes
2
answers
49
views
If a two-state system with $N >> 1$ has zero energy, can it still access any possible microstate?
I understand that the number of microstates in a two-state system is $W = 2^N$. However, if the energy of the system is fixed at zero (for example, exactly half of a paramagnet's N dipoles point up ...
- 287
0
votes
1
answer
50
views
Does blowing hot air through cooler water, heat or cool the water?
Inspiration for this question was a discussion about hot tubs in desert locations.
Supposed we have a mass of water with a temperature of 90°F. What is the effect on the temperature of the water of ...
- 924
0
votes
1
answer
98
views
Advection equation of heat transfer during fluid flow in pipe with heat loss
I am trying to model transient temperature profile during fluid flow in pipe considering heat exchange with the surrounding. I am trying to use overall heat transfer coefficient to model heat exchange ...
0
votes
0
answers
44
views
Joule expansion: Experimental evidence for temperature change
In his original experiment, Joule found that there was no change in temperature after releasing air from one volume into a larger one [1]. However, we know now that for real gases there should be ...
- 469
10
votes
4
answers
1k
views
Matter made of neutral charges does not radiate?
We know that any blackbody that has a certain non-zero temperature radiates. This happens due to the jiggling of charged particles (protons and electrons), and accelerated charges create ...
- 111
0
votes
0
answers
29
views
Thermodynamics: complete vaporization of liquid via isenthalpic expansion
I am trying formulate an equation for enthalpy involving an isenthalpic throttle valve that completely vaporizes a liquid.
Here is what I have so far:
$\int_{T_1}^{T_{sat-vap}} c_{p,liq}(T)dT + h_{vap}...
- 154
0
votes
1
answer
823
views
Confused about empty plastic bottle in the freezer situation
Note: When I say the bottle is "empty", take it to mean, "with just air inside", as we use in everyday life! :)
My question: Suppose we put an "empty" closed common ...
- 95
1
vote
4
answers
115
views
Definition of Statistical/Thermodynamic Equilibrium
Suppose we have some system $A$ coupled with a reservoir $R$ where $A$ can exchange energy with $R$ but not particles or volume. The system $A$ will have some (time) average energy $U= \langle E \...
- 2,740
0
votes
1
answer
44
views
Why Gifford-Mcmahon cycle's Refrigeration Effect is $Q=V(P_1-P_2)$?
This extract is from Advances in Cryogenic Engineering (Vol 11). They do give an explanation for my question in Volume 6, but I am struggling to understand that
- 19
2
votes
1
answer
179
views
How do electronegativity triggered interactions in redox reactions translate to molecular motion (heat)?
In a Redox reaction, a valence electron is transferred/shared from one atom to another. The Electronegativity of the atom will dictate its tendency to attract shared electrons.
More specifically for ...
- 272
1
vote
1
answer
45
views
Structure of a quantity which is conserved under collision processes
In a book about statistical physics it is stated, that for each quantity which is conserved under elastic collisions,
$$\Psi(\vec v_1)+\Psi(\vec v_2)= \Psi(\vec v_1') + \Psi(\vec v_2')$$ there is only ...
- 1,391
1
vote
1
answer
70
views
Considerations for phase change through throttle valve
I am looking at characterizing, as well as I can, the exit velocity and density downstream of an isenthalpic throttle valve as a function of the downstream pressure. What is throwing me off is the ...
- 154
1
vote
1
answer
74
views
How much does the Gibbs state differ from the ground state at low tempratures
If we take the Gibbs state $\rho _G = e^{-\beta H}/Z$, at very low tempratures $\beta \to \infty$, then we get the ground state. I understand this comes up because only the first term survives in the ...
- 13
-2
votes
1
answer
84
views
Where did $1/2$ of this come from? [duplicate]
Work done by an external force $F$ upon a particle displacing from point 1 to point 2 is defined as
$$
W_{12} = \int_1^2 F \cdot dr
\, .$$
Kinetic energy and work-energy theorem: According to Newton's ...
1
vote
2
answers
55
views
In an Otto cycle engine, why not have the crankcase in a vaccuum?
