# What is Ideal gas law: Definition and 238 Discussions

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:

P
V
=
n
R
T

{\displaystyle PV=nRT}
where

P

{\displaystyle P}
,

V

{\displaystyle V}
and

T

{\displaystyle T}
are the pressure, volume and temperature;

n

{\displaystyle n}
is the amount of substance; and

R

{\displaystyle R}
is the ideal gas constant. It is the same for all gases.
It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently) by August Krönig in 1856 and Rudolf Clausius in 1857.

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1. ### Volumetric flow rate ratio calculation

I'm using two tanks of nitrogen and oxygen and mixing them in different ratios to change the oxygen partial pressure in the system. System is opened to the atmosphere through the venting pipe which therefore sets the total pressure of the system to 1 bar. System is opened and gases flow through...
2. ### I State equations for a thermodynamic substance/system

Hi, as follow up to this thread I believe for any substance/thermodynamic system there exists actually a set of 3 state equations between the 5 variables ##(U,T,S,p,V)##. For example in the case of ideal gas which are the 3 equations ? Thanks.
3. ### Calculating the central temperature of the Sun using the ideal gas law

I derived the equation for P so I substituted that into this equation. I'm struggling with finding rho_c (central density) and rho. Am I supposed to use the average density for rho (can calculate this since I know the radius of Sun and mass)? That still leaves the problem with the central...
4. ### Work done during quasi-static, isothermal expansion from P_i to P_f

I am posting this question after I thought I had easily solved the problem, but then when I checked the back of the book I saw that I was incorrect. Here is what I did. (a) $$W=-\int_{V_i}^{V_f} PdV\tag{1}$$ $$V=V(P,T)-\frac{nRT}{P}\tag{2}$$ dV=\left ( \frac{\partial V}{\partial P}\right...
5. ### Verification of ideal gas law experiment

TL;DR Summary: I measured the mass of CO2. Can someone verify my calculations? I took a soda bottle and filled it with Carbon Dioxide then weighted its mass as I changed pressures. My figures get very close (5-10%) within the calculated values for psig but not psi-absolute. Can someone confirm...
6. ### A Why are the Navier-Stokes equations inconsistent in this case?

Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of the pipe from the one dimensional assumption, let us denote the velocity of the fluid down the...
7. ### Predicting Remaining Pressure in Compressed Gas Cylinder

Well, it's been nearly 10 years since my last post, and it's been about that long since I've thought about ideal gases, so here we go :smile:. Description of Setup I have a system that uses compressed gas cylinders as a source to slowly purge an optical payload. The source is 12x compressed...
8. ### Why must we use absolute temperature for the Ideal Gas Law?

For this problem, The solution is, However, why must we use absolute temperature for the ideal gas law (i.e why can we not use Celsius for T) Many thanks!
9. ### Mixing two ideal gases with different V, T at constant pressure

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...
10. ### Total force from air spring model (double acting piston)

Hi everyone, I'm an electrical engineer working on making a linear model for a power take-off system. I've gotten inertial, friction, and hydraulic/electric components done, but what is really confusing me is the gas system; I haven't taken ANY thermodynamics. To simplify it, it is modeled as a...
11. ### B Ideal gas formula not working?

Hi! I wanted to do some basic calculations for temperature T on a water-filled pot. I noticed something strange on my calculations, and couldn’t figure out what was wrong... So here it is: The ideal gas formula: k=PV The actual formula Relates equally the product PV with the a constant...
12. ### Ideal gas law- Find the pressure

Question: Answer: In the third last line of working, I do not understand why the pressure variable is changing? Shouldn't pressure remain constant and only the Volume change?
13. ### Thermodynamics problem (ideal gas law, kinetic theory, processes, etc.)

It is a long problem, but it is simple to understand. I am having trouble with part A. My attempt: Pressure outside > pressure inside container. pV = constant (isothermal). At equilibrium, all gases are at atmospheric pressure. Because it is quasi-static, the pressures of both compartments are...
14. ### 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
15. ### (Dry) Volume Ideal Gas Law Calculation

If the question was asking for (dry) volume, how would you do that?
16. ### Pressure in a bomb calorimeter at the moment of combustion

First, I calculated the number of moles of glucose. n = m / M n = 1.8 / 180 n = 0.01 moles of glucose So I checked the combustion reaction. 1 C6H12O6 + 6 O2 -> 6 CO2 + 6 H20 1 + 6 -> 6 + 6 0.01 + 0.06 -> 0.06 + 0.06 I considered the number of moles at the end of the reaction. I subtracted...
17. ### 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)...
18. ### How is the Ideal Gas Law Derived from Temperature and Pressure Relationships?

