Second law of Thermodynamics

What is Second Law of Thermodynamics ?

The Second Law of Thermodynamics defines the direction of heat transfer and the limitations of energy conversion. While the first law deals with energy conservation, the second law explains why energy transformations are not 100% efficient.

Statements of the Second Law

1. Kelvin–Planck Statement

It is impossible to construct a heat engine that operates in a cycle and converts all heat absorbed into work without rejecting some heat to a sink.

Meaning:

• No heat engine can have 100% efficiency.
• Some energy is always lost as waste heat.

2. Clausius Statement

It is impossible to construct a device that transfers heat from a colder body to a hotter body without external work.

Meaning:

• Heat naturally flows from hot → cold.
• Refrigerators require external work.

Equivalence of Statements

• Violation of one statement implies violation of the other.
• Hence, both statements are equivalent forms of the second law.

Heat Engine, Refrigerator, and Heat Pump

Heat Engine

• Absorbs heat $Q_1$Q1​ from a high-temperature source
• Produces work $W$W
• Rejects heat $Q_2$Q2​ to a low-temperature sink

Efficiency:$$\eta = \frac{W}{Q_1}$$

Refrigerator

• Removes heat from a low-temperature region
• Requires work input

Coefficient of Performance (COP):$$COP_R = \frac{Q_2}{W}$$

Heat Pump

• Supplies heat to a high-temperature region

$$COP_{HP} = \frac{Q_1}{W}$$

Carnot Cycle (Ideal Cycle)

The Carnot cycle is an ideal reversible cycle consisting of:

1. Isothermal Expansion
2. Adiabatic Expansion
3. Isothermal Compression
4. Adiabatic Compression

Carnot Efficiency:

$$\eta_{Carnot} = 1 – \frac{T_2}{T_1}$$

Where:

• $T_1$T1​ = Temperature of source (K)
• $T_2$T2​ = Temperature of sink (K)

Key Points:

• It is the maximum possible efficiency.
• Depends only on temperature limits.

Entropy (S)

Definition

Entropy is a measure of disorder or randomness in a system.

For a reversible process:$$dS = \frac{\delta Q}{T}$$

Important Principles

1. Entropy increases for irreversible processes.
2. For isolated systems: $$\Delta S \geq 0$$ΔS≥0
3. Reversible process: $\Delta S = 0$ΔS=0
4. Irreversible process: $\Delta S > 0$ΔS>0

Irreversibility

Real processes are irreversible due to:

• Friction
• Heat loss
• Unrestrained expansion
• Mixing of fluids

Hence, real efficiency is always less than Carnot efficiency.

Key Conclusions

• Heat cannot be fully converted into work.
• Energy degrades in quality during conversion.
• Entropy of the universe always increases.
• Perfect engines or perpetual motion machines of second kind are impossible.

Applications

• Thermal power plants
• Refrigeration & air conditioning
• Internal combustion engines
• Turbines and compressors

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