What is Ideal gases: Definition and 82 Discussions
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.)
To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows:
- there are two ideal gases (ideal gas law applies)
- the pressure remains constant (isobaric process), so p1= p2 = p
- I imagine there being two...
For part(b)
The solution is, ##1:10##, however, is the wording correct? I don't see how to find the ratio of atomic mass, however, I can solve for the ratio of the molar mass.
##n_A = n_B## from part(a) by setting the internal energy equation for each ideal gas equal
##\frac{M_A}{m_A} =...
I have been trying to make sense of the derivation of pressure under Kinetic Theory of Gases chapter, but it's not making sense to me when the impulse momentum equation is used for the collision between a gas molecule and the wall of the container.
The book says that for the elastic collision...
Hi,
I am unfortunately stuck with the following task
I started once with the hint that at very low temperatures the diatomic ideal gas behaves like monatomic gas and has only three degrees of freedom of translation ##f=3##. If you then excite the gas by increasing the temperature, you add two...
I am able to solve part (a) using the relationship ##\frac {P_1} {T_1} = \frac {P_2} {T_1}##, where ##T_1 = 273.16## since its the triple point of water and ##T_2 =T_s## ##(T_s = ## melting point of sulphur). I use the two readings for thermometer A to get ##P_1## and ##P_2## as mentioned in the...
This is the Two-Balloon Experiment: https://en.wikipedia.org/wiki/Two-balloon_experiment#cite_note-MW78-1
The claim on Wikipedia which I am a little confused over is that when 2 balloons (at the 2 red points) are connected via a tube, the smaller balloon at a higher pressure would push air...
Hello there, is my solution for part d logically correct? Here is my attempt at the solution :
Part a :
where : P1 = 3P2
Part b :
Since P1=3P2, therefore, T1=3T, where T=300K. Thus, T1=900K
Part c :
Because the final pressure at the end of the cycle is exactly the same as the pressure at...
Hi,
Considering the question bellow from a government work selection process:Check the FALSE alternative on the use of thermodynamic properties.
In a cylinder-piston type system, the variation of the enthalpy property (Δh) is usually applied to determine the heat (per kilogram) exchanged with...
Attempted Solution:
Gas Entropy
This system is isothermal: the energy of each gas remains constant.
$$dU = 0$$
By the combined statement of the first and second laws,
$$dU = TdS - PdV$$
Therefore,
$$0 = TdS - PdV$$
$$dS = \frac {PdV}{T}$$
Therefore,
$$dS_1 = \frac {P_1 dV_1}{T} = \frac {P_1...
We are learning the lesson about gases/gaseous states at our school and I couldn't help but wonder, why learn about IDEAL GASES... How do ideal gases help us to analyze about real gases?
I have a box with a wall in mid dividing it in 2 sections, and the wall has a hole of diameter d. There is ideal gas in both sections at 150 K in one section and at 300 K in another. How am I supposed to calculate ratio of mean free paths in 2 sections.
My attempt: L ~ Volume / Number 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...
I've learned that ideal gases have the same average kinetic energy, but this doesn't necessarily mean that they have the same speeds within a container..Instead, is it right to say that (according to kinetic molecular theory) that the speed of molecules at an instance is a wide range of speeds?
Hello everyone. I stumbled across a problem while studying for my exam that I cannot confidently answer.
Can we assume nitrogen at the temperature of 27˚C and the pressure of 100 kPa an ideal gas? Justify your answer.
The definition of an ideal gas is "...a gas whose molecules are spaced far...
I read from a website that Most gases behave like ideal gases at many temperatures and pressures.
and we have learned that the gases behave like ideal one only in high temperature and low pressure . so which one is true .
Homework Statement
Two monatomic ideal gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average translational kinetic energies KA/KB is:
Homework Equations
KE=0.5xmxVavarage^2...
Hello,
I want to make sure I understand the following considering ideal gases.
Assuming I have two different types of gases, say, O2 and H2 (each at thermal equilibrium), is it correct to say that the kinetic energy of the O2 gas equals to the kinetic energy of the H2 gas since they're both...
How would Dalton's law be affected when there are two ideal gases in a container at different temperatures?