In a 4-stroke engine, it is extremely difficult to have high efficiency because the hot gases are not allowed to expand until they are atmospheric pressure. But what if they weren't expanding against ...
user431618
-1
votes
3
answers
290
views
The development of Clausius Inequality
The reversible cyclic device absorbs $\delta Q_R$ from the thermal reservoir at $T_R$ and rejects heat $\delta Q$ to the piston-cylinder device, whose temperature at that part of the boundary is $T$ (...
- 105
0
votes
0
answers
63
views
Force in thermodynamic configuration space
Consider a thermodynamic system whose internal energy $U$ may not be conserved in general. It's a direct consequence of the First Principle that the variations in internal energy do not depend on the ...
- 1,880
3
votes
0
answers
42
views
On The Existence of The Single-Valued Entropy *Function* Via Caratheodory's Adiabatic Inaccessibility
I am looking for an explanation why the impossible example of a thermodynamic systemm see $^{[\mathbf 1]}$, or its obvious generalization that is to follow below, is not allowed by Caratheodory's ...
- 20.4k
0
votes
2
answers
117
views
Help me to understand why we have $pV$ in the enthalpy equation
I'm learning (slowly) about enthalpy. My understanding is that enthalpy is the sum of internal energy and the work done on the environment, in order to occupy a volume $V$ at pressure $p$?
$$H = U + ...
- 145
1
vote
1
answer
91
views
Water at zero degrees Celsius: proportions of liquid vs ice?
Suppose I put water on a dish, and I put it in contact with a heat bath whose temperature is zero degrees Celsius. I have two questions:
Given enough time, will the proportions of liquid water vs ice ...
- 242
2
votes
3
answers
146
views
Is absolute zero an arbitrary number or would an alien civilization agree it is -273.1° C? [closed]
Can absolute zero be calculated from pure mathematics or does it depend on definitions (such as the boiling point of water and freezing point) and experimentally derived values?
user429115
0
votes
0
answers
50
views
What is the reason for the presence of phases in materials?
Why is it that the physics of the iron-carbon solid solution system supports such a variety of different microstructures each with different iron-carbon ratios?
1
vote
1
answer
98
views
Proving a Superfunction Identity
I am trying to figure out the proof of the identity given between equations (1.11.7) and (1.11.8) in ref. [1], i.e.
\begin{align}
\Phi'(e^{-K}\,z\,e^K)=e^{-K}\Phi'(z) \tag{1}
\end{align}
where $z=(...
- 49
2
votes
1
answer
103
views
Maximum decrease in entropy per unit of energy?
They say we can decrease the entropy of a system by doing work. For example, this online physics text states, near Eq. 15.6.26, that: "If I pick up marbles that are scattered about the room and ...
- 121
0
votes
0
answers
47
views
Universe: Isolated or not? [duplicate]
Yesterday in our class, we were taught that an isolated system has the following boundaries: Non movable, adiabatic, impermeable. We were told that the universe can be considered an isolated system. ...
- 11
0
votes
3
answers
68
views
Can temperature of a body be increased without heating it? Is the converse true? [duplicate]
How can we change temperature without adding or removing heat? Are other form of energies added to the body to increase it's temperature?
0
votes
0
answers
24
views
How is Brayton cycle heat injection isobaric?
I'm trying to analyze a gaseous working fluid at the exit of the heating chamber as it heads to a nozzle in a Brayton cycle. My understanding is that the injection of heat creates a rise in internal-...
- 154
5
votes
1
answer
330
views
Divergence of vector field term-wise
In a spacetime $(M, g)$ the following identity for the divergence of a vector field $X$ holds
$$ \nabla_{\mu} X^{\mu} = \frac{1}{\sqrt{-\det g}} \,
\partial_{\mu} \big( \sqrt{- \det g} \ X^{\mu} \big)...
- 695
0
votes
2
answers
77
views
Understanding Thermal Expansion in a Bimetallic Strip: Do Different Parts of the Same Metal Expand Differently?
