A Carnot engine is an ideal reversible heat engine operating between hot and cold reservoirs through two isothermal and two adiabatic processes.
Learning Outcomes
The Carnot engine is an ideal reversible engine introduced by Sadi Carnot.
It operates between a hot reservoir at T₁ and a cold reservoir at T₂.
Its working substance is modeled as an ideal gas.
The stages are isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
The gas absorbs Q₁ at T₁ and rejects Q₂ at T₂.
After one cycle ΔU = 0, and the P–V loop area is W = Q₁ − Q₂.
Intermediate Level
Ideal Reversible Engine
The Carnot engine is theoretical. Its processes are performed reversibly between two fixed reservoir temperatures while thermal and mechanical equilibrium are maintained.
The Four Stages
Path
Process
Heat
Temperature
Work by gas
a → b
isothermal expansion
Q₁ absorbed
T₁ constant
positive
b → c
adiabatic expansion
Q = 0
falls T₁ → T₂
positive
c → d
isothermal compression
Q₂ rejected
T₂ constant
negative
d → a
adiabatic compression
Q = 0
rises T₂ → T₁
negative
Energy Balance and P–V Diagram
The gas returns to its initial state, so net internal-energy change is zero. Net work equals heat absorbed minus heat rejected and is the enclosed area of the P–V loop.
Key equation
Δ Ucycle=0
Key equation
W=Q1-Q2
Why the Stages Alternate
The isothermal stages exchange heat at fixed reservoir temperatures. The adiabatic stages connect T₁ and T₂ without heat transfer.
Identify the Stage
Explanation: The gas does work using internal energy, so its temperature falls.
Common Mistakes
The cycle has two isothermal and two adiabatic stages.
Heat is exchanged only during isothermal stages.
T₁ is greater than T₂.
Net work is the enclosed loop area.
Short-Question Preparation
Q. What is a Carnot engine?
A. An ideal reversible heat engine operating between two reservoir temperatures.
Q. Name the four stages.
A. Isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
Q. When is heat exchanged?
A. Q₁ is absorbed during isothermal expansion and Q₂ is rejected during isothermal compression.
Q. What does the P–V loop area represent?
A.Net work W = Q₁ − Q₂ per cycle.
Sticky Notes
The Carnot engine is an ideal reversible engine introduced by Sadi Carnot.
It operates between a hot reservoir at T₁ and a cold reservoir at T₂.
Its working substance is modeled as an ideal gas.
The stages are isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
The gas absorbs Q₁ at T₁ and rejects Q₂ at T₂.
After one cycle ΔU = 0, and the P–V loop area is W = Q₁ − Q₂.
60-Second Revision
a→b: isothermal expansion at T₁; b→c: adiabatic expansion to T₂; c→d: isothermal compression at T₂; d→a: adiabatic compression to T₁. ΔUcycle = 0 and W = Q₁ − Q₂.
Summary
A Carnot engine is an ideal reversible heat engine operating between hot and cold reservoirs through two isothermal and two adiabatic processes.
Ask-the-Tutor Modes
Explain it simply.
Walk through the cycle.
Derive the efficiency.
Solve a numerical.
Test me with an MCQ.
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Exam preparation
Exam Focus
Important points
The Carnot engine is an ideal reversible engine introduced by Sadi Carnot.
It operates between a hot reservoir at T₁ and a cold reservoir at T₂.
Its working substance is modeled as an ideal gas.
The stages are isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
The gas absorbs Q₁ at T₁ and rejects Q₂ at T₂.
After one cycle ΔU = 0, and the P–V loop area is W = Q₁ − Q₂.
Common mistakes
The cycle has two isothermal and two adiabatic stages.
Heat is exchanged only during isothermal stages.
T₁ is greater than T₂.
Net work is the enclosed loop area.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Carnot Engine and Carnot Cycle
Sticky Notes · Quick Revision
1.
Key Point 1
The Carnot engine is an ideal reversible engine introduced by Sadi Carnot.
2.
Key Point 2
It operates between a hot reservoir at T₁ and a cold reservoir at T₂.
3.
Key Point 3
Its working substance is modeled as an ideal gas.
4.
Key Point 4
The stages are isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
