An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.710947(13) litres at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 105 Pa) as defined by IUPAC since 1982.The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size becomes important. It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor. At high pressures, the volume of a real gas is often considerably larger than that of an ideal gas. At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid. The model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state. The deviation from the ideal gas behavior can be described by a dimensionless quantity, the compressibility factor, Z.
The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.
If the pressure of an ideal gas is reduced in a throttling process the temperature of the gas does not change. (If the pressure of a real gas is reduced in a throttling process, its temperature either falls or rises, depending on whether its Joule–Thomson coefficient is positive or negative.)
TL;DR Summary: Struggling to structure the problem and derive an analytical solution for gas expanding into other gas in a rigid tank. Preferred formulation is fixed control volumes. This is not a homework problem.
The problem:
Two control volumes (A and B) are in a rigid tank filled with air...
The answer given for part (c) in the back is that temperature doesn't change as the gas in cylinder A expands to fill cylinder B.
The thermodynamic system here is composed of the two cylinders A and B joined by some pipe.
But, I cannot find a satisfactory explanation for temperature...
Homework Statement:: I am trying to understand a formula given in our book for determining molar heat capacity of an ideal gas under different thermodynamic processes using a single formula, but it is confusing. The exact formula for different processes is in the screenshots below. Can someone...
1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid?
Why does/doesn’t the distribution change depending on the shape of the container...
For a freely expanding ideal gas(irreversible transformation), the change in entropy is the same as in a reversible transformation with the same initial and final states. I don't quite understand why this is true, since Clausius' theorm only has this corrolary when the two transformations are...
(The equation of ideal gas is PV=NRT.if P=1atm,N=1mole,T=0°K,R=gas constant then volume = zero. Hence, the volume of an individual molecule of ideal gas is zero)
An individual molecule of ideal gas is assumed to have zero volume. The molecules of ideal gas are assumed to be dimensionless points...
Hello.
Firstly, I've calculated the density of Kr ( = 3.74 g/dm3), and I know that the p (fluid) = ρ * h * g. And then I've used the following equation: p1*V1 = p2*V2, and therefore: p1*V1 = ρ * h * g * (m/ρ) => p1*V1 = h * g * m. (h = 3.0153 m) Is that correct? Please, how could I calculate...
So for a collection of particles each with mass m, the pressure beneath them, ##p(z)## should be higher than the pressure above them ##p(z + \Delta z)##.
This is a change in force per unit area (force per unit volume I suppose) times a volume to equate with the gravitational force
$$ \frac...
Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume
I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...
We know that
$$dU=\delta Q + \delta W$$
$$dU = TdS - pdV$$
So from this:
$$dS = \frac{1}{T}dU + \frac{1}{T}pdV \ (*)$$
For an ideal gas:
$$dU = \frac{3}{2}nkdT$$
Plugging that into (*) and also from ##p=\frac{nRT}{V}## we get:
$$S = \frac{3}{2}nk \int^{T_2}_{T_1} \frac{1}{T}dT +...
Do particles have air in between them in the ideal gas model?
I think the answer is 'no, but I am not quite sure about the explanation. Is it because in an ideal gas model, the volume of the particles is negligible? Thank you.
It even gives a hint, it says "consider two horizontal surfaces z1 and z2 and think about what thermodynamic equilibrium means for particles traveling from one surface to the other". This really trips me up because I am not sure what to do with this. Obviously in equilibrium the number of...
Solution from the textbook:
My work:
I constantly get 1.55kg. I also tried dividing the first and the second equation (pxV=m/M x R x T with different values). How did they come up with the equation in the solution? Also, I am sorry if I posted it in the wrong place and didn't follow the...
By using PV=nRT formula, I have found the volume of the vessel. As far as I have learned to calculate the number of collision in a unit volume. So, it is being difficult for me to find the right way to solve.
I searched on the internet and have got this...
I've first calculated the partial pressures of each gas:
##N_2: 0.4\times 7.4\times 10^4=3.0\times 10^4 Nm^{-2}\\##
##O_2: 0.35\times 7.4\times 10^4=2.6\times 10^4 Nm^{-2}\\##
##CO_2: 0.25\times 7.4\times 10^4=1.9\times 10^4 Nm^{-2}\\##
From here, I do not know how to continue. Could someone...
