Questions tagged [ideal-gas]
A gas that behaves as randomly moving, non-interacting molecules. This allows a simplified equation of state.
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Entropy of mixing canonical ensemble
I am solving a problem that analyzes a classical ideal monoatomic gas. After determining the partition function, free energy and entropy, it asks me to analyze the variation of entropy if I had a wall ...
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Deformation of a sphere
I am currently building a computational model for a simulation of a rover landing on the surface of mars. As part of the assignment I need to model airbags being used to cushion the fall. (Assuming ...
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Where is the mistake in this derivation of $U(T)$ for an Ideal Gas?
I have tried to develop this alternative derivation of the relationship between internal energy $U$ and temperature $T$ of an ideal monoatomic gas. From kinetic theory, it is well known that $PV=2/3U$ ...
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Indistinguishability in statistical mechanics
I have two questions about using the concept of indistinguishability to determine the partition function in statistical mechanics, like for instance when determining the partition function of an ideal ...
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1answer
160 views
Doubt regarding proof of $pV = nRT$ [closed]
In my textbook, the proof for this formula is as follows:
$$F \propto \text{Area}_{\text{wall}} \cdot \text{(number of density of particles I.e here m is const) I.e} \frac{n}{V} *\text{Average ...
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A question about collisions and probability, from an élite university admission test [closed]
Good afternoon, I have come across this question, from a recent admission exam to my country's top physics university, which I have found particularly interesting as the text seems to be deliberately ...
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Ideal gas partition function
I am studying how to calculate the density of states and the partition function of $N$ non-interacting particles. My question is why the integral of the momentum, in the density of states calculation, ...
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2answers
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Why is volume of gas independent of its molecule size?
According to the ideal gas law:
$pv = nRt $
My question is, why is the volume $v$ independent of the volume of individual components of the gas, i.e. molecules? As the sizes of individual molecules ...
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3answers
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How can you increase the temperature of a fixed amount of gas by increasing the volume of the container?
You have a fixed amount of gas. How can you increase its temperature T by increasing the container's volume V while keeping the pressure P constant? Technically, it can be done when considering,
pV=...
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How can kinetic theory be used to verify Dalton's law of partial pressures?
I have been told Dalton's law of partial pressures can be proved from kinetic theory. This is my reasoning for why this might be:
Since in kinetic theory there are no forces of attraction between the ...
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1answer
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Barometric formula with variable gravity
Recently, I have wondered about what would be the atmospheric pressure as a function of altitude in a planet that only consists of gas. The equation that does just that is the barometric formula (see ...
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Energy-temperature relationship for classical, Fermi and Bose gasses
I have been trying to visualise the energy-temperature relationship for classical, fermi and bose gasses. For small T, I have that the Fermi gas avg. energy will be $\frac{\epsilon_f}{2}$, being half ...
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How to solve this basic thermodynamics problem? [closed]
This is just no question about an specific problem, but it rose while doing it, and it englobes some quality of problem solving in which different expressions can be used:
After i got this problem &...
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What is the single particle translational partition function for a single gas atom in unknown volume?
In the standard expression for the ideal gas translational partition function, we have a V for the volume. How do we compute this partition function for a gas when the volume is unknown, like the ...
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1answer
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Confusion about number of molecules in a gas [closed]
I have solved the following exercise but the answer I get is different from the one stated in the book I am using: I can't see what I am doing wrong so I would be grateful if someone pointed it out to ...
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In a sealed chamber, can a vapor be heated enough, that the pressure increases enough, to condense to liquid?
Assuming a sealed chamber, containing a vapor, where volume is constant:
Given that the ideal-gas law states $PV = nRT$, if heat is added to an ideal-gas, the pressure will increase as a function of ...
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What is contribution of Rotational Kinetic energy in temperature of gas according to kinetic theory of gasses?
We know that, for one molecule of ideal gas,
$U = \text{Kinetic energy} = \frac{f}{2}RT$
where $f$ is the number of degrees of freedom, $R$ is the gas constant and $T$ is the absolute temperature.
So ...
