Questions tagged [thermodynamics]
Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Consider also using tag: [statistical-mechanics].
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Help with thermodynamic relation $n= \dfrac{N}{V} = \left( \dfrac{\partial N}{\partial V} \right)_{T, \mu}$
In my statistical mechanics book I ran into this relation , not sure how I can prove this.
For context, it is a chapter on the grand canonical partition function, so I tried the grand potential ...
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Is it possible to raise an object's temperature by reflecting or absorbing and re-radiating its own radiation back on it?
I am a layman with a little beginners knowledge.
This question is an effort to prove or disprove the Greenhouse Effect (GHE) theory as this is the basis of "back radiation" as described by ...
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Physics in the kitchen: does heat transfer faster from air into oil or from air to food when in an oven?
It is usually said that foods cook faster in an oven when coated in oil. While I can understand that the underside of the food will cook faster where the oil forms an thermal interface between the ...
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Phase Changes: Energy Loss During Expansion
Does an object lose a little bit of energy during a phase change, such as when an ice cube melts and expands? When the object expands, it does work on the surrounding air particles, but does this ...
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Need help solving a problem about the heat transferred by a transformation cycle [closed]
While making a practise exam, i found the following problem and dont know how to solve it.
I don't know how to calculate the heat transferred $Q_{ADB}$ without there being a temperature given
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Can the four Seasons of planet Earth be defined in terms of Energy? [closed]
Can the four Seasons of planet Earth be defined in terms of Energy?
The definition of Energy gotten from Google is:
ability to do work, which is the ability to exert a force causing displacement of ...
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Why putting a piece of ice in carbonated drink, generates foam? [duplicate]
I'm a mathematician, not a physicist.
Perhaps the cold made the liquid reduce its solubility of gas?
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Are meteors heated primarily through radiation or convection (or both)?
From what I read meteors compress the air in front of them, increasing the air's temperature massively; this in turn is what heats the meteor. My question, which I can't seem to find a clear answer to ...
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How to optimize the air pressure produced by a black pipe in the sun? [closed]
So, I'm thinking of ways of overdoing the passive aeration of my compost bin. Basic setup is a (60L) bin with a pipe with holes through the middle; air is supposed to flow into the pipe and its holes ...
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Why is the heat flux in atmospheric models downgradient the potential temperature (=entropy) and not downgradient the temperature? [closed]
Atmospheric scientists express the vertical heat flux $H$ in their models often as $H=- c_p \varrho \Pi K_h \partial_z \theta$, where $\theta$ is the potential temperature, which is related to the ...
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Thought regarding Newton's law of cooling [closed]
I learnt that when a body cools by a small temperature say 5-10 k, from T1 to T2 we can approximately write rate of decrease in temp as c ((T1+T2)/2 - To) c is a constant
To representing surrounding ...
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Relation between the coefficients of Virial expansion and fugacity expansion?
One can write pressure of an interacting dilute gas as an expansion in its fugacity $\xi = e^{\beta \mu}$ as,
$$\frac{P}{n_0T} = \sum_{l =1}^\infty b_{l} \xi^{l}$$
From this we can calculate the ...
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Find the value of $Q/RT_0$ is [closed]
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle. On each side of the partition, there is one mole of an ideal gas, with specific heat at ...
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How much electricity be generated from air humidity?
There have been some recent papers on harvesting electrical energy from air humidity using nanoengineered materials:
"Power generation from ambient humidity using protein nanowires" in ...
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Internal pressure in rigid gasoline tank from increase in temperature [closed]
I was hoping to find a chart (or detailed table) that depicts the increase in internal pressure for a rigid tank full of gasoline from increases in temperature.
If this is not available then I wanted ...
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Work done by piston cylinder [duplicate]
If expansion in the piston cylinder take place, we get the work.
What if this expansion takes place in vacuum; will there be work done by gas?
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Why isn't the Boltzmann factor the inverse of what it is defined as?
