THERMODYNAMICS
Chapter 5: Second Law of Thermodynamics – Extended
Reversibility, Carnot, Entropy & Irreversibility
10 Questions | Easy · Medium · Hard | Full Worked Solutions
Questions at a Glance
Q# Topic Level Key
Concept
1 Statements of the Second Law Easy Statements
2 Perpetual Motion Machines Easy Perpetual
3 Carnot Efficiency Comparison Medium Carnot
4 Entropy — Clausius Definition Medium Entropy
5 Entropy Change of Ideal Gas Medium Entropy
6 Isentropic Efficiency — Turbine Medium Isentropic
7 T-ds Relations Medium T-ds
8 Entropy Generation in Heat Transfer Medium Entropy
9 Increase of Entropy Principle Medium Increase
10 Carnot Refrigerator vs Heat Pump Medium Carnot
Q1. Statements of the Second Law
[Easy]
State both the Kelvin-Planck and Clausius statements of the Second Law. Show they are equivalent
by proving one implies the other.
✔ SOLUTION
KELVIN-PLANCK STATEMENT:
It is impossible for any device that operates in a cycle to receive heat from a single
thermal reservoir and produce a net amount of work.
(No heat engine is 100% efficient.)
CLAUSIUS STATEMENT:
It is impossible to construct a device that operates in a cycle and produces no effect
other than the transfer of heat from a lower-temperature body to a higher-temperature body.
(Refrigerators require work input.)
EQUIVALENCE — Violation of Clausius → Violation of Kelvin-Planck:
Suppose a refrigerator runs without work (violates Clausius): moves Q_L
from cold to hot.
Combine it with a heat engine: engine takes Q_H from hot, produces W,
rejects Q_L to cold.
Net: hot reservoir loses (Q_H – Q_L), net work W is produced — a PMM2
(violates K-P). ✓
The reverse equivalence can be shown similarly.
Thermodynamics — Practice Q&A | Page 1 of 6
, KEY ANSWER: K-P: no 100% heat engine | Clausius: no unaided heat pump |
They are logically equivalent
Q2. Perpetual Motion Machines
[Easy]
Distinguish between a PMM1 and a PMM2. Give an example of each and explain why each violates
a law of thermodynamics.
✔ SOLUTION
PMM1 — Perpetual Motion Machine of the First Kind:
Produces energy from nothing (violates conservation of energy / First
Law).
Example: A device that produces 100 kW of work while receiving only 50 kW of heat.
NET energy creation: ΔE = W_out – Q_in = 100 – 50 = +50 kW from nowhere.
VIOLATION: First Law (energy balance fails).
PMM2 — Perpetual Motion Machine of the Second Kind:
Converts all heat input to work with 100% efficiency (violates Second Law).
Example: A ship powered by extracting heat from the ocean — single reservoir!
The ocean is massive, so heat is abundant — looks attractive, but impossible.
VIOLATION: Second Law (Kelvin-Planck: cannot convert ALL heat to work).
KEY DISTINCTION:
PMM1 creates energy; PMM2 doesn't violate energy conservation
but still violates the directional (quality-degrading) nature of energy processes.
KEY ANSWER: PMM1: violates 1st Law (creates energy) | PMM2: violates 2nd
Law (100% efficiency)
Q3. Carnot Efficiency Comparison
[Medium]
Three heat engines operate between the same source (T_H = 1000 K) and sink (T_L = 300 K).
Engine A: η = 68%, Engine B: η = 70%, Engine C: η = 65%. Classify each as reversible, irreversible,
or impossible.
✔ SOLUTION
Carnot (maximum possible) efficiency:
η_Carnot = 1 – T_L/T_H = 1 – 300/1000 = 0.70 = 70%
CLASSIFICATION:
Engine A (η = 68%): η < η_Carnot → IRREVERSIBLE
Real engine with internal irreversibilities (friction, heat loss).
Possible but not ideal.
Engine B (η = 70%): η = η_Carnot → REVERSIBLE (Carnot engine)
Only achievable as a theoretical ideal.
No real engine can achieve this without perfect conditions.
Engine C (η = 65%): η < η_Carnot → IRREVERSIBLE
Also possible, less efficient than A.
