Perfect gas

Содержание и основные понятия

The ideal gas ignores its own amount of molecules and its interaction without collision. The pressure is caused by the transmission of impulse to the vessel walls.
GEF · 10 grade
PIF · Baseline
Interactive model
ideal gas
pressure
concentration
Status equation
01
The physical picture
What happens and what boundaries the model has.
Main message
The ideal gas ignores its own amount of molecules and its interaction without collision. The pressure is caused by the transmission of impulse to the vessel walls.
The model is more accurate for diluted gas far from condensation.
The state of the target gas is bound by pressure, volume, and temperature.
The isoprocesses are obtained by recording one of the parameters.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
p
V
=
ν
R
T
pV=\nu RT
p
V
=
ν
RT
Mendeleev-Clapeyron equation
p
=
n
k
T
p=nkT
p
=
nk
T
Microscopic shape
Review of the situation
At constant temperature, doubling the specified mass of the ideal gas reduces the pressure by half.
04
Links and application
In the real world
At constant temperature, doubling the specified mass of the ideal gas reduces the pressure by half.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of "ideal gas" through the model, not just the formula.
Outcome 2
Diluting and correctly using terms: ideal gas, pressure, concentration.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
ideal gas
A single point particle gas model that interacts only in the event of a flexible collision.
pressure
The ratio of normal force to the surface area on which it operates.
concentration
Number of particles per unit volume.
Status equation
Relationship between macroscopic parameters of the equilibrium thermodynamic system.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
p
V
=
ν
R
T
pV=\nu RT
p
V
=
ν
RT
Postulate or Model
Equation of the Mendeleev-Clapeyron.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
V
∝
ν
T
pV\propto\nu T
p
V
∝
ν
T
The gas tests show that, at low density, the product pV is proportional to the quantity of the substance and absolute temperature.
R
=
8.314
…
Дж
мол
ь
−
1
К
−
1
R=8.314\ldots\ \mathrm{Дж\,моль^{-1}К^{-1}}
R
=
8.314
…
J
Like,
♪ I'm not ♪
−
1
K
−
1
The proportionality factor is determined experimentally as the universal gas constant.
p
V
=
ν
R
T
pV=\nu RT
p
V
=
ν
RT
The idealization of neglected small particles without long-term interaction brings empirical gas laws together into the state equation.
Conditions:
For ideal gas in equilibrium state, actual diluted gases are subject to closeness, especially far from condensation.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
p
=
n
k
T
p=nkT
p
=
nk
T
model effect
Microscopic shape.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
V
=
ν
R
T
pV=\nu RT
p
V
=
ν
RT
Take the equation of the state of the perfect gas.
N
=
ν
N
A
,
R
=
k
N
A
N=\nu N_{\mathrm A},\quad R=kN_{\mathrm A}
N
=
ν
N
A
​
,
R
=
k
N
A
​
The quantity of the substance is linked to the number of particles and the gas constant to the constant Boltzmann.
p
=
N
V
k
T
=
n
k
T
p=\frac{N}{V}kT=nkT
p
=
V
N
​
k
T
=
nk
T
After dividing by volume, the N/V ratio is the particle concentration n.
Conditions:
Equivalent ideal gas; n = N/V is the volume concentration of particles, and T is the absolute temperature.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this topic is that the model is more accurate for diluted gas than condensation.
How to Check the Mind
The state of the target gas quantity is bound by pressure, volume and temperature. Then check the units, vector direction, and the behaviour of the result at zero or very large parameter.
Gas mixture and Dalton law
In an ideal mixture, the components almost do not interact, and each creates a partial pressure as if one takes up the whole volume. The full pressure p = p1 + p2 + ... . . piV = .iRT shows that the input of the component is determined by the amount of its substance and the total temperature.
Σ
Conclusion on the topic
Perfect gas
The ideal gas ignores its own amount of molecules and its interaction without collision. The pressure is caused by the transmission of impulse to the vessel walls.
The model is more accurate for diluted gas far from condensation.
The state of the target gas is bound by pressure, volume, and temperature.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.