First, I tried using the Archimedes principle and calculated the weight of the surrounding air displaced when taking off.
##W = 2500\times 1.29\times 9.81 = 31637.25 N##
But then, I got stuck and do not know how to proceed from here on.
I don't want the full solution yet but can I get some...
Attempt at a Solution:
Heat Absorbed By The System
By the first law of thermodynamics,
dU = dQ + dW
The system is of fixed volume and therefore mechanically isolated.
dW = 0
Therefore
dQ = dU
The change of energy of the system equals the change of energy of the gas plus the change of energy...
It looks more like a computational obstacle, but here we go.
Plugging all of these to the partition function:
$$Q = \frac{1}{N! h^{3N}} \int -\exp(\frac{1}{2m}(p^2_{r}+p^2_{\phi}/r^2+p^2_{z})+gz)d\Gamma=$$
$$= \frac{1}{N! h^{3N}} \int \exp{(\frac{-1}{2m}p^2_{r})}dp_{r_{1}}...dp_{r_{N}}...
The actual data for the problem and my (and my friend's) attempt at a solution are in the attached file.
In a nutshell, this is what happened.
I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold...
Since the spherical wave equation is linear, the general solution is a summation of all normal modes.
To find the particular solution for a given value of i, we can try using the method of separation of variables.
$$ ψ(r,t)=R(r)T(t)ψ(r,t)=R(r)T(t) $$
Plug this separable solution into the...
Summary: U=3/2*n*R*T
Can some of you help me with this
The total internal energy of an ideal gas is 3770 J. If there are 3 moles of the gas at 1 atm, what is the temperature of the gas?
I use U=3/2*n*R*T but get the wrong answer, (101 K) but it should be 303 K
[Moderator's note: Moved from...
I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity.
Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign...
Hi, so I found this on another old "AP" High School Finals Exam.
I think I may be super lost.
Because the only way that I can think about is KE = 3/2kT. And then that the difference of the Kinetic Energy of the air Particles is the Q supplied by the heater inside the air dryer.
So ## \frac...
I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2.
There's a great example in wikipedia which is almost...
I have the definition of change in internal energy.
$$ \Delta U = Q - W $$
I can get the work by
$$ W = \int_{V_1}^{V_2} p dV = p \Delta V $$
however the pressure isn't constant so this won't do.
## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system.
I'm...
Homework Statement
After a free expansion to quadruple its volume, a mole of ideal diatomic gas is compressed back to its original volume isobarically and then cooled down to its original temperature. What is the minimum heat removed from the gas in the final step to restoring its state...
Homework Statement
An ideal gas has a molar mass of 40 g and a density of 1.2 kg m-3 at 80°C. What is its pressure at that temperature?
Homework Equations
PV=nRT
R constant= 8.314
n= number of moles
T= tempreture in kelvin
density=Mass/ Volume
The Attempt at a Solution
i simply solved it like...
Hi everyone, I'd really appreciate any help with this problem:
A helium cylinder for the inflation of party balloons hold s 25.0L of gas and is filled to a pressure of 16500kPa at 15 degrees celsius. How many balloons can be inflated from a single cylinder at 30 degrees celsius if the volume of...
Homework Statement
A J-shaped tube has an uniform cross section and it contains air to atmosphere pression of 75 cmo of Hg. It is pours mercury in the right arm, this Compress the closed air in the left arm. Which is the heigh of the mercury's column in left arm when the right arm is full of...
Homework Statement
Let 3/2kT be the kinetic energy of ideal gas per molecules. T the absolute temperature and N the avogadro number. Answer the following questions :
1) when the volume doubled at constant temperature. How many times the kinetic energy per molecule become greater than before...
My question to you is this...
Can the interior of the Sun be described as an ideal gas?
From my knowledge, to describe a body of gas as an ideal gas, the separation between the particles must be much greater than the size of the actual particles.
How could one justify whether the Sun fits this?
Homework Statement
Kinetic energy per mol is 3/2KT
Homework Equations
Q = nC##\Delta##T
U = Q + W
W = -P##\Delta##V
The Attempt at a Solution
1) internal energy = 3/2NKT
2) heat needed to increase temperature of 1 mol ideal gas by 1 degree at constant volume?
