The Second Law of Thermodynamics sets fundamental limits on energy conversion processes. It explains why heat engines need temperature differences to produce work and why refrigerators require external power to move heat from cold to hot.

This law has far-reaching implications, from determining the efficiency of engines to explaining the direction of natural processes. It introduces the concept of entropy, which measures disorder and helps us understand why certain processes are irreversible.

Statements of the Second Law

Statements of Second Law

• Kelvin-Planck statement
  • Impossible for a heat engine to produce net work in a complete cycle when exchanging heat with a single fixed-temperature body
  • Heat engine must exchange heat with high-temperature reservoir and low-temperature reservoir to produce net positive work in a cycle (car engine, power plant)
• Clausius statement
  • Impossible for a refrigeration machine to operate in a cycle transferring heat from cooler body to warmer body without external aid
  • Heat cannot spontaneously flow from colder body to hotter body without external work performed on the system (refrigerator, air conditioner)

Implications for heat transfer

• Direction of heat transfer
  • Heat naturally flows from high-temperature body to low-temperature body (hot coffee cooling down)
  • Second Law states heat cannot spontaneously flow from cold body to hot body without external work (ice cube melting in warm room)
• Efficiency of heat engines
  • Second Law limits maximum efficiency of heat engine operating between two reservoirs at different temperatures
  • Carnot efficiency $\eta_{Carnot} = 1 - \frac{T_L}{T_H}$ is theoretical upper limit for efficiency of heat engine, where $T_L$ and $T_H$ are absolute temperatures of low-temperature and high-temperature reservoirs
  • Real heat engines always have efficiencies lower than Carnot efficiency due to irreversibilities like friction, heat loss, and other factors (gasoline engine, steam turbine)

Feasibility of thermodynamic processes

• Determining feasibility of a process
  • Second Law used to determine whether proposed thermodynamic process is feasible or not
  • If process violates either Kelvin-Planck or Clausius statement, considered impossible according to Second Law
• Examples of infeasible processes
  1. Heat engine that converts all heat input into work (100% efficiency) is impossible, violates Kelvin-Planck statement (perpetual motion machine)
  2. Refrigerator that transfers heat from colder body to warmer body without external work input is impossible, violates Clausius statement (spontaneous heat flow from cold to hot)

Second Law vs entropy concept

• Entropy and Second Law
  • Entropy measures disorder or randomness in a system (messy room vs organized room)
  • Second Law states entropy of isolated system always increases or remains constant during spontaneous process
  • In any real process, total entropy of system and surroundings always increases (mixing hot and cold water)
• Irreversibility and entropy generation
  • Irreversible processes like friction, heat transfer through finite temperature difference, and unrestrained expansion always generate entropy
  • Entropy generated during irreversible process measures lost work potential or decrease in quality of energy (waste heat from engine)
• Entropy and arrow of time
  • Second Law and increase in entropy provide direction for flow of time, known as "arrow of time"
  • Arrow of time consistent with everyday experiences, where natural processes tend to move from ordered to disordered states and heat flows from hot to cold bodies (broken glass doesn't spontaneously reassemble)