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.)
For this question
http://tinyurl.com/3bmkhg
Followed is my working
P1/T1=P2/T2
T2=(T1/P1)*P2
=(T1)*(P2/P1)
=25 * 2
=50
But the answer is D. 323,
may I know what is my problem?
[SOLVED] ideal gas law numerically
If I calculate the pressure of water vapor at stp (in mmHg),
P= 1000*7.502e-3*R*(0+273)*.804/18;
where the 7.502e-3 factor converts from Pa to mmHg, 1000 is because my density (.804) is in grams/cm^3, 18 is the molar mass of water, etc etc. and this comes out...
Homework Statement
A gas at 293.15 degrees kelvin and atmospheric pressure is compressed to a volume one fifteenth as large as its original volume and absolute pressure of 3000kPa. What is the new temperature of the gas?
Homework Equations
p1v1/t1=p2v2/t2
The Attempt at a Solution...
Should there also be an assumption for ideal gaes that states:
The gas molecules/atoms do not vibrate and rotate
I was considering a case of a gas expanding at a dropping pressure such that the value of
PV remains a constant. Work is done since there is an increase in volume. If there is...
Homework Statement
The law for an ideal gas is given by P = n*R*T/V. In our case, n and R are constant, so P = f(V,T).
I have found dP/dT, dT/dV and dV/dP. I have to find the result when these three differentials are multiplied with each other.
The Attempt at a Solution
I get -1 - can...
Homework Statement
In general, which of the following gases would you expect to behave the most ideally?
a) N_2
b) CO
c) H_2
Homework Equations
N/A
The Attempt at a Solution
Okay, so I know that CO would definitely not behave the most ideally. I tried looking this up on the...
The atoms of a solid possesses some certain min. zero point energy even at 0k, while no such restriction hold for the molecukles in an ideal gas. Use the uncertanity principle to explain these these statements.
ok, so what i am thinking is the at 0k the atoms of a solid have some energy...
Homework Statement
I need to find the volume for 1 kg of diatomic oxygen for a pressure of 150,000 Pa and a temperature of 100K. This is really part of a larger project, and I need to make sure I'm not tripping up on little details. It's that 1 kg of diatomic oxygen that I am a bit unsure...
Homework Statement
Even at low density, real gases don't quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial expansion. Just working with the first order virial expansion we have:
PV=nRT(1 + B(T)/(V/n))
B(T) is a virial coefficient. A...
Hi,
Im having problems with my ideal gas equations. I am able to do the actual equation but when I comes to the answer, I have difficuly understanding.
Here is an example.
If i want to discover the pressure...
V-1000litres
n-800moles
r-0.08206
t-373kelvin
Pressure-?
Now the answer...
Homework Statement
an ideal gas is allowed to expand adiabatically until its volume increases by 50%. By what factor is the pressured reduced?(gamma=5/3)
Homework Equations
P1V1^gamma=P2V2^gamma
The Attempt at a Solution
P1V1^gamma=P2V2^gamma
v2=v1+.5V1=3/2V1...
Homework Statement
Calculate the volume expansivity, β, for one mole of ideal gas at constant pressure and at room temperature.
Homework Equations
β=1/V(dV/dT)
The Attempt at a Solution
Bit stumped on this one, I'm guessing they want it in terms of P as P is not specified.
I...
Homework Statement
What condition must the gas be in for this equation to hold true?
Homework Equations
The Attempt at a Solution
the gas has to be in constant pressure and volume and temperaute
Homework Statement
Im given an ideal Gas confined in an container with quadratic bottom area of size L^2 and open at the top.
The whole thing is set in V(z) = m*g*z surely and contains N Atoms at Temperature T.
Compute the Helmoltz Free Energy.
Homework Equations
Yea surely the...
This is much longer than the normal post, so please bear with me.
I was wondering if anyone here knows the complete derivation of Ideal Gas Law (or can recommend a book that describes it clearly and fully), who can tell me whether its conclusions are valid for any shape of gas particle, and...
The relative humidity is 55% on a day when the temperature is 30.0°C. Using the graph below, determine the number of moles of water vapor per cubic meter of air.
on the graph, Vapor pressure of water is on the y-axis and temperature on the x-axis 30C cordinates with 4200 Pa of water vapor...
