New answers tagged thermodynamics
0
votes
how come the pressure gradient is equal to the divergence of pressure in incompressible fluids?
Your use of the same notation $\vec F$ is confusing. But yes, you are correct, the divergence is essentially replaced by a gradient. This is because you are integrating vector fields:
$$
\oint p d^2x =...
- 9,452
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Calculating temperature when it is lower than your thermometers can read?
The freezing point of water ethylene glycol mixtures depends in the concentration of ethylene glycol. You can find data for this on the Engineering Toolbox web site (a valuable source of all sorts of ...
- 351k
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Calculating temperature when it is lower than your thermometers can read?
Mass of polystyrene cup + lid (with hole for thermometer) = $m_{\rm c}\,\rm g$ (assume thermal capacity is negligible)
Mass of polystyrene cup + lid + water = $m_{\rm c+w}\,\rm g$
Mass of water = $m_{\...
- 93.3k
1
vote
Accepted
Planck's assumption on blackbody radiation
$g(\nu)$ would be the number density of oscillators per unit frequency at a frequency $\nu$.
$u(\nu)\ d\nu$ would be the energy density in a frequency band $d\nu$ at a frequency $\nu$.
The $d\nu$ is ...
- 128k
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How can power be defined as the derivative of work with respect to time if work is not a function?
My two cents. I think that's because sometimes it's possible to convert inexact differential to the exact one using integrating factors. For example, if the process is quasi-static adiabatic , then ...
- 11.3k
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How can power be defined as the derivative of work with respect to time if work is not a function?
If so, why do I usually find power defined as the derivative of work
with respect to time if work is not a function
Just because work is shown as an inexact differential in the differential form of ...
- 68.8k
1
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Second Law of Thermodynamics and heat flow
The cold water "gain" heat and the air in the dining room "loose"
heat. But, why the temperature in the dining room remain the same?
Should it be colder?
It is cooler. But the ...
- 68.8k
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A Jet of Steam passed into a Block of Ice
Just before all the ice had melted, the temperature of the mixture of water and ice was 0 C. So, when the final bit of ice melts, the temperature will be 0 C.
- 32.8k
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Second Law of Thermodynamics and heat flow
The answer is yes to both, if heat is transferred from a large object to the small one, it changes the temperature of both large and small objects.
In the case of the room we consider that the room is ...
- 4,457
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Zeroth Law of Thermodynamics on Thermometer
You place a thermometer in thermal contact with system $A$ and get a "reading" $R$ on the thermometer.
As an example $R$ could be a mark at the position of the top of the mercury column in a ...
- 93.3k
0
votes
Sum of two state functions is not path independent
I would venture to offer a simple formal explanation of why the arguments leading to the paradoxical inequality of mixed partial derivatives of the state function are incorrect. There were adequate ...
- 4,610
0
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Do black holes recapture the CMB?
An isolated black hole has capture cross-section $A=\pi (27/4) R_S^2=\pi 27 G^2M^2/c^4$ and hence absorbs $P_{in}=\sigma A T_{CMB}^4$ Watt from the CMB. Meanwhile it emits Hawking radiation with power ...
- 30.8k
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Do black holes recapture the CMB?
No, because black holes themselves eventually evaporate into heat. It's known as Hawking radiation.
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In this Stirling Engine process, how do we know that the fluid is heating up?
...the diagram seems to show that the displacer...in the middle of the fluid, causing the volume of the fluid in contact with the cold and hot source to be the same - so I'm still quite confused ...
- 13.7k
2
votes
Accepted
Counting microstates - simple example with boxes
I think you are already happy with
$$\tag1W=\frac{(n+g-1)!}{n!(g-1)!}$$
so that I can focus upon explaining the horrible sudden logical flow swap that happens next.
Yes, you correctly found that there ...
- 7,295
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What is the number of quantum states compatible with isolated ideal gas macrostate $N,V,U$ and molecular mass $m$?
Preliminaries: Your question touches the connection of statistical mechanics with combinatorics and number theory, see e.g. Ref. 1. I think it is not possible to give a definite answer to your ...
- 7,165
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Can Isobaric compression increase the internal energy of an ideal gas?
As you mention in question that some heat is given out,you must consider the walls of container of gas are ideal diathermics,which means Heat can Exchange freely between Surrounding and container-gas ...
