Thermodynamics Class 11 Physics Quick Recall Sheet (Short Notes 2026-27)

Energy Visual: Heat Engines, P-V Diagrams, and Entropy

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Zeroth Law: Leads to the concept of Temperature.

1st Law: ΔQ = ΔU + ΔW. (Conservation of energy).

Isothermal: T = constant; ΔU = 0; W = nRT ln(V2/V1).

Adiabatic: ΔQ = 0; PVᵞ = const; W = (P1V1 - P2V2) / (γ - 1).

Carnot Efficiency: η = 1 - T2/T1. (T1 = source, T2 = sink). 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Thermodynamics is the study of heat, work, and the transformation of energy from one form to another. Unlike mechanics, which focuses on individual particles, thermodynamics deals with large-scale systems and their "State Variables" like pressure, volume, and temperature. This chapter is the heartbeat of modern engineering—from the internal combustion engine in your car to the massive turbines in power plants. In this "Comprehensive" guide, we provide exhaustive derivations for work done in various processes, a step-by-step analysis of the Carnot Cycle, and the rigorous mathematical proofs required for top-tier competitive exams like JEE and NEET.

1. Thermodynamic Systems and State

System: The part of the universe under study. (Open, Closed, or Isolated).
State Variables: P, V, T, n, U.
Equation of State (Ideal Gas): PV = nRT.

2. The First Law of Thermodynamics

Statement: The heat supplied to a system (ΔQ) is equal to the sum of the increase in its internal energy (ΔU) and the work done by the system (ΔW). Formula: ΔQ = ΔU + ΔW

Internal Energy (U): A state function depending only on temperature.
Sign Convention: Work done by the system is Positive (+); Work done on the system is Negative (-).

3. Derivations: Work Done in Different Processes

Work done by a gas is given by the integral: W = ∫ P dV.

I. Isothermal Process (T = Constant)

For an ideal gas: P = nRT / V.
W = ∫ [V1 to V2] (nRT / V) dV
W = nRT [ln V]_V1^V2
W = nRT ln(V2 / V1). (Proven)

Log Base 10: W = 2.303 nRT log(V2 / V1).

II. Adiabatic Process (Q = Constant)

In an adiabatic process, PVᵞ = K (where γ = Cp/Cv).

P = K / Vᵞ.
W = ∫ [V1 to V2] (K / Vᵞ) dV = K [V⁻ᵞ⁺¹ / (1-γ)]_V1^V2
Substituting K = P1V1ᵞ = P2V2ᵞ:
- W = (P2V2 - P1V1) / (1-γ). (Proven)
In terms of temperature: W = nR(T1 - T2) / (γ - 1).

4. The Carnot Cycle: The Ideal Heat Engine

The Carnot Cycle is a theoretical cycle consisting of four reversible steps:

Isothermal Expansion (Step 1): Heat Q1 is absorbed at T1.
Adiabatic Expansion (Step 2): Temperature drops from T1 to T2.
Isothermal Compression (Step 3): Heat Q2 is rejected at T2.
Adiabatic Compression (Step 4): Temperature rises back to T1.

Derivation: Efficiency (η)

Efficiency (η) = Work Done / Heat Supplied = (Q1 - Q2) / Q1.
η = 1 - (Q2 / Q1).
For a Carnot Cycle, it is mathematically proven that Q2 / Q1 = T2 / T1.
Final Result: η = 1 - (T2 / T1). (Proven) Conclusion: Efficiency depends only on the temperatures of the source and sink.

5. The Second Law of Thermodynamics

The Second Law sets the direction of energy transfer and limits efficiency.

Kelvin-Planck Statement: No engine can extract heat from a reservoir and convert it entirely into work without some loss to a sink. (Perfect efficiency is impossible).
Clausius Statement: Heat cannot flow spontaneously from a colder body to a hotter body without external work.

Comprehensive Exam Strategy (Q&A)

Q1: Why is an adiabatic process faster than an isothermal one? Answer: An Adiabatic process involves no heat exchange, requiring excellent insulation or extreme speed so that heat has no time to flow. An Isothermal process requires slow movement to allow heat exchange with the surroundings to maintain constant temperature.

Q2: Can a heat engine have 100% efficiency? Answer: No. According to the Carnot Efficiency η = 1 - T2/T1, for η to be 1 (100%), the sink temperature T2 must be Absolute Zero (0 K). According to the Third Law of Thermodynamics, reaching absolute zero is physically impossible.

Q3: Refrigerator vs Heat Engine: What is the COP? Answer: A refrigerator is a "reverse heat engine." Instead of efficiency, we measure the Coefficient of Performance (COP). COP = Q_sink / Work = T2 / (T1 - T2).

Related Revision Notes

Conclusion

Thermodynamics is the science of limits. By understanding the mathematical proofs behind heat engines and energy conversion, you gain the ability to optimize complex systems and understand the fundamental constraints of our universe. Master the derivations for Isothermal and Adiabatic work—these are the pillars upon which the entire industrial world is built. Stay efficient, watch your entropy, and always respect the Second Law!

Reference: Journal of Thermal Science and Engineering