# What is Ideal gas: Definition and 851 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.)

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1. ### I Why does an ideal gas satisfy ##(\partial U/\partial P)_T=0##?

The book I am reading says that by definition, the ideal gas satisfies the equations $$PV=nRT\tag{1}$$ $$\left (\frac{\partial U}{\partial P}\right )_T = 0\tag{2}$$ where does (2) come from? In other words, what justifies this equation in the definition above?
2. ### I Why is estimation of ##\frac{Pv}{RT}=1+BP+CP^2+...## interesting?

Consider ##n## moles of a gas at a constant temperature ##T##. If we vary pressure ##P## and measure the corresponding values of volume ##V##, we can make a plot of ##P\frac{V}{n}=Pv## against ##P##. This gives us some graph which has some form. Turns out that for a range of pressure starting...
3. ### Chemistry Calculate the pressure-volume work for the given reaction

I dont have an solution Attempt. Maybe something with PV=nRT but this is for ideal gas and H2O is liquid. An other formula they introduced us to is: dE=-P*V
4. ### I Irreversible adiabatic processes & entropy change (clarification needed)

Last month @Chestermiller opened the thread: Focus Problem for Entropy Change in Irreversible Adiabatic Process. I couldn't wrap my head around something apparently simple but the thread was not about that so I was instructed to open a new thread to discuss it separately and keep the original...

30. ### I Heat capacity for a real gas using the ideal gas (zero pressure) equation

Summary:: Heat capacity for real gas with ideal gas (zero pressure) equation I'm looking at this problem and I'm stuck. I usually question everything but this problem is confusing me. I don't know how they've made the jump from reduced properties (from generalized Cp charts(?)) to...
31. ### DeltaG and DeltaA calculation for heating a gas at constant volume

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)...
32. ### Solving Unusual Problems: Using the Polytropic Ideal Gas Equation

My teacher likes to make really weird problems. How can I start this problem? The only thing I thought of doing is using the polytropic ideal gas equation when cp= constant. (p2/p1)^k-1/k = T2/T1 and making p1 and t1 in each case the normal state of the lungs
33. ### Engineering Final volume of a gas using the ideal gas equations

Hey there! for this problem i try to use the combinate gas ecuation. First of all the values its necesary to have it in absolutes: 70 F = 527.67 K 90 F = 549.67 K The ecuation looks like: (200 psig) (1 ft^3)/529.67 K = (0.3 InHg) V2/549.67 K I can eliminate "K" but not psig with InHg for obtain...
34. ### Relating the entropy of an ideal gas with partial derivatives

It looks very easy at first glance. However, the variable S is a variable in the given expression. I have no clue to relate the partial derivatives to entropy and the number of particles.
35. ### Equation of a sound wave with viscous damping in ideal gas

How can we find a equation of a 1D sound wave in a non-differential form in an ideal gas with viscosity? How does the damping work? How does the wave lose energy at each layer as it propagates? To be clear I am looking for a simple exponential-sinusoidal function for it just in the case of...

38. ### Chemistry Ideal gas law problem with two cylinders

my answer will be ##P_1=2 P_2## but I have some doubts, if that is correct or not
39. ### Thermodynamics: Ideal gas model

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.
40. ### Position of piston related to ideal gas

a. The piston will be at rest when all its kinetic energy converted into work to push the gas, so: $$\frac{1}{2}m_0 c^2=P_0. \Delta V$$ $$\frac{1}{2}m_0 \frac{29}{4} \frac{P_0.V_0}{m_0}=P_0.\Delta V$$ $$\frac{29}{8} V_0=\Delta V$$ $$\frac{29}{8} L_0 = L_0 - L$$ $$L=-\frac{21}{8} L_0$$ My...
41. ### (Dry) Volume Ideal Gas Law Calculation

If the question was asking for (dry) volume, how would you do that?
42. ### Non-interacting gas in homogeneous gravitational field

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...
43. ### Ideal gas law problem -- Pneumatic piston movement with air temperature changes

I have come up with the change in height as 170 cm. My professor does not want to solve for the problem for a reason I do not understand. 170 cm is not part of the answer key. The answer according to the answer key is 65 cm. My attempt is: Initial temperature: p=F/A; (50 *9.8) / (pi * 0.05^2)...
44. ### Ideal gas law understanding

I figured that T' is a common factor for both relationships and from there deduceted that T'=p2xt1/p1=v1xt2/v2. However, I don't understand how that can be further manipulated to PV=KT.
45. ### I Help with an ideal gas canonical ensemble partition function integral

Where does the volume even come from? Any help would be appreciated!
46. ### Engineering Differences between an Ideal gas and a perfect gas?

Is this right for difference between idea gas and perfect gas. trying to get it into head but can't find simple explation.Idea gas it is a fictious matter that follows the PV=nRuT or PV = mRuT equation, which has predermined conditions of ideal conditions of the the gas. As temperature for...
47. ### Problem related to the Ideal Gas equation -- Nitrogen under pressure

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 rules...
48. ### Proof question related to the Ideal Gas Law

A cylinder contains an initial volume V1 = 1m^^3 of a perfect gas at initial pressure p1 = 1 bar, confined by a piston that is held in place by a spring. The gas is heated until its volume is doubled and the final pressure is 5 bar. Assuming that the mass of the piston is negligible and that the...
49. ### MHB Maths in Temperature and ideal gas Thermometer

Hi, I didn't understand the maths involved in the below article in regard to temperature and ideal gas thermometer. If any member knows it, may reply me. If triple point of water is fixed at 273.16 K, and experiments show that freezing point of air-saturated water is 273.15 K at 1 atm...
50. ### Finding the Volume of an Ideal Gas

Hi, I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08. Can...