Let the gas with higher temperature be gas A and the gas with lower temperature be gas B. Then heat will be transferred from gas A to gas B due to which kinetic energy of the molecules of...
Homework Statement
Calculate the volume of 1 mol of steam at 100°C and a pressure of 1 atm assuming that it is an ideal gas.
Homework Equations
PV=nRT
The Attempt at a Solution
Well, if I am honest I was just going to re arrange the above equation for V and plug the numbers in but that seems...
Homework Statement
Two subsystems within a 20 l cylinder are separated by an internal piston. Each of them is initially composed of 1 mole of component 1 and one mole of component 2, both of which will be treated as a monatomic ideal gas. The cylinder has diathermal walls and is in contact...
Homework Statement
I have been tasked with designing a feasible experiment to determine the ration between 2 vessels. I think i have a way that works on paper.
Homework Equations
pV = nRT and the conservation of mass.
The Attempt at a Solution
1.Start with 2 vessels of unknown volume x and y...
Homework Statement
Homework EquationsThe Attempt at a Solution
I chose 1&2, but all three are correct. I thought for a constant pressure, if temperature is doubled, then the volume would doubled too? As P=V/T ?
I don't understand how Delta(U) = Cvdelta(T) is always true for Ideal Gases...Shouldn't this only be true for constant volume processes? Yet it seems to be used even when a gas is expanding or being compressed...
Any ideas...Thanks in advance.
I'm interested in predicting the index of refraction of atmospheric air and several nonpolar gases at room temperature for pressures of 1 atm - 0 atm. I'm not really sure where to get started. I have found the relation n=\sqrt{1+\frac{3AP}{RT}} but I don't really get where it comes from. Well...
Is it that ideal gases do not possesses potential energy because there are no intermolecular forces. But, real gases do have potential energy and its potential energy is the highest among the different phases. ( Potential Energy of Gas>Liquid>Solid ). I need someone to make these things clear to...
Homework Statement
A mixture of two gases, A and B, exists at pressure p1, volume V, and temperature T1. Gas A is subsequently removed from the mixture in a constant-volume process. The remaining gas B is found to have a pressure p2, volume V, and temperature T2. Express the ratio of the...
Hi,
I understand that vapor pressure is independent of initial pressure, and depends only on temperature.
However, is this true of a non ideal gas at high pressures?
(I am specifically interested in the vapor pressure of a meg/water mixture at approx. 100 bar),
Thanks
Hello
1. I was wondering why internal energy is usually expressed as a function of temperature and specific volume and enthalpy a function of temperature and pressure (ie why is u(T,v) and h(T,p)) and some other set of two properties?
2. For du = \frac{∂u}{∂T}dT + \frac{∂u}{∂v}dv and dh =...
I am not sure how to properly use the scientific notation in this problem. I have attempted to solve it several different ways to no avail.
A house has a volume of 1.45 x 10(4)m(3). At 20.0° C and 740 mm Hg, the air fills the house. If the temperature and pressure increase to 35.0°C and...
A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is
placed in a chamber ﬁlled with helium gas at 1 atmosphere and at a room temperature. A
few months later, the experimenter happens to read in a journal article that the particular
glass of which the bulb is...
This might be a stupid question, but I am confused about the ideal gas theory. I know that we assume high temperatures and low pressures, and that the volume is negligible when we compare it to a container, but my textbook is very confusing about this point.
It says assume zero/negligible...
How does decreasing the volume increase the temperature of the gases?
I was doing an experiment today and when i decreased the volume of the gas from 65ml at 1atm to 20ml the temperature detected an increase of 0.5°C. However, in Boyle's Law temperature is a constant.
So would this mean...
What does it mean by 21% oxygen and 79% nitrogen by volume?
Because won't the oxygen and nitrogen have the same volume which is the volume of the whole container?
nTRT/VT=nO2RT/VT+nN2RT/VT so why would we say oxygen is 21% by volume since the volume of the oxygen and nitrogen is the same...
Homework Statement
A moster of a gas has 4 moles and first is in the temperature 300 K and pressure 10 atmosphere.After a change of state, ∆T= -50 K and ∆V=10 liter.Find the final temperature ,volume and pressure of the gas.