Since constant volume, W = 0
Q...
Consider the following problem:
Gaseous helium (assumed ideal) filled in a horizontal cylindrical vessel is separated from its surroundings by a massless piston. Both piston and cylinder are thermally insulating. The ambient pressure is suddenly tripled without changing the ambient temperature...
Homework Statement
A closed, thermally-insulated box contains one mole of an ideal monatomic gas G in thermodynamic equilibrium with blackbody radiation B. The total internal energy of the system is ##U=U_{G}+U_{B}##, where ##U_{G}## and ##U_{B} (\propto T^4)## are the energies of the ideal gas...
1. Two equal glass bulbs are connected by a narrow tube and the whole is initially filled with a gas at a temperature of T0 and pressure of P0. Then, one of the bulbs is immersed in a bath at a temperature, T1 and the other in a bath at a different temperature, T2. Show that in this problem, the...
Assuming all gases in the combustion reaction of benzoic acid (C6H5COOH) behave ideally, what is the "exact" change in internal energy?
The context in which this question is being asked is after a calorimetry experiment. For all the intents and purposes of calorimetry, the change in internal...
Hi there, i am struggling with the following problem. Air is pumping into a bottle with volume V and pressure Pi until it reaches a final pressure Pf. The temperature remains the same during the process and the gas is an ideal one.
We have to calculate the work that is done.
I am not quite...
Homework Statement
Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A.
The internal energy of the gas in container B is
(a) twice that for container A
(b) the same as that for...
Homework Statement
The dot in Fig. 19-18b represents the initial state of a gas, and the isotherm through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the change Eint in the internal energy of the gas is positive, negative, or zero: (a)...
Homework Statement
A cylinder with a heavy ram/piston contains air at T = 300 K. Pi = 2.00 * 105 Pa, Vi = 0.350 m3, Mr = 28.9 g/mol & Cv = 5R/2
(a) What's the Molecular Specific Heat of an Ideal Gas, with a constant volume, computed at J/KgC ? (Cv)
(b) What's the mass of the air inside the...
Homework Statement
[/B]
Two ideal gases are contained adiabatically and separated by an insulating, fixed piston that blocks the molecules of gas 2 but allows the molecules of gas 1 through(in both directions). The initial pressures, volumes, temperatures and number of molecules on each side is...
Homework Statement
I'm reading the book about Statistical Physics from W. Nolting, specifically the chapter about quantum gas.
In the case of a classical ideal gas, we can get the state functions with the partition functions of the three ensembles (microcanonical, canonical and grand...
hello, i am trying to calculate the volume of a balloon (which is quite large). It has been filled with helium via a valve connecting helium storage tanks to the balloon. The knowns I have are the volume of the storage tanks, the intital pressure in the tanks, and the final pressure in the tanks...
Hi everyone,
I remember years ago at school memorising the derivation of the formula for pressure in the kinetic theory of gases, as explained in this Youtube video:
Thinking a little more deeply about this derivation there are two things I don't get:
1) At 0:53, the video says the molecule...
Homework Statement
Please look at the below images which is the derivation of the relation between the internal energy of an ideal gas and the molar specific heat at constant volume. (Snaps taken from Fundamentals of Physics
Textbook by David Halliday, Jearl Walker, and Robert Resnick)
As...
Homework Statement
An ideal gas with Cv = 5/2R, and γ = 1.4 starts at a volume of 1.5m3 , a pressure of 2.0×105Pa, and a temperature of 300K. It undergoes an isobaric expansion until the volume is V , then undergoes an adiabatic expansion until the volume is 6.0m3 , and finally undergoes an...
Hello,
I have some trouble understanding the virial expansion of the ideal gas.
1. Homework Statement
I have given the state equation:
$$ pV = N k_b T \left(1+\frac{A\left(T\right)}{V}\right) $$
Homework Equations
[/B]
and a hint how to calculate the caloric equation of state $$...
Hi everyone
I'm having trouble with solving an exercise in statistical physics. I need to argue why the average number of particles with a velocity between ##v## and ##v+dv## that hit a surface area ##A## on the container wall in a time interval ##\Delta t## is $$N_{collision}=v_{x}A\Delta t...