Isoprocesses

Содержание и основные понятия

The isothermic, isobaric and isochoric processes describe the state changes at the constant of one parameter, and their graphs vary in different coordinates.
GEF · 10 grade
PIF · Baseline
Interactive model
isotherma
isobara
isochor
Status diagram
01
The physical picture
What happens and what boundaries the model has.
Main message
The isothermic, isobaric and isochoric processes describe the state changes at the constant of one parameter, and their graphs vary in different coordinates.
Isotherma in p(V) is hyperbola.
At constant pressure, the volume is proportional to absolute temperature.
With constant volume, the pressure is proportional to absolute temperature.
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
=
c
o
n
s
t
pV=\mathrm{const}
p
V
=
const
Insulated process
V
T
=
c
o
n
s
t
\frac{V}{T}=\mathrm{const}
T
V
​
=
const
The process
p
T
=
c
o
n
s
t
\frac{p}{T}=\mathrm{const}
T
p
​
=
const
isochorous process
Review of the situation
The heating of the gas in a rigid closed vessel is an isochorous process: the volume is constant, the pressure is rising.
04
Links and application
In the real world
The heating of the gas in a rigid closed vessel is an isochorous process: the volume is constant, the pressure is rising.
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 the topic "Isoprocesses" through the model, not just through the formula.
Outcome 2
Clear and correctly use terms: isotherma, isobar, isochor.
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.
isotherma
Line or process at constant temperature.
isobara
Line or process at constant pressure.
isochor
Line or process at constant volume.
Status diagram
A graph showing the state of the system and the processes between them in the co-ordinates of thermodynamic values.
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
=
c
o
n
s
t
pV=\mathrm{const}
p
V
=
const
model effect
It's an isothermic process.
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
The contents of this portion of the ideal gas are linked by the equation Mendeleev-Clapeyron.
ν
=
c
o
n
s
t
,
T
=
c
o
n
s
t
\nu=\mathrm{const},\quad T=\mathrm{const}
ν
=
const
,
T
=
const
The amount of the substance is constant in a closed portion and the insulated process remains at the temperature.
p
V
=
ν
R
T
=
c
o
n
s
t
pV=\nu RT=\mathrm{const}
p
V
=
ν
RT
=
const
The right part is constant, so the pressure is inversely proportional to the volume.
Conditions:
This mass of the ideal gas is in equilibrium at constant absolute temperature.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
V
T
=
c
o
n
s
t
\frac{V}{T}=\mathrm{const}
T
V
​
=
const
model effect
It's a mess.
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
The ideal gas state equation is used.
V
T
=
ν
R
p
\frac{V}{T}=\frac{\nu R}{p}
T
V
​
=
p
ν
R
​
The equation is divided into pT.
p
=
c
o
n
s
t
,
ν
=
c
o
n
s
t
⇒
V
T
=
c
o
n
s
t
p=\mathrm{const},\quad\nu=\mathrm{const}\quad\Rightarrow\quad\frac{V}{T}=\mathrm{const}
p
=
const
,
ν
=
const
⇒
T
V
​
=
const
For this portion, the right side does not change in the isobar process.
Conditions:
This mass of ideal gas passes equilibrium at constant pressure; T is expressed in celvins.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
p
T
=
c
o
n
s
t
\frac{p}{T}=\mathrm{const}
T
p
​
=
const
model effect
It's an isochorous process.
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 Mendeleev-Clapeyron equation for perfect gas.
p
T
=
ν
R
V
\frac{p}{T}=\frac{\nu R}{V}
T
p
​
=
V
ν
R
​
They divide both parts into VT.
V
=
c
o
n
s
t
,
ν
=
c
o
n
s
t
⇒
p
T
=
c
o
n
s
t
V=\mathrm{const},\quad\nu=\mathrm{const}\quad\Rightarrow\quad\frac{p}{T}=\mathrm{const}
V
=
const
,
ν
=
const
⇒
T
p
​
=
const
The ratio is constant at constant volume and quantity.
Conditions:
This mass of ideal gas passes equilibrium at constant volume; T is expressed in Kelvin.
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
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that isotherma in p(V) is hyperbola.
How to Check the Mind
At constant volume pressure, absolute temperature is proportional. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Real gas, vapour saturation and humidity
The ideal model does not take into account the size and gravity of molecules. In the vicinity of condensations, the variations become significant. The saturated vapour is in dynamic equilibrium with the liquid, and its pressure at this temperature is not dependent on the volume as long as both phases are retained. This explains the non-linearity of the isotherm of the real substance.
Σ
Conclusion on the topic
Isoprocesses
The isothermic, isobaric and isochoric processes describe the state changes at the constant of one parameter, and their graphs vary in different coordinates.
Isotherma in p(V) is hyperbola.
At constant pressure, the volume is proportional to absolute 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.