Density of water vapour in the air involving compression
Homework Statement
A volume Vi = 23.2 L of air at temperature T = 22 °C is compressed at constant temperature to a volume Vf = 11.0 L. The relative humidity of the air before compression is H = 59.4 %. The saturated vapour pressure of...
An ideal gas at a temperature of 17.7°C is compressed adiabatically from an initial volume 70.0 l to a final volume 43.0 l. Find its final temperature (in °C) if CV = 2.50R.
so T1V1^g=T2V2^g
to find g=cp/cv=(cv+nR)/cv and cv=2.50R
g=(2.50R+nR)/2.50R factor out an R...
Problem with ideal gas law and a spring! Help please!
Homework Statement
We have a box divided in two parts by a piston without friction, and in one part there are n moles of an ideal gas and a Spring orf constant K and natural longitude L which keeps the piston in equilibrium. According to...
im studying building systems engineering technology. yeh i know it's only a technology program at the cegep level but when I'm done with it, I'm going to do software engineering in university. anyways I'm having trouble to understand two problems in the book. if anyone can help me with this, it...
Hi every body,
We are taught in school that the gas law : pv=nRT can not be applied at high pressure, say a hundred atm. Now I just think of the fact that can we use that equation at very low pressure? Several mTorr for example.
Thanks
1. A rigid tank contains .5 kmol of Ar and 2kmol of N2 at 250 kPa and 280 K. The mixture is now heated to 400 K. Determine the volume of the tank and the final pressure of the mixture.
2. PV=NRT
Can you find the initial volume by using PV=NRT?
V=NRT/P
V=(2.5)(8.314)(280)/250=23.2...
Homework Statement
A cylinder has its lid connected to a spring with k = 2000 N/m. The cylinder is filled with 5.00 L of gas witht he spring relaxed at a pressure of 1.00 atm and a temperature of 20.0C. (a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will...
I have a box divided by a partition. On one side I have n mole ideal gas, on the other side there's vacuum.
If I remove the partition the ideal gas will expand into the vacuum. Since the box is adiabatic and no work is applied to or by the gas, \Delta U = 0.
But what about the work used...
Hi everyone ^^! I hope you had a great holiday season. I have a homework problem that I'm a little confused on. I will provide my answers/work as usual, and would like it if someone could check my work, or tell me if an explanation is wrong/needs more information. My teacher would like us to be...
Homework Statement
Unknown: Pressure
Given:
V: 0.002 L
n: 0.019 mol
R: 8.31 (uh..any units here..?)
T: 498 K
Homework Equations
PV= nRT
The Attempt at a Solution
For some reason, the units don't cancel out when I attempt to reach the solution when I try to get the Pressure. So what are the...
Ideal Gas Law Problem :)
Homework Statement
A balloon is filled with helium at a pressure of 1.0 x 10^5 Pa. The balloon is at a temperature of 23°C and has a radius of 0.13 m.
(a) How many helium atoms are contained in the balloon?
(b) Suppose we increase the number of helium atoms in...
Homework Statement
Suppose 0.50 mol of a monoatomic ideal gas is changed from state A to state D by one of the processes shown on the PV diagram of the figure below.
http://img382.imageshack.us/img382/784/untitledsc4.png
(This is my edited version of the image)
(a) Find the...
Homework Statement
An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. If the initial rms speed is 1800 m/s, what is the final rms speed?
Homework Equations
v(rms)=square root of [v(avg)]^2=square root of (3kT)/m
The Attempt at a...
Homework Statement
A monatomic, ideal gas is in a sealed container (the number of gas molecules is always constant: n = 2 moles); the initial pressure is Pi = 1.01 x 10^5 Pa and the initial volume is Vi = 0.0224 m^3.
* First, the volume of the gas is decreased at a constant pressure (at...
A cylinder is closed by a piston connected to a spring of constant 2.00 X 10^3 N/m. With the spring relaxed, the cylinder is filled with 5.00L of gas at a pressure of 1.00 atm and a temperature of 20.0ºC. A) If the piston has a cross-sectional area of 0.0100 m^2 and neglible mass, how high will...