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Why doesn't Charles law apply to a gas flask in a manometer when being heated?
So Charles law states that when volume is not constant and you heat up a gas, the pressure stays constant. Example, if I have a syringe and I heat up the gas in the syringe, the syringe in would ...
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Volume Ratio of Carnot Engine
Consider a Carnot engine operating between a hot reservoir with temperature 700 °C and a cold reservoir with temperature 70 °C. The engine contains 0.13 mol of gas, and outputs a net 630 J of work.
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Duration of adiabatic expansion
I have a problem in which an adiabatic expansion occurs in a vertical piston and ideal gas system.
There is a piston that is being held down, and then when it is released, the gas expands in such way ...
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2answers
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Do Relativistic Gasses of Identical Particles Obey the Ideal Gas Law?
I am trying to determine the equation of state and see if $PV = nRT$ is satisfied. For an ultra-relativistic gas of identical particles in a volume $V$ the energy (I am assume there is no potential) ...
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4answers
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Why isn't pressure from surroundings on the gas always equal to the pressure from gas on surroundings?
This way wouldn't the pressure applied by the air on the gas always be equal to the pressure applied by the gas on the air. If this is the case wouldn't the gas always be in equilibrium,even if the ...
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1answer
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How fast do very small particles diffuse through still air?
I have been trying without success to find the rate at which small particles, on the order of $3\cdot10^{-10}\mathrm{g}$, diffuse in air at room temperature $-$ say 20 to 25 degrees C.
The purpose of ...
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What is the value of the universal gas constant in atomic units? [closed]
On Wikipedia the value of the universal gas constant is given for various units but not for atomic units. It should be easy to figure it out but I keep getting it wrong.
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Why does this thermodynamics problem seem to have two answers? [closed]
The problem goes as:
For an ideal gas, molar heat capacity varies as: $C = C_v + aV$, where $a$ is a constant.
Now we are asked to find a relation between Temperature and Volume.
The way I approached ...
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2answers
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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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Expansion coefficient for an ideal gas at constant pressure is $α = 1/Τ$. Explain this relation
How the coefficient of expansion for an ideal gas is given by $α=1/Τ$, (at constant pressure). How could it be inversely proportional to it. Doesn't gas expand more on higher temperature, but this ...
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Relation between the Ideal gas constant and Boltzmann's constant
If $R=N_A\cdot k_B$ how can the following equation be true as well?
$$\frac{R}{M}=\frac{k_B}{m}$$
That would result in: $R=\frac{1}{n}\cdot k_B$, which is different from the first equation.
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Can the number of microscopic configurations of a gas be expressed in terms of its temperature?
I'm new to the field of thermodynamics, but have been thinking about it recently, and wondered whether this statement has any truth in it. I doubt it is true, however I need to see whereabouts the ...
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Entropy of Mixing Derivation
In Thermodynamics and an Introduction to Thermostatistics 2nd Edition, Callen states that the Entropy of a mixture of ideal gases is given by (3.39)
$$S = \sum_j N_js_{j0} + \left(\sum_j N_jc_j\right)...
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Thermodynamic limit for an ideal gas
In S. Salinas, Introduction to Statistical Physics (Springer, 2001), the author states (p. 68):"...the thermodynamical limit is essential to allow the connection between the average values of ...
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Derivation of the Adiabatic Relations
My professor offered this derivation of the adiabatic relation $TV^{\gamma-1}=\text{const.}$ :
Since $\delta Q=0$:
$$dU=\delta W,$$
using $C_V=\left(\frac{\partial U}{\partial T}\right)_V\implies dU=...
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Temperature decreases in adiabatic expansion and gas laws
So I understand that the temperature decreases when a gas expands adiabatically. This is because there is no gain of heat from the surroundings, so the kinetic energy of molecules decreases in doing ...
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Pressure inside a closed water bottle due to vapour pressure?
Suppose I have a standard, partially filled bottle of distilled pure water (filled up to around 75%) that's open to the environment at room temperature and pressure. Now suppose I close the lid of the ...
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Does hero's engine have an upper limit for the rotational speed under ideal conditions?