Let me explain a bit more what I mean. To derive the Boltzmann factor, one usually talks about the ratio of the probability that a system is at some specified energies $E_1$ and $E_2$. This is taken ...
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What is pressure energy in a closed system?
Let's consider a gas inside a closed cylinder with a piston. This can be considered a closed system. The First Law of Thermodynamics (FLD) for a closed stationary system can be given as
Q = U + W
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Where can I find interpolation formulas or tabulated data for phase diagram(s)?
In order to program it, where can I find accurate representations of the water (or others - e.g.: CO2) phase diagrams, in the form of mathematical functions or in the form of interpolable tabulated ...
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How to calculate the reference Gibbs energy?
I want to calculate the Zr-O diagram based on the data from this article. The article contains 4 tables with data for:
pure elements,
stoichiometric phases,
phases of solutions,
gases.
How should I ...
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Temperature is discrete but not countable? [closed]
So I was reading a a question and top comment on math stack exchange that didn't make sense to me.
you can measure the temperature of something, but you can't count it. Incidentally, I claim ...
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Humidity Ratio Approaching Infinity [closed]
Based on a resource I found here:
I am trying to understand why/how the humidity ratio approaches infinity. Given that the saturation vapor pressure is massively exponential in temperature and that ...
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Isobaric process in Thermodynamics [closed]
I have some confusion in isobaric processes, like in these kind of process, is the internal pressure constant or external pressure, please tell whether internal pressure can vary or not in isobaric ...
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Solving heat equation with fixed temperature at $x=0$ [closed]
Suppose, there is an insulated 1d rod of length $L$ with initial temperature of $T_{0}$. Suddenly, the beginning of the rod is heated such that its temperature is fixed at $T_{f}$, while the other end ...
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Relation of first adiabatic exponent to adiabatic index
I'm going through a fluid dynamics text and I'm a little confused by a listed relation. The first adiabatic index is defined as
$$ \Gamma_1 = \left(\frac{\partial \ln P}{\partial \ln \rho}\right)_s, $$...
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Idea of temperature function from the 0th law of thermodynamics [closed]
my question is that is it actually possible to derive the idea of temperature function just from the 0th law?, if not what are the other assumptions that allow us to do that?
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Is $S = k\ln(W)$ also in grand canonical ensemble?
In grand canonical ensemble, we consider two systems A' and A in thermal contact that allow the exchange of particles and energy. When we consider all possible microstates configurations with distinct ...
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A violation of the Maximum Work Theorem?
Consider the PV diagram I've drawn at the end of this post. Consider the processes drawn thereon: (1-2-3) is an isobaric step followed by an isochoric step, while (1-3) is an adiabatic expansion (I ...
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What is the grand partition function of a single fermion in contact with a thermal and particle reservoir?
If we have a fermion system consisting of a single-particle state in contact with a thermal and particle reservoir with allowed microstates with energy $E_i$ and occupancies $N_i$ what is the grand ...
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Can internal energy and entropy move in opposite directions?
Is it possible for there to exist system for which there is some quasistatic process which causes this system to have $\Delta U < 0$ while $\Delta S > 0$? No constraints on the type of system as ...
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Derive partition sum for ideal gas (sum to integral)
Having the grand canonical partition sum:
$$\mathrm{Z} = \sum_{\{n\}}\exp{\left(-\beta \{\varepsilon_n(N_n) -\mu\,N_n\}\right)}$$
how to arrive at: $$\mathrm{Z} = \sum_{N = 0}^{\infty} \dfrac{V^N}{h^{...
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Statistical proof of the principle of least action
In statistical thermodynamics we can prove that the evolution of a system minimises some potential with units of energy (e.g. energy). This can be done purely statistically, by using the first two ...
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On the non-quasistatic transfer of heat
Suppose we have two bodies at different temperatures, and we let them interact thermally in such a way that the process is not quasistatic (e.g. two different metal spheres touching). Do we arrive at ...
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In non-metals, does low specific heat capacity correlates with good thermal conductivity and vice versa?
