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.
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...
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...
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...
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...
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...
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?
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.
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...
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...
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...
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...
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...
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...
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...
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...
Homework Statement
for number 3,4,5 I'm still trying
Homework 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 -----...
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...
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...
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...
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...
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...
The question I'm stuck on is:
P = NKBT/(V-Nb) - aN2/(V2) -----> (1)
Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b kBT/(8a). Call these...
I have acquired a new compressor rated at 540 L/min @ 7 bar 150L tank
I decided to test this at 23 degC, timing compression at 2 bar intervals (0-2, 2-4 etc.)
I was surprised to find that it maintained 34 seconds at each interval up to 8 bar (but this could be poor experimental...
Homework Statement
An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high...
Homework Statement
A bubble comes from the bottom of the tank of water to the surface and triples in its volume. If the temperature of the tank of water doesn't deppend on the depth what is the depth of the tank that the bubble was at?
Homework Equations
##PV=nRT##
The Attempt at a Solution...
In the derivation the first step used F=Δmv/t and for t, they used t=2L/v where L is the distance between one end to the other end of the wall.
But I don't understand why we use 2L as the distance. Isn't the force exerted by that molecule only for the very short period where the molecule is in...
Homework Statement
Two kilograms of air at 5 bar, 350 K, and 5 kg of carbon monoxide, initially at 4 bar, 450 K, are confined to opposite sides of a rigid, well-insulated container by a partition. The partition is free to move and allows conduction from one gas to the other without energy...
Two Thermally insulated cylinders, A and B, of equal volume, both equipped with pistons, are connected by a valve. Initially A has its piston fully withdrawn and contains a perfect monatomic gas at temperature T, while B has its piston fully inserted, and the valve is closed. Calculate the final...
Homework Statement
Problem from the book "Engines, Energy and Entropy", Page 55, question 7 has me stumped. It doesn't feel like their is sufficient information to work out the mass of the air. They've given us density (as seen in the picture, if the upload works) , which is mass over volume...
Homework Statement
A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00260 m3 of helium at an absolute pressure of 1.10 x 105 Pa. The cylinder contains helium at an absolute pressure of 1.80 x 105 Pa and...
Homework Statement
Assume that in an alternate universe, the laws of physics are very different from ours and that "ideal" gases behave as follows:
(i) At constant temperature, pressure is inversely proportional to the square of the volume.
(ii) At constant pressure, the volume varies directly...
Homework Statement
96 grams of oxygen and 50 grams of hydrogen gas occupy separate, equal sections of 200 liter tank. The divide is removed and the gases are allowed to mix and react with each other. Temperature is kept constant at 120 degrees celsius
2. Homework Equations [/B]
b) find the...