This is a simple hero's engine. The source of the gas and the rotating part is seperated by a frictionless bearing. So only the upper part rotates. My question is this:
Given ideal conditions ( no ...
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1answer
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Confusion in the graph of Maxwell Boltzmann distribution of speed
So, I was reading about maxwell boltzmann distribution of speed and the function for fraction of molecules with a speed v was given as $$\frac{dN}{N}=4\pi \biggl[\frac{M}{2\pi RT}\biggr]^{\frac{3}{2}}...
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Why Pascal's law is applicable for ideal gases?
Pascal's law is about incompressible fluids. But ideal gases are compressible. Still, Pascal's law is applicable to ideal gases as far as I know (might be wrong). Why is it applicable for ideal gases?
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A temperature variation in one of the two Gay-Lussac formulas
The first law of Gay-Lussac, also called first law - Gay-Lussac, known abroad as Charles law or as Charles - Volta - Gay-Lussac law, at the constant pressure, the volume of an ideal gas is directly ...
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How the mass affects on this sphere? [closed]
The problem states:
A paper ball is made which has a volume of V=0.1m3 and filled with the hot air of temperature T=340K. Outside temperature is T=290K while the pressure inside the ball and outside ...
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1answer
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Mean potential energy per particle of Ideal gas in uniform gravitational field (high temp. limit)
I'm trying to show that for an ideal gas in a uniform gravitational field $\vec{g} = (0, 0, -g)$, confined to a box of height $L$ and base area $A$, the mean potential energy per particle is
$$\langle ...
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2answers
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Does the Joule-Thomson effect violate the Ideal gas laws?
I've got a question that's been baffling me. Does the "Joule-Thomson's effect", in which the temperature drops when the gas passes through a valve, violate the Ideal gas laws, which state ...
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1answer
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I have no idea how to do this? i am trying to use Boyle's law, but I can't [closed]
so we have crockery with 0.5-litre volume, in this crockery is water of 0.3 litres. how many litre waters can we pour out, if air mustn't go in. after this pour pressure will be 80kpa.
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Why is the slope of pressure and volume almost zero below critical point for liquefaction of gas?
Image shows the Andrews isotherms regarding liquefaction of gases.
Why is the $PV$ curve almost horizontal from point $B$ to $C$?
I want to understand why does a small increment in pressure result in ...
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Are stars ideal gases?
In Townsend's lecture notes on Black Holes, he describes stars as 'self gravitating balls of hydrogen atoms supported by thermal pressure $P \approx nKT$, where $n$ is the number density of atoms.'
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Balloon in a container inside a vacuum chamber
The question I'm trying to understand is and getting a bit stuck with:
Let's say we have a put a small balloon filled with air of volume, e.g. 1cm^3 inside a container. This container is not sealed i....
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Work done in Free Expansion of an Ideal gas
We define the work done in gaseous expansion as (External Force)*(Displacement of the piston)
The work done in free expansion, therefore, comes out to be 0 as the external pressure is 0.
But if we let ...
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How can we take pressure of ideal gas be equal to pressure of atmosphere if container is open
I can better put my doubt in form of problem:
The temperature of a gas placed in an open container is raised from $27^o$ C to $227^o$ C. The percent of the original amount of the gas expelled from the ...
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Calculating canonical partition function and pressure of ideal gas under uniform gravitational field
The problem as given to us is this:
I am mostly interested in the a and b parts. For a I have the following working out:
The Hamiltonian is given by:
$$ H = \sum_{i=1}^N \frac{\vec{p_i}^2}{2m} + \...
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1answer
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Doubts related to some assumption of kinetic theory
I have doubts related to the kinetic theory of gases which are mostly conceptual which I cannot find in my textbooks.
How assumptions the molecules to be perfectly rigid and spherical be good since ...
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1answer
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How can ideal gases be “elastic” and “ideal” at the same time?
The elastic properties of any substance is because of the restoring intermolecular forces operating in it.
And I read that the isothermal elasticity of an ideal gas is given by
$E_{isothermal} = P$
...
