All Questions
Tagged with degrees-of-freedom thermodynamics
92 questions
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Vibrational degree of freedom for monoatomic gases
I read that, when the temperature of a gas becomes high enough, a third type of degree of freedom becomes accessible, viz. the vibrational degree of freedom.
Also (at high temperatures) there is a ...
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Holographic principle with infinitely many degrees of freedom?
The holographic principle entails a limit to the number of degrees of freedom or possible states in a system (which would be givem by its surface rather than its volume, thus they would be "...
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Cells in phase space in Maxwell-Boltzmann statistical analysis of thermodynamics
Can't the states overlap? For example, for one particle the value of spread of its $p_x$ is 1 unit from $p_x=0.5$ to $p_x=1.5$ whereas, for the other particle, is 1 unit from $p_x=1$ to $p_x=2$. Isn't ...
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Why potential energy is not considered in the internal energy of diatomic molecules?
In thermodynamics, I am taught that there are 5 degrees of freedom in diatomic molecules since there are 3 for translational and 2 for rotational. I interpret degrees of freedom as "ways you can ...
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Equal average energies in translational and rotational degrees of freedom
In, An Introduction to Thermal Physics, Schroeder states
It’s not obvious why a rotational degree of freedom should have exactly the same
average energy as a translational degree of freedom. However, ...
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How many degrees of freedom does a diatomic and triatomic molecule have at high temperatures?
I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is ...
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Is the equation for degrees of freedom $f=3N-k$ valid for all cases?
Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of ...
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Regarding Degrees of Freedom and dynamics of polyatomic molecules [closed]
Justify how a molecule with N atoms have $3N-5$ vibrational degrees of freedom(Linear) and $3N-6$ vibrational degrees of freedom (Non-linear). Will this be valid for large number of N?
Taking $H_2O$ ...
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Difference between Kopp-Neumann and Dulong-Petit law?
So this is basically a follow-up to this question: How many degrees of freedom does the water molecule have?
I've done some further research and found that the main difference between Dulong-Petit and ...
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Why expansion of real gases lead to cooling?
Paul Hewitt writes in his book
Expansion of real gases lead to cooling as average translational kinetic energy per molecule decreases.
The reason given is:
During Expansion molecules collide with ...
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The equipartion theorem and degree of freedom in case of vibration
I have been taught in chemistry that,
the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational)
The degree of freedom which I found in chemistry, for the vibrational ...
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Number of degrees of freedom for a gaseous mixture
I came across the formula to find the number of degrees of freedom in a gaseous mixture which is as follows:
$$f_\mathrm{mix}
=\frac{\sum n_if_i}{\sum n_i}$$
Now it has been mentioned in this lecture ...
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Why is the heat capacity of water $9R$ and not $6R$?
From the equipartition theorem, the relationship between energy and temperature in a substance is $U=\frac{NRT}{2}$ for $N$ quadratic degrees of freedom associated with a particle of that substance. ...
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Why don't we use the "degree of freedom" as a factor in the ideal gas equation?
For an adiabatic process, the ideal gas follows the equation
$$ PV^{\gamma}= constant$$
The equation above implies that the pressure of an ideal gas (under adiabatic process) depends on the "...
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Is there a way to calculate the number of degrees of freedom of water?
Say we have liquid water. We are given specific heat of water $C=4.2kJ(kg*K)$, a number of molecules in a mol $N_A=6*10^{23}$. The atomic weight of water is $18g/mol$, and the Boltzmann's constant is $...
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Independent variables in thermodynamics
When we are dealing with a gaseous thermodynamic system, in books it's written that state of the system can be described by only two independent variables from the three $(p,V,T ) $. But it's not ...
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Is $n=1$ (degrees of freedom) for monatomic?
In $PV=nRT$, $n$ is degrees of freedom. While in $PV=Nk_BT$, N is number of moles in a molecule. So value of $n$ is $3$, $5$ and $6$ for monatomic, diatomic and polyatomic respectively. But in the ...