Thermodynamics — Practice Q&A | Page 2 of 6
Chapter 5: Second Law of Thermodynamics – Extended
Reversibility, Carnot, Entropy & Irreversibility
10 Questions | Easy · Medium · Hard | Full Worked Solutions
Questions at a Glance
Q# Topic Level Key
Concept
1 Statements of the Second Law Easy Statements
2 Perpetual Motion Machines Easy Perpetual
3 Carnot Efficiency Comparison Medium Carnot
4 Entropy — Clausius Definition Medium Entropy
5 Entropy Change of Ideal Gas Medium Entropy
6 Isentropic Efficiency — Turbine Medium Isentropic
7 T-ds Relations Medium T-ds
8 Entropy Generation in Heat Transfer Medium Entropy
9 Increase of Entropy Principle Medium Increase
10 Carnot Refrigerator vs Heat Pump Medium Carnot
Q1. Statements of the Second Law
[Easy]
State both the Kelvin-Planck and Clausius statements of the Second Law. Show they are equivalent
by proving one implies the other.
✔ SOLUTION
KELVIN-PLANCK STATEMENT:
It is impossible for any device that operates in a cycle to receive heat from a single
thermal reservoir and produce a net amount of work.
(No heat engine is 100% efficient.)
CLAUSIUS STATEMENT:
It is impossible to construct a device that operates in a cycle and produces no effect
other than the transfer of heat from a lower-temperature body to a higher-temperature body.
(Refrigerators require work input.)
EQUIVALENCE — Violation of Clausius → Violation of Kelvin-Planck:
Suppose a refrigerator runs without work (violates Clausius): moves Q_L
from cold to hot.
Combine it with a heat engine: engine takes Q_H from hot, produces W,
rejects Q_L to cold.
Net: hot reservoir loses (Q_H – Q_L), net work W is produced — a PMM2
(violates K-P). ✓
The reverse equivalence can be shown similarly.
Thermodynamics — Practice Q&A | Page 1 of 6
, KEY ANSWER: K-P: no 100% heat engine | Clausius: no unaided heat pump |
They are logically equivalent
Q2. Perpetual Motion Machines
[Easy]
Distinguish between a PMM1 and a PMM2. Give an example of each and explain why each violates
a law of thermodynamics.
✔ SOLUTION
PMM1 — Perpetual Motion Machine of the First Kind:
Produces energy from nothing (violates conservation of energy / First
Law).
Example: A device that produces 100 kW of work while receiving only 50 kW of heat.
NET energy creation: ΔE = W_out – Q_in = 100 – 50 = +50 kW from nowhere.
VIOLATION: First Law (energy balance fails).
PMM2 — Perpetual Motion Machine of the Second Kind:
Converts all heat input to work with 100% efficiency (violates Second Law).
Example: A ship powered by extracting heat from the ocean — single reservoir!
The ocean is massive, so heat is abundant — looks attractive, but impossible.
VIOLATION: Second Law (Kelvin-Planck: cannot convert ALL heat to work).
KEY DISTINCTION:
PMM1 creates energy; PMM2 doesn't violate energy conservation
but still violates the directional (quality-degrading) nature of energy processes.
KEY ANSWER: PMM1: violates 1st Law (creates energy) | PMM2: violates 2nd
Law (100% efficiency)
Q3. Carnot Efficiency Comparison
[Medium]
Three heat engines operate between the same source (T_H = 1000 K) and sink (T_L = 300 K).
Engine A: η = 68%, Engine B: η = 70%, Engine C: η = 65%. Classify each as reversible, irreversible,
or impossible.
✔ SOLUTION
Carnot (maximum possible) efficiency:
η_Carnot = 1 – T_L/T_H = 1 – 300/1000 = 0.70 = 70%
CLASSIFICATION:
Engine A (η = 68%): η < η_Carnot → IRREVERSIBLE
Real engine with internal irreversibilities (friction, heat loss).
Possible but not ideal.
Engine B (η = 70%): η = η_Carnot → REVERSIBLE (Carnot engine)
Only achievable as a theoretical ideal.
No real engine can achieve this without perfect conditions.
Engine C (η = 65%): η < η_Carnot → IRREVERSIBLE
Also possible, less efficient than A.
Thermodynamics — Practice Q&A | Page 2 of 6
