Second law and heat machines

Содержание и основные понятия

The second law sets the direction for spontaneous processes: heat passes from hot to cold, and a cyclical machine cannot completely turn it into work.
GEF · 10 grade
PIF · Baseline
Interactive model
Entropy
irreversibility
cycle
heater
Fridge
01
The physical picture
What happens and what boundaries the model has.
Main message
The second law sets the direction for spontaneous processes: heat passes from hot to cold, and a cyclical machine cannot completely turn it into work.
The entropy of the isolated system is not decreasing.
The refrigerator carries heat against the natural direction at the expense of external work.
The Carno cycle sets the upper limit of the KPA between the two temperatures.
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.
η
Карно
=
1
−
T
2
T
1
\eta_{\mathrm{Карно}}=1-\frac{T_2}{T_1}
η
Carno
​
=
1
−
T
1
​
T
2
​
​
RAP limit
Q
1
=
A
+
Q
2
Q_1=A+Q_2
Q
1
​
=
A
+
Q
2
​
Vehicle balance
Review of the situation
Neither improved lubricant nor ideal thermal insulation will allow the machine to reach 100 per cent of the final temperature.
04
Links and application
In the real world
Neither improved lubricant nor ideal thermal insulation will allow the machine to reach 100 per cent of the final temperature.
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 "Second law and heat machines" through the model, not just the formula.
Outcome 2
Clear and correctly use terms: entropy, irreversibility, cycle.
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.
Entropy
Status function describing the number of microstates available and the direction of thermal processes.
irreversibility
The property of a real process that does not automatically go exactly backwards without changing around.
cycle
Combination of processes after which the system returns to its original state.
heater
A device that cyclically converts the heat received into mechanical work.
Fridge
In a heater, a body with a lower temperature, to which the working body gives part of the heat.
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.
η
Карно
=
1
−
T
2
T
1
\eta_{\mathrm{Карно}}=1-\frac{T_2}{T_1}
η
Carno
​
=
1
−
T
1
​
T
2
​
​
model effect
It's the limit.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
A
=
Q
1
−
Q
2
,
η
=
A
Q
1
=
1
−
Q
2
Q
1
A=Q_1-Q_2,\quad\eta=\frac{A}{Q_1}=1-\frac{Q_2}{Q_1}
A
=
Q
1
​
−
Q
2
​
,
η
=
Q
1
​
A
​
=
1
−
Q
1
​
Q
2
​
​
For a cyclical machine, work is equal to the difference of heat received and delivered.
Q
1
T
1
=
Q
2
T
2
\frac{Q_1}{T_1}=\frac{Q_2}{T_2}
T
1
​
Q
1
​
​
=
T
2
​
Q
2
​
​
In the reversible Carno cycle, the total change in entropy is zero.
Q
2
Q
1
=
T
2
T
1
⇒
η
=
1
−
T
2
T
1
\frac{Q_2}{Q_1}=\frac{T_2}{T_1}\quad\Rightarrow\quad\eta=1-\frac{T_2}{T_1}
Q
1
​
Q
2
​
​
=
T
1
​
T
2
​
​
⇒
η
=
1
−
T
1
​
T
2
​
​
The setting of the heat ratio gives the maximum CDR between the two temperatures.
Conditions:
Carno's ideal reversible machine between the thermostats T1 > T2 > 0; the temperature in the celvins. The real machines have a smaller CPD.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
Q
1
=
A
+
Q
2
Q_1=A+Q_2
Q
1
​
=
A
+
Q
2
​
model effect
The balance of the car.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
U
цикл
=
0
\Delta U_{\mathrm{цикл}}=0
Δ
U
cycle
​
=
0
After the complete cycle, the working body returns to its original state, so its internal energy does not change.
0
=
(
Q
1
−
Q
2
)
−
A
0=(Q_1-Q_2)-A
0
=
(
Q
1
​
−
Q
2
​
)
−
A
Under the first law, the resulting heat in the cycle is equal to the work done.
Q
1
=
A
+
Q
2
Q_1=A+Q_2
Q
1
​
=
A
+
Q
2
​
The heat from the heater is spent on the work and heat transfer to the refrigerator.
Conditions:
The heater is cycled; Q1 and Q2 indicate the positive heat modules from the heater and to the refrigerator, and A is the machine's cycle work.
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 formula cannot be transferred to any situation simply because of the coincidence of letters. The key condition of this topic is that the entropy of the isolated system is not diminished.
How to Check the Mind
The refrigerator shall transfer heat to the natural direction by external work. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Second law and heat machines
The second law sets the direction for spontaneous processes: heat passes from hot to cold, and a cyclical machine cannot completely turn it into work.
The entropy of the isolated system is not decreasing.
The refrigerator carries heat against the natural direction at the expense of external work.
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.