- 334
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Can Isobaric compression increase the internal energy of an ideal gas?
For a reversible isobaric compression of an ideal gas the following holds true
$\frac{V}{T}$=constant
It follows that a reduction in volume results in a reduction in temperature. Since the internal ...
- 68.8k
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Can Isobaric compression increase the internal energy of an ideal gas?
I think it's just a consequence of 1 st law of Thermodynamics,
dU = dQ + dW
(Heat added is +ve and Work done by system is -ve)
Cases when dU is +ve
dQ and dW both are +ve (1)
dQ is +ve dW is -ve, |...
- 11
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Does electron have a temperature in the atom?
I have little to say about QCD, but I will try to analyse this question from thermodynamics perspective. And I think I have a decent answer.
Save Time: In essence, protons and neutrons exhibit ...
- 11
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Steam from a cup of coffee
I think it's rather simple question.
For a steam you may use PV= RT as equation of state.
atmosphere is constant pressure system.
for constant P , V is directly proportional to T. And density (d) is ...
- 11
0
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Can any irreversible work source be simulated by a reversible work source?
It briefly explains the reason; what the work source does is simply to
apply force to the piston, and therefore it does not matter how the
force is applied, whether or not it is applied by an ...
- 68.8k
2
votes
Accepted
Clausius inequality and negative value of entropy
I was wondering...if entropy is a "state function" then why does going
through an irreversible cycle give a negative value for entropy
(Clausius inequality),
The Clausius inequality is not ...
- 68.8k
1
vote
Steam from a cup of coffee
The amount of water that air can take up before the water creates fog or visible steam depends on temperature. The colder the air, the less water it needs to create fog/steam. It is the same principle ...
- 377
-1
votes
Adiabatic expansion from a large vessel to a smaller one to fin volume ratios of vessels
This is a trick question.
Let $T_{1f}$ represent the final temperature in vessel 1, $T_{2f}$ represent the final temperature in vessel 2, $P_f$ represent the final pressure in both vessels, $T_0$ ...
- 32.8k
1
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Does electron have a temperature in the atom?
From the way the question was formulated, I deduce that some clarification on some basic concepts is needed.
If we speak of electrons in an atom, we can safely ignore physics at much larger energy ...
1
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Does electron have a temperature in the atom?
There is technically a way to incorporate the concept you are trying to talk about; I gave you an upvote to undo the downvotes you are getting on this question.
There is a reason why there is a ...
- 7,295
0
votes
Does electron have a temperature in the atom?
You cannot speak of a temperature of a single particle, Temperature is an ensemble property. The electron is - as far as we can tell - a fundamental particle unlike the proton (which is a composite ...
- 1,378
1
vote
Accepted
Constant shift in the Gibbs free energy
When you add a constant, the formula:
$$
\mu = \frac{G}{N}
$$
is not valid anymore. Indeed, it uses the fact that $G$ is extensive:
$$
G(\lambda N,T,P) = \lambda G(N,T,P)
$$
When you add your constant,...
- 9,452
2
votes
Accepted
Find the ideal gas law from the internal energy
I am not totally sure if this is the most straightforward way, but you will receive the ideal gas law by varying $U$, that is
$$\operatorname{d}U = \dfrac{\partial U}{\partial V} \operatorname{d}V + \...
- 56
3
votes
Hamiltonian as a quadratic function
$$ H= \sum_j A_j P_j^2 + \sum_j B_j Q_j^2 $$
For such a system, "we clearly have"
$$ \sum_j \left( P_j \frac{\partial H}{\partial P_j}+ Q_j \frac{\partial H}{\partial Q_j}\right) = 2H. $$
...
- 17.4k
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votes
Availability of system with constant pressure and temperature
But, dG = dU - d(ST) + d(pV)= Vdp - SdT
If p and T is constant, dG is always zero... What's wrong in my reasoning?
$$
dG = dU - d(ST) + d(pV) = VdP - SdT + \mu dN\;,
$$
where $\mu$ is the chemical ...
- 17.4k
0
votes
Why does increasing the volume in which a gas can move increase its entropy?
The formula $dS=\frac{dQ}{T}$ can only be used when the process is reversible. In fact many text books adopt the notation $dQ_{\text{rev}}$.
The process described in this question is not quasi-static ...