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.
19. ### 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...
20. ### Chemistry Ideal Gas Law and Partial Pressures

I had already found the Mass of the product (C3H3N) produced by this reaction (theoretical mass at 100% yield) in a previous problem. I did this by finding the Limiting Reagent (C3H6) in the reaction , calculating the number of moles of C3H6 and using the Molar Ratios in the balanced reaction...
21. ### Ideal Gas Law: Question about a compressor exam question

This is a question in my midterm. I calculated for the answer as c) 11.7 atm by the Ideal Gas Law. The professor states that "all the air is originally at 1 atm" in the prompt indicates an idea of "both 70 L of air and existing 6 L of air in the tank are at 1 atm", and he grades d) 12.7 atm as...
22. ### Triple Product Rule Equivalency

##p=\frac {RT} v;~p=p(T,v)~...1## ##v=\frac {RT} p;~v=v(T,p)~...2## ##T=\frac {pv} R;~T=T(p,v)~...3## ##Considering~eq.~1:## ##p=\frac {RT} v \Rightarrow (\frac {\partial p} {\partial v})_T=-\frac {RT} {v^2}## ##Considering~eq.~2:## ##v=\frac {RT} p \Rightarrow (\frac {\partial v}...
23. ### Ideal Gas Law in Two Dimensions

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...
24. ### Calculations using the Ideal Gas Law

2.1 * 10^-4m/3 Temperature 310K Pressure: 5.3 * 105 Pa So the Ideal gas formula is PV = nRT 2.1*10^-4m^3 Times 5.3*105Pa = n * Gas Constant * Temperature 2.1*10^-4m^3 (*) 5.3*105Pa = # of moles * I'm not sure what I was doing, but the whole equation stuff got hard and I stopped. I left...
25. ### What do the symbols in the gas equation represent?

This was the equation that they showed me. I thought P was for pressure, V for Volume, T for Temperature, R for Gas Constant, and n for the number of moles. Was I correct for the initials?
26. ### Find Vol 2 in Ideal Gas Law Problem with V1 and V2 Open and V3 Shut

Please refer to diagram. V1 is open initially then V2 is open for 5 minutes for pressure to equalize. V1 and V2 are then shut. V3 is opened. What is Vol 2 ? P(final)*V(final) = n(final)* R*T => (Vol1 + Vol2) = n(final)*R*25C/ 0.070 Torr where n(final) = n(Vol1) + n(Vol2) If I shut V3, I...
27. ### Thermodynamics and ideal gas law concepts

I'm having trouble wrapping my head around some thermodynamics and ideal gas law concepts. I don't have a specific textbook question but Just a concept I'm having trouble with. What I'm struggling with is understanding some of the relations between pressure, volume and temperature...
28. ### B Confused about the ideal gas law

Ok, i am struggling to figure something out. I don't know why math is so much easier than physics haha. ok, here is my struggle. I have two states, state 1 and 2, which i will call just 1 and 2. 1: T=298kelvin V=0.025m(cubed) P=310Kpa Mass1=Mass2 R=0.2870 2: T=323kelvin V=0.025m(cubed) P=...
29. ### Exploring the Ideal Gas Law: A Balloon Problem

Homework Statement Homework Equations Ideal gas law The Attempt at a Solution The solution to this problem assumes the pressure inside the balloon is the same as the outside pressure, i.e. atmospheric pressure. Is this a valid assumption? I would guess otherwise.
30. ### What would be a real-life example of the ideal gas law?

Homework Statement What is a real-life example of the ideal gas law? Homework Equations PV = nRT (Pressure x volume = number of moles x the gas constant x temperature in Kelvin) The Attempt at a Solution https://www.reference.com/science/ideal-gas-law-used-everyday-life-3dacbd6ebd3b5949...
31. ### Ideal Gas Law and Pressure at 80°C

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...
32. ### Basic physics units problems involving the Ideal Gas Law

Homework Statement The following is the equation of ideal gas law, where p is pressure (Force/Area), V is volume, n is number of moles and T is temperature in Kelvin. What is the fundamental unit of R? pV = nRT A. kg^−1 · m^−2 · s^ 2 · K · mol B. kg^−1 · m^−4 · s ^2 · K · mol C. kg · m^4 · s...
33. ### Using Ideal Gas Law to Calculate Vertical Pressure Gradient

Homework Statement Consider a cylindrical parcel of air of area A and infinitesimal height dz. If this air parcel is to remain stationary, the difference between the total pressure forces exerted on its top and bottom faces must be equal to its weight. Use this information and the ideal gas...
34. ### I Application of the ideal gas law

Hi, I want to calculate the amount of liquid nitrogen (at boiling temp.) needed to build a pressure of 10.1 bar in a vessel of volume 66 m3. The liquid will be poured slowly into the vessel, boil off and fill the volume with gas at the specified pressure. I make the assumption that the process...
35. ### Relation between boltsmann/gas constant and temperature

so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation : PV=nRT is true. i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird. each molocule should be only deflected in the...
36. ### How do I calculate the gauge pressure?

