# 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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### Sound velocity in ideal Bose gas

Speed of sound is related to the derivative of pressure with respect to density: $v_s=\sqrt{(\frac{\partial P}{\partial \rho})_S}$ where S tells us the derivative must be taken while keeping entropy ...
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### Rate of effusion in kinetic molecular theory?

According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is $$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the ...
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### Ideal Gas Constant

Wikipedia states that the ideal gas constant relates the energy scale to the temperature scale. It serves as the constant of proportionality. This is obvious from the units. If temperature is a ...
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### Estimate temperature and pressure of steam in a pot of boiling water

Suppose we have a pot of known dimensions filled to level L with boiling water on a stove, covered by a lid with a vent of known dimensions. Given the steady-state temperature of the stove (bottom of ...
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### Would the temperature of a gas change when accelerated in a train?

I was thinking about a situation where some gas is enclosed inside a container and kept in a train at rest. The train accelerates, gains a maximum speed and then suddenly stops. Would the temperature ...
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### Simple explanation of relation between speed of sound and r.m.s. speed?

In an ideal gas, the speed of sound $v_s$ is related to the r.m.s. molecular speed $v_m$ by $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}} \qquad ,$$ where $\gamma=C_p/C_v=7/5$ for a diatomic gas. I ...
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### Adiabatic filling of a container

Suppose a thermally insulated container is filled with atmospheric air until the pressure reaches 5000 psi. This could represent the filling of a diving cylinder, before thermal dissipation becomes ...
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### Heavy vs Light Particle Ideal Gases

Assume there are two ideal gases. The first is made of a light particle, and the second is made of a heavy particle. The two are of the same amount, in the same volume container, and at the same ...
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### How do I find the amount of atoms in a pure gas in a confined area?

Say I have Argon gas in an area such as a cube with pressure around pressure between 10-5 and 10-3 Torr (pressure) at 25 degrees at 320 Kelvins . How do I find the amount of atoms in that cube? Any ...
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### How does a gas of particles with uniform speed reach the Maxwell-Boltzmann distribution?

Take an empty container and fill it with $N$ gas particles (ideally a monoatomic gas), each having the same kinetic energy $E$, then isolate the container. Since initially the speeds don't follow the ...
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### How is the degenerate electron gas state “degenerate”?

What is "degenerate" in the degenerate electron gas state? Why is it called degenerate?
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### Density of Air in a balloon

A balloon with volume 2800 m³ is heated up to 60 °C. If the outer temperature is 12 °C and the air has a pressure of 960 hPa, what is the density of the air inside the balloon and on the outside? ...
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### What portion of impulse is received by the cylinder?

Condition: A cylinder with a piston are situated along Y axis. Piston receives an impulse (P1) along Y axis and transmits it to the cylinder through a gas medium with which cylinder is filled. The ...
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### Combined gas law in an open atmosphere

The question was asked about pressure vs. Volume increasing in an ideal gas as temperature is increased. My question then is this. What is the formula to determine how much volume and pressure will ...
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### In an ideal gas, if temperature increases, will pressure or volume increase?

This question came up when I was talking about the atmosphere. Someone had mistakenly claimed that as temperature increases, the density of the atmosphere should increase as well. I reasoned from the ...
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### Understanding Charles's Law

Charles's law states that, The volume of a given mass of an ideal gas is directly proportional to its temperature on the absolute temperature scale (in Kelvin) if pressure and the amount of gas ...
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### Why is steam used to spin turbines?

