4.4 Statements of the Second Law of Thermodynamics

The Second Law of Thermodynamics sets limits on energy conversion and heat flow. It explains why engines can't be 100% efficient and why heat naturally moves from hot to cold objects. This fundamental principle shapes how we design and use machines in everyday life.

Understanding the Second Law helps us grasp why refrigerators need electricity and why car engines waste some energy as heat. It's crucial for improving energy efficiency and tackling real-world engineering challenges in power generation and cooling systems.

The Second Law of Thermodynamics

Statements of second law

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• Kelvin-Planck statement
  • Impossible for a heat engine to produce net work in a complete cycle if it exchanges heat only with objects at a single fixed temperature
  • Heat engine must exchange heat with a high-temperature reservoir (heat source) and a low-temperature reservoir (heat sink) to produce net work in a cycle
  • Examples: steam turbines in power plants, internal combustion engines in vehicles
• Clausius statement
  • Impossible for a cyclical machine to transfer heat from a cooler body to a warmer body without external work input
  • Heat naturally flows from a hot object to a cold object (thermal equilibrium), not the other way around, unless work is done on the system
  • Examples: refrigerators, heat pumps, air conditioners

Efficiency of heat engines

• Reversible heat engines
  • Operate at maximum theoretical efficiency, known as Carnot efficiency [object Object],[object Object]
    • $T_C$: cold reservoir temperature (K)
    • $T_H$: hot reservoir temperature (K)
  • All processes in the cycle are reversible, can be reversed without any net change in the system or surroundings
  • Examples: idealized Carnot cycle, Stirling cycle
• Irreversible heat engines
  • Lower efficiencies than Carnot efficiency due to irreversible processes (friction, heat loss, turbulence)
  • Real-world heat engines are irreversible, cannot achieve maximum theoretical efficiency
  • Examples: gasoline engines, diesel engines, gas turbines
• Comparison
  • Reversible heat engines always have higher efficiency than irreversible heat engines operating between the same two reservoirs
  • Greater temperature difference between hot and cold reservoirs leads to higher efficiency for both reversible and irreversible heat engines

Prohibition of perpetual motion

• Perpetual motion machines of the second kind
  • Hypothetical machines that violate the second law of thermodynamics
  • Claim to convert heat completely into work without any heat rejection to a low-temperature reservoir
  • Examples: overbalanced wheel, capillary power device
• Violation of Kelvin-Planck statement
  • Perpetual motion machine of the second kind would exchange heat with a single reservoir and convert it entirely into work, violating Kelvin-Planck statement
• Violation of Clausius statement
  • Perpetual motion machine of the second kind would transfer heat from a cold reservoir to a hot reservoir without any external work input, violating Clausius statement
• Impossibility of 100% efficiency
  • Second law of thermodynamics limits efficiency of heat engines to less than 100%, making perpetual motion machines of the second kind impossible

Entropy and irreversibility

• Entropy is a measure of the disorder or randomness in a system
• Spontaneous processes in isolated systems always lead to an increase in entropy
• The concept of irreversibility is closely tied to the increase of entropy in real-world processes
• The thermodynamic arrow of time is defined by the direction of increasing entropy
• The heat death of the universe is a hypothetical scenario where the universe reaches maximum entropy