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Why is there a $1/2$ in the definition of energy per degree of freedom $E=(1/2)kT$?
I was looking for an authoritative definition of Boltzmann's Constant. That led me to this discussion on NIST's site: Kelvin: Thermodynamic Temperature
Thus, internal energy and temperature are ...
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Entropy - can we express number of microstates as a function parameterized by degrees of freedom?
In some of the answers and comments from this question people contended (not in so many words) that because entropy is parameterized by number of microstates $\Omega$, and the definition of $\Omega$ ...
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What does it mean for a degree of freedom to come to thermal equilibrium?
I'm learning about diffusion speeds of particles in aqueous solution and the fundamental concept is thermal energy.
The notes I'm working from say that "every degree of freedom comes to thermal ...
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Degrees of Freedom contributing to dynamic?
I had a question regarding considering how many degrees of freedom (dof), contributing to dynamics, a $\rm CCl_4$ Molecule has.
In General there are 5 Atoms in the Molecule, so the maximum would be 15,...
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Why do we not consider rotation as a Degree of Freedom in Monoatomic Gases?
I completely understand that the average energy of each degree of freedom in a thermodynamic system is (1/2)kT and that we do not consider the spin about an axis of symmetry in a polyatomic molecule ...
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Why are constant volume and constant pressure heat capacities basically the same for solids? Are degrees of freedom involved?
I knowv that $C_V=\frac{\frac{f}{2} Nk_B}{m}$ and $C_P=\frac{(\frac{f}{2} +1)Nk_B}{m}$. Since for solids their values are very close to each other, I would assume $\frac{f}{2} +1$ is very close to $\...
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What is the proof of law of equipartition of energy?
In thermodynamics, law of equipartition of energy states that if we have any gas sample then the total kinetic energy will be distributed among the different degrees of freedom of the gas sample. Each ...
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What is the proof of $C_{V} = \frac{fR}{2}$?
I came across this formula in thermodynamics. Please give me a rigorous proof to this formula. My teacher did not even give any proof neither do any of my books. The formula is :
$C_{V}=\frac{fR}{2}$ ...
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Degrees of Freedom of water and $\rm CO_2$ at high temperatures
How do I calculate the degrees of freedom for $\rm CO_2$ and water at high temperatures? I'm confused because I know $\rm CO_2$ is linear while $\rm H_2O$ is nonlinear, and am wondering how this would ...
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How many degrees of freedom would water have at $\rm 500K$?
At this temperature, and lower, the rotational degrees of freedom would already be in action, then at this higher temperature id think vibration degrees of freedom are no longer frozen out. So this ...
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All possible choices for two independent thermodynamic variables for a one-component, one-phase system
I am confused about the independent variables in thermodynamics. I know that for a one-component, one-phase system, there are only two independent intensive variables that can be chosen and which ...
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What is the theoretical justification for the Law of Equipartition of Energy?
What is the theoretical justification for the Law of Equipartition of Energy?
Why are equal energies distributed in each degree of freedom even though sometimes they are completely different (like ...
user280583
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Understanding vibrational mode of a molecule and its contribution to average energy
I'm facing difficulty understanding how vibrational energy modes contribute to a molecule's average energy (or heat capacity). What I know is : For a polyatomic non-linear molecule, there are $3N-6$ ...
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What is the internal energy of water vapor? OR How many degrees of freedom does $\rm H_2O$ have?
Here are the "knowns" that I'm working with.
Internal Energy for a monatomic gas is
$$U = (3/2)nRT$$
For a diatomic gas its
$$U = (5/2)nRT$$
All of my textbooks and online sources indicate ...
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Does the ideal gas law apply to gases which consist of more than one atom?
In the derivation of the ideal gas law, one sets for the average kinetical energy $f = 3$ degrees of freedom. This refers to the transition in x,y,z axes. This is true for gases, which consist of only ...
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Does emergence or the second law create more degrees of freedom total? [closed]
Here's my layman thought process:
By emergence and the second law, new "modes" or points in configuration space become "unlocked" with macroscopic systems. One is a brain, which ...