As i understand, when heat transfers by conduction, there are two main mechanisms that can take place: either by the vibrations of the lattice (mostly non-metals) or with the movement of free ...
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Why should this thermodynamics problem be indeterminate?
Callen asks us to consider the following
A cylinder of length $L$ and cross-sectional area $A$ is divided into two equal-volume chambers by a piston, held at the midpoint of the cylinder by a ...
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Why is any real process which proceeds through non-equilibrium states necessarily irreversible?
As per the title, why is any real process which proceeds through nonequilibrium states necessarily irreversible?
The question came up when reading Callen's definition of "reversible process" ...
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Callen Postulate II
In his classic text, Callen gives the key postulate (Postulate II) as
There exists a function (called the entropy $S$) of the extensive parameters of any composite system, defined for all equilibrium ...
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Doubt on thermodynamics equilibrium
Is thermodynamics equilibrium related to mechanical equilibrium in anyway?
For eg if the net Torque on a system is not zero does that still mean the system can be in thermodynamic equilibrium?
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Quantum vs Classical solution to the Gibbs Paradox [duplicate]
The thermodynamic probability of a gas
with distinguishable particles having spin-$0$ is given by the expression:-
$Ω_{MB} = N!~Π_i\frac{g_i^{n_i}}{n_i!}$
If the particles were indistinguishable, the ...
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How does one "invert" derivatives for intensive variables?
Consider a magnetic system which is characterized by the extensive variables $U,V,N,I$, with $I$ the total magnetic moment of the (homogeneous) system. By the postulates, one can easily swap $S$ for $...
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Designing mercury in glass thermometer
Should the stem of a mercury-in-glass thermometer be marked off in equal
divisions for equal temperature intervals if the coefficient of thermal expansion of glass is assumed to be strictly constant?
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An alternative approach to proving the Carnot's theorem using the equality of areas of $pV$ and $TS$ diagrams
According to Carnot's theorem, the efficiency of a reversible heat engine operating between two reservoirs at different temperatures is independent of the working substance and depends only on the ...
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On using intensive variables to describe the macrostate
I am currently reading through Callen and, though Callen is very thorough, I find myself puzzled at the following question.
In Callen's treatment, the thermodynamic formalism is introduced ...
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How to understand this derivation of Raoult's Law?
A derivation of Raoult's Law in a textbook is as follows:
I cannot follow the chain of arguments: Why should $p_{A0}=p_{B0}$ ?
A and B are basically two different substances, each of which has a ...
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Can a single element material be a black body? [duplicate]
I want to ask this becuase I am curious that if a black body emits differnt em waves only based on its temperature, then I wonder if a single element material (hydrogen, e.G.) or a pure substance like ...
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Proof that thermometer will measure higher temperature than that of an enclosure if radiated heat is same in all directions
I am reading the English translation of J. Fourier book "The Analytical Theory of Heat".
In para 47, the author states "If the rays which escape from a heated surface had the same ...
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Osmotic pressure "equilibrium"?
Consider a box with two compartments separated by a semipermeable membrane. The first compartment is initially at pressure $P_0$ and contains the solvent ; the second compartment is initially at ...
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Jacobian determinants in thermodynamics and a different approach to deriving the Maxwell relations
In a PV diagram, the area enclosed by the Carnot cycle represents the work done by the system. Let's denote this area as $A_{\text{PV}}$. In a TS diagram, the area enclosed by the Carnot cycle ...
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Bosonic Gas vs Ideal Gas
Bosonic Gases and Ideal Gases have these properties in common:
They are composed of
indistinguishable particles.
The particles of both gases do not
obey the Pauli Exclusion
Principle.
As far as I ...
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Can heat flow from colder to hotter body breaking the second law of thermodynamics? [closed]
In an isothermal process, the whole heat is converted to work but not in a cycle so it doesn't break the 2nd law of thermodynamics.
$$dQ=dW$$
But let's imagine a scenario with it. If we connect an ...