If a bimetallic strip is made by tightly joining two metals (one red and one blue), and the blue metal has a higher coefficient of linear expansion than the red metal, the strip will curl when heated, ...
- 15
0
votes
1
answer
36
views
Universal equation of state for fluids and gases
I would like to ask, is there any universal equation of state that holds for any and all classical fluids and gases, derived purely from first principles (though constants in it should be measurable, ...
- 1
1
vote
3
answers
93
views
Why should the Boltmann distribution maximize entropy with average energy constrained?
In statistical mechanics, when working with the canonical ensemble (e.g. a system able to exchange energy with a large thermostat at temperature $T$, the system together with the thermostat being ...
- 304
0
votes
0
answers
24
views
Einstein Relation; Equilibrium State of a Diffusive system
Consider the convection-diffusion equation with no sources/sinks:
$$\frac{\partial c}{\partial t} = \mathbf{\nabla} \cdot (D \mathbf{\nabla} c - \mathbf{v} c)$$
Where $c$ is the concentration of the ...
- 2,740
5
votes
3
answers
139
views
Why is the entropy change for a system in irreversible transformations the same as in reversible transformations in some cases, not in other cases?
Generally, the entropy change for a closed system for an irreversible transformation is not the same in a closed system for a reversible transformation.
A clear counterexample is that of an adiabatic ...
- 1,723
0
votes
1
answer
61
views
What is actually temperature in case of solids and liquids?
We know that temperature in case of ideal gases is caused due to the translational component of the velocity, which causes pressure and then we define temperature according to $pV=nRT$.
But for solids ...
6
votes
2
answers
675
views
How can I calculate derivative of eigenstates numerically?
I want to calculate $\langle n | \partial_{k_x} n \rangle$ where $| n \rangle \equiv | u_{n,\mathbf{k}} \rangle $ is the $n$-th Bloch eigenstate of a $6\times6$ Hamiltonian $H\equiv H(\mathbf{k})$. ...
- 1,437
0
votes
1
answer
41
views
Helmholtz free energy density proof
We see Helmholtz free energy density is given as $f(n,T)$, with $n = N/V$. (fig.2: DOI: 10.3390/e17074563, Solid States Notes, Hadley)
Given that Helmholtz free energy $F = E - TS$, is such that $dF=−...
6
votes
3
answers
649
views
Is internal energy dependent on the acceleration of the system? [duplicate]
Consider an ideal gas confined in an adiabatic container.
We know that internal energy does not depend on the velocity of a uniformly moving system, because relative to the walls of the container, the ...
0
votes
0
answers
18
views
Fixed points above the decompactification scale vs black hole entropy
Asymptotic safety is the hypothesis that there is a UV fixed point in quantum gravity. One critique is that this is incompatible with the holographic understanding of how black hole entropy scales (i....
- 13.4k
0
votes
1
answer
101
views
Why is the thermal expansion coefficient of an incompressible substance constant with pressure?
Upon learning that $C_P=C_V$ for incompressible substances, the takeaway for why this is true is due to volume being constant, which comes from the thermal compressibility, $\beta_T=0$ for an ...
- 3
0
votes
1
answer
52
views
Some clarifications on the derivation of adiabatic process equation conducted on uninsulated container very fast
Assume a situation where an adiabatic process is carried out in an uninsulated container. So, for the process to be adiabatic, it should be carried out very fast.
Also, in the derivation of the ...
3
votes
4
answers
2k
views
Do black holes convert 100% of their mass into energy via Hawking radiation?
And if so, does that mean that we do not need matter/antimatter annihilations for 100% mass to energy?
- 461
0
votes
0
answers
24
views
How can I calculate the heat transfers caused in Venus's atmosphere by a stellaser?
In Isaac Arthur's video Winter on Venus, he discusses using a stellaser to heat Venus’s atmosphere and remove its gases, but he doesn't go into much detail about the heat transfer involved in it.
The ...
- 101
0
votes
0
answers
41
views
Linear response theory for dry friction at steady state
In this paper, Brownian motion with dry friction has been studied rigorously. The formulae for the propagator and the steady state are given. Since it is not reversible, the steady state should be a ...
- 111