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Factor $f$ of internal energy of a gas
For a $n$-atomic gas in any sort of geometry,
The formula for $f$ is
$$f = 3n- \text{number of constraints}.$$
The way I was taught this formula was like each $n$ particles< there is $3$ ways it ...
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The degree of freedom in kinetic gas theory
What is the degree of freedom in kinetic gas theory? How can I determine how much degree of freedom some molecule has?
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How many degrees of freedom does the air have?
Very simple question that I am overthinking... But how many degrees of freedom does the air have? Assuming let's say the air is confined in a rigid box.
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About Degrees of Freedom and Energy
We know that the degree of freedom of oxygen is 5.
For this the total kinetic energy of oxygen must be (5/2)nRT.
But maximum books say that it should be (3/2) nRT where as our college teacher said it ...
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According to equipartition theorem, how a harmonic oscillator has two degree of freedom?
I was reading a book on kinetic theory. In the part of equipartition theorem, I found a line as follows,
" The average energy corresponding to one vibration is equal to twice the K.E. corresponding to ...
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Validity of equipartition theorem and choice of coordinate axis
While reading through the basic derivation of how kinetic energy is related to temperature, I stumbled upon equipartition theorem where $\frac{1}{2}mv^2 = \frac{1}{2}kT$ thus $\frac{3}{2}kT$ in 3-...
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Degree of freedom of diatomic molecule [duplicate]
Is there any justification for degree of freedom of diatomic molecules to be two? I believe that degree of freedom are the number of coordinates needed to specify the position of a molecule so how ...
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graph relativistic degrees of freedom
I'm trying to graph the relativistic degrees of freedom, which should look like the figure
And I am trying to guide me with this Phys.SE answer: Number $g(T)$ of relativistic degrees of freedom as a ...
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Degrees of freedom of a molecule
We all know that if we consider a mono-atomic molecule, it has $3$ translational degrees of freedom only, along the $3$ principal coordinates of the Cartesian coordinate system.
In case of a ...
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Law of equipartition of energy, shouldn't kinetic energy per molecule by $(3/2)kT/f$
I study that according to the law of equipartition of energy the average kinetic energy associated with each degree of freedom is equal to $(1/2)kT$. But shouldn't it be $\frac{(3/2)kT}{f}$
where $f$ ...
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Equipartition theorem - concerning the square dependence of energy
So the equipartition theorem states that if the energy dependence is square
($\langle\,E\,\rangle= as^2$ + ...(something not dependent on $s$))
then each variable (degree of freedom) contributes ...
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Why we fill dU/dT value in Cv(specific heat at constant volume) only and why not in Cp?
According to equipartition of energy, the energy ossociated with each degree of freedom is $\frac{K_{b}T}{2}$ for one molecule .
For 'x' molecule which has degree of freedom f it's energy is given by ...
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How is the relationship of the value $kT$ and a degree of freedom derived?
Sources that discuss the derivation of the Maxwell-Boltzmann Statistics end up with two unknown constants ($\alpha$ and $\beta$) through the Lagrange Multipliers, of which $\alpha$ is derived by ...
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Query about working out the Specific heat ratio of a gas
The specific heat ratio for $\rm CO_2$ at room temperature is $1.28$ according to my tables.
Since $C_V= \left.\frac{\partial U}{\partial T}\right|_V$ and $C_P=\left.\frac{\partial U}{\partial T}\...
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Why doesn't a monoatomic particle have 6 degrees of freedom? [duplicate]
A monoatomic particle can move in three directions: $x$, $y$, and $z$. So the number of degrees of freedom (DOF) for translation is 3. The particle can also rotate around three axes. So the number of ...
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A problem on degree of freeedom?
[The problem is roughly]
Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges
of the ...
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What is degree of freedom in thermodynamics? [duplicate]
I have read a lit bit of degree of freedom in classical mechanics and hope to understand as if the number of variable used to describe a system in the configuration space. But in thermodynamics I read ...
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