Topic 8.87 min read
Carnot Engine and Carnot Cycle
A Carnot engine is an ideal reversible heat engine operating between hot and cold reservoirs through two isothermal and two adiabatic processes.
Choose Your Level
Beginner Level
A Carnot engine is a perfect theoretical model. Its gas expands at the hot temperature, expands without heat to cool, is compressed at the cold temperature, and is compressed without heat to return to the start.
Recommended for Class 11
Carnot Engine and Carnot Cycle
Overview
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.
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.
Exam Focus
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.
Important formulas
- ΔUcycle = 0
- W = Q₁ − Q₂
Common exam traps
- 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.
Long question structure
Definition → assumptions → stages or derivation → graph → numerical.
Common Mistakes
Common Mistakes
- Mistake
The cycle has two isothermal and two adiabatic stages.
- Mistake
Heat is exchanged only during isothermal stages.
- Mistake
T₁ is greater than T₂.
- Mistake
Net work is the enclosed loop area.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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.
A Carnot engine is an ideal reversible heat engine operating between hot and cold reservoirs through two isothermal and two adiabatic processes.
- Definition
- A Carnot engine is an ideal reversible heat engine operating between hot and cold reservoirs through two isothermal and two adiabatic processes.
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Exam Practice
Important Question
Q1. What is a Carnot engine?
Important Question
Q2. Name the four stages.
Important Question
Q3. When is heat exchanged?
Important Question
Q4. What does the P–V loop area represent?