Here's an ideal gas law question:
A scuba diver is 32 m below the surface of a lake, where the temperature is 5°C. He releases an air bubble with a volume of 12 cm^3. The bubble rises to the surface, where the temperature is 25°C. What is the volume of the bubble right before it breaks the...
For the first part of my lab, I have a graph with pressure(atm) as a function of temperature(K).
For the second part of my lab, I have a graph with pressure(atm) as a function of inverse volume(mL^-1)
For both of these, i am supposed to find the value for R, the gas constant.
So far far...
Problem: An oxygen sample of 1.62 L is at 92.3 kPa and 30.0 degrees celsius.
(a) What volume would the oxygen occupy if the pressure was 120.0 kPa and the temperature was 0.0 degrees celsius.
(b) How many moles of oxygen are in the sample?
My Approach:
Conversions: 0 degrees celsius...
THe Question asks 'Derive the entropy of an ideal gas when its molar specific heat at constant volume is constant.'
So I've taken
\Delta S = \int_{S_0}^{S} dS = \int_{T_0}^{T} \frac{\partial_S} {\partial_V} dT + \int_{V_0}^{V} \frac{\partial_S}{\partial_V} dV
in this context what...
In preparation for a demonstration, your professor brings a 1.2 L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 78 psi and the lecture hall is 23°C, how many moles of sulfur dioxide are in the bottle? (Hint...
That came out in my qualifying exam.
The question was if a gas with rotational and vibrational energies enhanced, does obey the Ideal Gas Equation PV=NKT.
You can answer with all the tools you have at hand. My comitee member didn't agree with me, but anyway I persisted in my answer and I...
Two moles of N2 gas undergo the cycle abcd. The pressure of the gas in each state is
pa = pd = 5500 Pa;
pb = pc = 1500 Pa.
Note that 5500 Pa > 1500 Pa. The volume of the gas in each state is
Va = Vb = 1.80m^3 ;
Vc = Vd = 8.70m^3.
Note that 8.70 m^3 > 1.80 m^3. The gas may be...
Hey
Could somebody please explain what the difference between an ideal gas and a real gas are? Or post a suitable link from which I can understand the concept surrounding this issue.
Thanks
Pavadrin
Sir,
An experiment is carried on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of PV/RT with P is shown in the following diagram. Is it right? Suppose a graph is plotted between PV/RT and T. At high...
Sir,
An ideal gas is taken from state 1 to state 2. How does the volume change? The P-T diagram is as shown.
I solved it in the following way:
From the diagram it is clear that P/T is a constant. From ideal gas equation,
PV = nRT...
Sir,
One mole of an ideal gas undergoes a cycle change as shown in figure. The process A-B is isothermal. The pressure and volume at A is 1.1 x 10^5 N/m^2 and 22.4 litres respectively. What is the temperature of the gas at C?
If the temperature at one point was given the temperature at...
A standard cylinder of oxygen used in a hospital has the following characteristics at room temperature (295 K): gauge pressure = 13,800 kPa (2000 psi), volume = 16 L (0.016 m^3). How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 liters/min...
So I know the volume of a hot air balloon and the temperatures of the air (ideal gas) inside the balloon and outside of it. I know the pressure of the air. And I need to find the Net force on the balloon and contents but neglecting the weight of the balloon itself. I thinkthere must be some way...
For example there is change state on an ideal gas. The temperature of states are X and Y. The change on X and Y is a change of constant pressure but increasing in volume. Let the quantity of the ideal gas be 1[mol], and let R[J/mol*K] denote the gas constant. Find the work which the gas did on...
The diagram below shows state changes of an ideal gas. The temperature of states (1), (2), (3) are T_1[K], T_2[K] and T_3[K] respectively. The state change from (1) to (2) is an adiabatic change (not an isothermal change). The state change from (2) to (3) is a change at constant pressure...
Hi,
I have a question about the ideal gas law.
I have been under the impression that if volume goes down then pressure and temperature go up. But, if you look at the equation T=PV/nR, it seems that if volume, say, doubles, pressure will be halved and vice-versa. While that makes sense, it...
The questions is that
The equation of state (the equation relating pressure, volume, and temperature) for an ideal gas is pV=nRT, where n and R are constants.
a.) Show that if the gas is compressed while the temperature T is held constant, the bulk modulus is equal to the pressure.
b.)...