Homework Equations
P*v=n*R*T
The Attempt at a Solution...
Homework Statement
A horizontal cilindre with a piston of mass M = 0.5 kg is filled with air (the specific heat of air is Cp = 1000 Joule/Grad*kmole). The heating of the gas results in the piston's accelerated displacement (with constant acceleration) until the velocity v = 1 m/s. Determine...
Homework Statement
Two different ideal gases are separated by a sliding barrier that can move vertically. The gas in the upper chamber 1 has n moles of material, whilst the gas in the lower chamber 2 has 3n moles of material. At T0 the weight of the barrier is such that the volumes of the two...
Homework Statement
A cylinder contains 0.2mol of Helium at 30 degrees C and is heated different ways.
How much heat is needed to raise the temperature to 70C while keeping thevolume constant?
Homework Equations
dQ=dU+dT
nCpdT=nCvdT+nRdT
The Attempt at a Solution
What I am...
I'm having trouble understanding what happens to the internal energy of an ideal gas being compressed adiabatically.
If DU = DQ + DW,
then as we do work PdV compressing the gas, since in adiabatic processes DQ=0, W the change in internal energy is non-zero, so U must increase.
But if...
1. Homework Statement
A balloon behaves such that the pressure is P = CV3
where C
= 100 kPa/m3
. The balloon is blown up with air from a starting volume of 1 m3
to a volume
of 3 m3
. Find the work done by the air.
2. Homework Equations
W=PdV
3. The Attempt at a Solution...
Homework Statement
A balloon behaves such that the pressure is P = CV3
where C
= 100 kPa/m3
. The balloon is blown up with air from a starting volume of 1 m3
to a volume
of 3 m3
. Find the work done by the air.
Homework Equations
W=PdV
The Attempt at a Solution
What I...
(I):
dU=dW+dQ
also (II):
dU=\frac{3}{2}RdT
if you compress a gas dW in dU is positive from pV=nRT lesser volume could either mean more pressure or more T. If dV gives dp only then dT=0 how can then dU for dW in (I) be equal dU in (II)?
Well i know real gases behave as ideal gas (almost) when pressure is low and temperature is high. I want to understand this - When pressure is low attractive forces in the gas moelcules will be stronger(as compared to high pressure) but the fast movement due to high temperature compensates it...
Homework Statement
An ideal monoatomic gas is characterized by the two equations PV=NRT and U=\frac{3NRT}{2} in which R is a constant.
Find the fundamental equation corresponding to a monoatomic ideal gas.
Homework Equations
S=\left ( \frac{1}{T} \right ) U+\left ( \frac{P}{T} \right )...
Homework Statement
Hey guys, I am having trouble understanding how the ideal gases behave and I got these 3 questions in homework:
If an ideal gas is transferred, at constant temperature, 10 Joules of heat, does the internal energy change?
If an ideal gas is transferred, at constant...
Homework Statement
I want to start by saying that my instructor is a particle physics guy. He loves to talk about particles seems to want to rush through fluids and thermo so he can get to particles and the 'real modern physics.' He is skipping, skimming and not really covering a lot of this...
Homework Statement
See attachment ecxample001.
Homework Equations
See attachment D11.
The Attempt at a Solution
In the first equation (Cp/R = a+bT+cT^2...etc.), Cp/R is the constant pressure specific heat. The general formula for enthalpy change is h2-h1 = integral[Cp]dT, so does...
A rigid tank with a volume of 0.75 m3 initially contains air at 70 kPa and 25 degrees C. A small hole develops in the tank. The surrounding air at 100 kPa and 25 degrees C slowly leaks into the tank due to the hole. Heat transfer between the surroundings and the tank maintains a constant air...
Homework Statement
I attached the problems. The first one is D) at the top of the page parts a) and b). The second one is E) at the top of the second attachment.
1) The rigid tanks shown below have volumes of .4m^3 and .004^3 respectively and each contains a water liquid-vapor mixture of...
Homework Statement
Two monatomic ideal gases are separated in a container by an impermeable wall, with volumes V_{1} and V_{2}, temperatures T_{1} and T_{2}, number of atoms N_{1} and N_{2}, and both are at the same, constant pressure P. The wall is then removed, and the pressure is continued...