Homework Statement An automobile tire is pumped up to a gauge pressure of ##2.0 \times 10^5 ## Pa when the temperature is 27◦ C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77◦ C? Assume that the volume remains fixed and take...
37. ### Heat and work when temperature increases by 1 degree

Homework Statement Kinetic energy per mol is 3/2KTHomework 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 =...
38. ### Thermodynamics: Ideal Gas Law, find the temperature

Homework Statement A 3-ft^3 container is filled with 2-lbm of oxygen at a pressure of 80 psia. What is the temperature of the oxygen?Homework Equations pV= nRT T= PV/nR R= 10.7316 psia x ft^3/ lbmol x R The Attempt at a Solution Hi everyone! So I understand how to use the Ideal Gas Law but my...
39. M

### Ideal Gas Law Homework: Calculating Number Density and Spacing Between Molecules

Homework Statement Consider an ideal gas at 25.0 degrees Celsius and with a pressure of 1.00 atm. a) What is the "number density" of the molecules, expressed as molecules per unit volume? (Cubic meter, cubic centimeter or liter) b) What is the typical spacing between molecules in the gas? Of...
40. ### What is the Ideal Gas Law for a Two-Bulb System with Varying Temperatures?

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...
41. ### What is the Power of Sound Waves in a Tube Filled with Helium Gas?

Homework Statement Suppose a tube is filled with helium gas at a pressure of 0.11MPa and a temperature of 297K. If a piston of area of 400mm2 at one end of the tube creates sound by moving sinusoidally with a frequency of 60Hz, creating a wave with amplitude of 3.8mm, what power goes into (I'm...
42. ### How to find added thermal heat in monoatomic gas?

Homework Statement for number 3,4,5 I'm still tryingHomework Equations PV/T = PV/T q = ΔU + W W = P ΔV The Attempt at a Solution (3) I used PV/T = PV/T to find the ΔT for each process for A→B I find PV/TA = P3V/TB ----- TB = 3TA (T increase) for B→C I find P3V/TB = 4P3V/TC ----- TC =...
43. ### Ideal Gas Law -- Isobaric Epansion followed by....

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...
44. ### Understanding the Different Forms of the Ideal Gas Law and Their Applications

Hey I was hoping someone could be me a succinct method of knowing what form of the Ideal gas law I need to use and in particular the different R's associated with each form. Form my Thermodynamics class we use PV = nRT Pv = RT PV = mRT Little v being the specific volume (which changes the R...
45. ### Density of an ideal gas as a function of height

Homework Statement If air has a density of ρ0 on the surface, calculate its density as a function of the height y for two scenarios: (a) the temperature is constant at T0; (b) the temperature decreases linearly T(y) = T0 − ay. Express your results using the given variables together the...
46. ### Physics of a Hot Air Balloon

Homework Statement A hot-air balloon stays aﬂoat because hot air at atmospheric pressure is less dense than cooler air at the same pressure.If the volume of the balloon is 500 m3 and the surrounding air is at 60◦F. What is the maximum load (including the weight of balloon, but excluding the...
47. ### First law of thermodynamics: why some equations can't be used

Homework Statement A cylinder fitted with a frictionless piston contains 5.0×10-4m3 of an ideal gas at a pressure of 1.0×105 Pa and temperature of 300K. The gas is then (i) heated at constant pressure to 450K, and then (ii) cooled at constant volume to the original temperature of 300K. The...
48. ### I Ideal Gas Law and Differentiation

Is it possible to calculate the rate of change of n with respect to rate of change of Pressure and rate of change of Temperature with V unknown but constant by PV = nRT? Rate of change of Pressure and rate of change of temperature can be measured. R and V are constants.
49. ### What are the units for the Universal Gas Constant?

Homework Statement Hello, I am not asking for the answer to an example, rather how the book got some numbers. The problem is an example from the book and shows me the solution but does not show the steps. Given: The compressed air tank has a volume of .84 ft^3. The temperature is 70 F and the...
50. N

### Calculating Internal Energy & Temperature Change of Ideal Gas

Homework Statement What is the change in internal energy (in Joules) of an ideal gas that does 4.675x10^5J of work, while 2.95x10^6J of heat is transferred into the system and 7.95x10^6J of heat is transferred from the system to the environment? Calculate the change in temperature of the two...