The ideal gas law tells us that the relationship between Pressure (P), Volume (V), Temprature (T), and quantity/amount (n) is $$PV = nRT$$ where R is the gas constant. Say your an engineer who ...
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### Costant volume gas thermometer [closed]

I have two constant volume gas thermometers, one with an ideal gas $pv=RT$ and the other following the Van der Waals equation $(p+\frac{a}{v^2})(v-b)=RT$. They are calibrated using the freezing point ...
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### ideal gas law modelization in a vacuum chamber

I am trying to model a pressure sensor in COMSOL. The basic work is that there is current flowing inside it, if the pressure of the gas around it drops down, the temperature goes down as well (ideal ...
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### What is the $\delta$ in fluctuation model [closed]

I found this formula : $G-G_0=\frac{-nkT}2\delta^2$ on this Site and I'd like to ask what does the $\delta$ stand for?
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### Average force and pressure in a 3D box due to quantum non-interacting particles

A gas of non-interacting quantum particles occupies a box with lengths $L_1, L_2, L_3$. Calculate its energy and thus the average force and pressure exerted by the gas on the walls of the box. I have ...
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### Compression of a liquid with a gas dissolved in it?

If I remember correctly you cannot compress a liquid, but I know you can compress a gas. (usually to the point it becomes a liquid then no further) What happens if I were to compress soda water? A ...
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### error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
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### Escape velocity for hydrogen molecules

The question: At what temperature is the RMS speed of Hydrogen molecules equal to the escape speed from the earth's surface? Values of radius of earth($r$) and gas constant $R$ has been supplied only....
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### Air pressure in balloon

I have to calculate the air pressure inside of an hot air balloon. After some searching I found out that I can use the ideal gas law: PV = nRT (from Wikipedia) So to get the pressure in the balloon I ...
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### Is it possible to obtain higher order corrections to the ideal gas law when one allows realistic phenomena to make their way into the equations?

I had an interesting thought today that caused me to ask whether it'd be possible to make corrections to the ideal gas law via introducing terms derived from more realistic phenomena to make their ...
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### How can I interpret negative values of potential evapotranspiration?

If I extract Potential Evaporation (PET, W/m$^2$) from the National Centers for Environmental Prediction (NCEP), climate reanalysis data (downloadable as netCDF files here), there are some negative ...
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### How fair is it to say that all chemistry arises from failures of the ideal gas law?

I was reading here about how the ideal gas law assumes point masses and non-interaction. Is it fair to say that all chemistry arises from failures of that? Of course, such a sweeping generalization ...
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### Volume of gas at which relative fluctuation of gas density occurs

I have the following question: In what volume of gas occurs 10 % relative fluctuation of gas density under pressure of $10^5\text{ Pa}$ and temperature of $293.15\text{ K}$? I don't understand ...
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### Conversion of ideal gas to real gas via $Z$ compression factor

The ideal gas equation $PV=nRT$ can be converted into real gas equation by compression factor $Z$ i.e $PV=Z~ nRT)$. My question is what is $Z$ and how does it arise? Is $PV/nRT$ a compression ratio of ...
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### What are the units of these virial coefficients?

I'm reading some papers for calculating the vapor pressure of alkali metals as a function of temperature, and I've come across some familiar-looking virial expansions, but when I tried to work out the ...
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### Calculating air density lapse with altitude (specifically, pressures)

This might be a bit more of an engineering question, but I'm calculating air density drop-off with altitude, and I'm having some problems calculating the pressure (I'll run through my method). This ...
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### Temperature change inside pressure chamber

Let's say there is a pressure chamber with some sort of sample / specimen (e.g. protein crystal) in it. Now I apply a certain amount of gas pressure, e.g. 10 or 20 atm. Let's say I use xenon as a gas. ...
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### In $PdV$, what is the value of $P$? $P_1$ or $P_2$?

Say I have an ideal gas that has a known $P_1$, $P_2$, $T_1$, and $T_2$ undergoing a reversible adiabatic process. I want to find the work done so I must use $PV = RT$ to get the change in $V$, so ...
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### Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$\mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
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### How to calculate the specific heat capacity of gases

Could someone explain why the Specific Heat Capacity (SHC) of dry air is 1.005kJ/kg.K whereas the accepted SHC for ventilation air is quoted 1.300kJ/kg.K? Assuming the air for the ventilation calc’s ...
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### Root Mean Square Speed of Gas

The RMS speed of particles in a gas is $v_{rms} = \sqrt{\frac{3RT}{M}}$ where $M$ = molar mass; according to this Wiki entry: http://en.wikipedia.org/wiki/Root-mean-square_speed The gas laws ...