Second Law of Thermodynamics

Second Law of Thermodynamics

• Overview

  • The second law of thermodynamics builds upon the first law (conservation of energy) by adding constraints on how energy transactions can occur.
  • A process that satisfies the first law may not take place unless it also satisfies the second law.

• Key Objectives

  • Understand the concept of the second law of thermodynamics.
  • Recognize valid processes according to thermodynamic laws.
  • Differentiate between thermal energy reservoirs, reversible and irreversible processes, heat engines, refrigerators, and heat pumps.
  • Comprehend the Kelvin–Planck and Clausius statements of the second law.

Major Uses of the Second Law

• Direction of Processes
  • The second law helps determine the direction in which natural processes occur.
• Quality of Energy
  • Energy has both quality (related to the second law) and quantity (related to the first law).
  • Quality refers to the degree of energy degradation during a process.
• Performance Limits
  • It provides theoretical limits for the performance of engineering systems like heat engines and refrigerators.

Thermal Energy Reservoirs

• Definition
  • A thermal energy reservoir is a hypothetical body with large thermal energy capacity that can absorb or supply heat without a temperature change.
• Examples
  • Large bodies of water (oceans, lakes)
  • Atmospheric air
  • Two-phase systems

Heat Engines

• Functionality
  • Heat engines convert heat into work through the following process:
  1. Receive heat from a high-temperature source.
  2. Convert a portion of this heat to work.
  3. Reject remaining heat to a low-temperature sink.
  4. Operate on a cyclic process.
• Working Fluid
  • Typically involves a fluid for heat transfer during cycles.

Key Terms

• Heat Transfers
  • Q_{in}: Heat supplied to the working fluid from a high-temperature source.
  • Q_{out}: Heat rejected to a low-temperature sink.
  • W_{out}: Work output from the engine.
  • W_{in}: Work required to compress fluids.

Thermal Efficiency of a Heat Engine

• Efficiency Formula
  • ext{Thermal Efficiency} ( ext{η}{th}) = rac{W{net,out}}{Q_{in}}
  • Also expressed as ext{η}{th} = 1 - rac{Q{out}}{Q_{in}}
• Waste Energy
  • A heat engine must reject some energy to function properly; a heat rejection process is crucial for completing the cycle.

Kelvin–Planck Statement

• Definition
  • It states that it's impossible for any cyclic device to convert heat from a single reservoir into work without rejecting some heat.
  • No engine can achieve 100% thermal efficiency due to inherent limitations, not just dissipative effects.

Refrigerators and Heat Pumps

• Purpose
  • Refrigerators transfer heat from a low-temperature medium to a high-temperature medium.
• Refrigeration Cycle
  • Typically employs the vapor-compression refrigeration cycle.
• Coefficient of Performance (COP)
  • For refrigerators:
  • ext{COP}{R} = rac{Q{L}}{W_{net,in}}
  • For heat pumps:
  • ext{COP}{HP} = rac{Q{H}}{W_{in}}
• Efficiency Expression
  • ext{COP}{R} = rac{Q{L}}{Q{H}-Q{L}}
  • ext{COP}{HP} = rac{Q{H}}{Q{H}-Q{L}}
• Example Calculations
  • Focus on practical applications for determining COP and efficiency.

Irreversible Processes

• Definition of Irreversible Process
  • A process that cannot be reversed without changes to the surroundings.
• Causes of Irreversibility
  • Factors like friction, unrestrained expansion, mixing fluids, and finite temperature differences cause irreversibilities.
• Reversible Processes
  • Types:
  • Internally reversible: No irreversibilities occur within the system.
  • Externally reversible: No irreversibilities occur outside the system.
  • Totally reversible: No irreversibilities at all.

The Carnot Cycle

• Carnot Principles
  • The cycle is an idealized engine cycle which is totally reversible.
• Efficiency of Carnot Engines
  • Involves considering high and low temperature reservoirs:
  • ext{η}{th} = 1 - rac{T{L}}{T_{H}}
• Applications
  • Understanding the Carnot efficiency helps analyze the theoretical limits of actual heat engines.

Summary of Key Statements

• Key Equations
  • Efficiency in Heat Engines: ext{η}{th} = 1 - rac{T{L}}{T_{H}}
  • Refrigerator Efficiency: ext{COP}{R} = rac{Q{L}}{W_{in}}
  • Heat Pump Efficiency: ext{COP}{HP} = rac{Q{H}}{W_{in}}
  • Understanding Relationships
  • Thermal efficiency and coefficient of performance showcase energy conversion limits in thermodynamic systems.