- 1
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What is an good book to study classical non-equilibrum thermodynamics?
So, if by classical you mean phenomenological, that is anything non-statistical, then I would suggest the general review book Lavenda: Thermodynamics of irreversible processes, see here, in which each ...
0
votes
Accepted
How do I calculate the Relative Humidity from number density and pressure?
Dividing the number density by avagadro's number gives you the number of moles per unit volume of water $\rho_w$. The partial pressure of water vapor is then $$P_{water}=RT\rho_{w}$$If, at ...
- 32.8k
-1
votes
How do I calculate the Relative Humidity from number density and pressure?
It appears to (non-expert) me that in the world our air is a very complex thing. It contains not only gases and water but a lot of biological materials such as bacteria, spores, dust... There are ...
2
votes
Accepted
Fluctuations of the center of mass of a confined fluid?
At equilibrium, if you believe Gibbs statistical mechanics, you expect the velocities to be uncorrelated since the kinetic part of the hamiltonian is just the sum of the kinetic energies of your ...
- 834
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What is the difference between enthalpy and internal energy?
As noted correctly above, enthalpy is just the sum of the internal energy and $PV$,
\begin{gather*}
H = E+PV
\end{gather*}
More formally, it is a Legendre transform of the internal energy that gives a ...
- 1,990
2
votes
Can any irreversible work source be simulated by a reversible work source?
It briefly explains the reason; what the work source does is simply to
apply force to the piston, and therefore it does not matter how the
force is applied, whether or not it is applied by an ...
- 68.8k
0
votes
Accepted
Evaluating Maxwell Relations with Constant Entropy for Arbitrary EOS
$$dS=\frac{C_V}{T}dT+\left(\frac{\partial S}{\partial V}\right)_TdV=\frac{C_V}{T}dT+\left(\frac{\partial P}{\partial T}\right)_VdV$$
Also,
$$dS=\frac{C_P}{T}dT+\left(\frac{\partial S}{\partial P}\...
- 32.8k
0
votes
Evaluating Maxwell Relations with Constant Entropy for Arbitrary EOS
The state of a thermodynamic system is uniquely defined by (usually) 2 variables which can be any of the properties of the system, i.e. $p,V,T,S$, etc. Consequently the properties of the system, which ...
- 705
2
votes
Accepted
How does the excess GPE of a mountain cause its base to melt?
However, does there exist a physical explanation of how this occurs, not just one based on the conservation of energy
From Weisskopf's response to comments:
I have used the melting heat...as a ...
- 23.7k
8
votes
Accepted
How to derive the Clausius Inequality?
The inequality for irreversible cycles follows from Carnot's theorem which states that no cyclic process can be more efficient than a Carnot cycle.
The basic idea for deriving the equality for ...
- 705
3
votes
How to derive the Clausius Inequality?
How do we get here, to the Clausius inequality for any cycle?
The Clausius inequality applies to any heat engine cycle, where $T$ is the temperature at the point of heat entry but which, unlike the ...
- 68.8k
3
votes
Accepted
Why is $\sum\limits_j {{v_j}{\mu _j}} = 0$ sometimes can't be achieved?
Brian Bi gave a good physical example of a situation where the equality $\sum_j v_j\mu_j = 0$ does not hold. I want to discuss the issue from a more formal point of view. The equality $\sum_j v_j\mu_j ...
- 4,610
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Why is $\sum\limits_j {{v_j}{\mu _j}} = 0$ sometimes can't be achieved?
The best known example is when a solid dissolves in water (though it can be any liquid, really): we model this as the reaction X(s) -> X(aq). If there is a sufficiently large amount of water ...
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How to derive the Clausius Inequality?
Personally, I find the Clausius inequality easiest to think of without considering cycles at all. Thermodynamic processes obey a succinct relationship between the reversible and irreversible work done ...
- 1,990
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How do I find the entropy change of the universe for a not-completely-irreversible isothermic expansion?
Does anyone know if what my professor is saying in these slides makes
any sense?
The following is an example to explain the slides. See the PV diagrams below.
The red and blue curves are two ...
- 68.8k
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How would a Stirling Engine's throttle work?
I would use a Stirling Engine in a vehicle just as an electric generator much as modern hybrid cars use a gasoline engine to generate electrical energy which powers an electric motor. Hybrid cars ...
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