Unit 4: Second Law of Thermodynamics

Limitation of First Law of Thermodynamics

• First law of thermodynamics states that energy is conserved, but it does not specify the direction of energy transfer.
• The first law is necessary but not sufficient for a process to occur.
• Examples of the limitation of the first law:
  • Ice cream melting when left open to the atmosphere, but it does not solidify back without external work.
  • Joule's experiment, where the fall of weight causes rotation of paddle and increases temperature of water, but increase in temperature of water does not lift the weight.
  • A running vehicle stopping due to brakes, where the internal energy of brakes increases, but the hot brakes do not cause the wheels to rotate.

Basic Definitions

• Thermal reservoir: a large system that can absorb or release energy as heat without changing its temperature.
• Heat engine: a cyclically operating device that absorbs energy as heat from a high-temperature reservoir, converts part of it into work, and rejects the rest to a low-temperature reservoir.
• Efficiency of a heat engine: ratio of work output to heat supply.
• Heat pump: a device that transfers heat energy from a cold body to a hot body, using a small amount of external work.

Second Law of Thermodynamics

• Kelvin-Planck statement: it is impossible to construct an engine that converts all the heat energy into work.
• Clausius statement: it is impossible to construct a heat pump that transfers heat from a cold body to a hot body without external work.
• Both statements are equivalent and imply that it is impossible to have a machine that violates the second law of thermodynamics.

Perpetual Motion Machines (PMM)

• PMM-I: a machine that violates the first law of thermodynamics, producing work without energy input.
• PMM-II: a machine that violates the second law of thermodynamics, converting internal energy into work with 100% efficiency.
• Both types of PMM are impossible.

Concept of Reversibility and Irreversibility

• Reversible process: a process that can be reversed without changing the system or surroundings.
• Irreversible process: a process that cannot be reversed, resulting in a change in the system or surroundings.
• Causes of irreversibility: friction, heat transfer, and other factors.

Carnot Cycle

• A reversible cycle that consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
• The Carnot cycle is the most efficient cycle possible, with an efficiency of 1 - (T_c / T_h), where T_c and T_h are the temperatures of the cold and hot reservoirs, respectively.

Carnot Theorem

• All heat engines operating between a given temperature source and sink have an efficiency less than or equal to the Carnot engine.
• The Carnot theorem is a fundamental limit on the efficiency of heat engines.

Absolute Thermodynamic Temperature Scale

• A temperature scale based on the principles of thermodynamics, with the triple point of water defined as 273.16 K and absolute zero defined as 0 K.
• The absolute temperature scale is a universal scale that is applicable to all systems, regardless of their composition or state.

Reverse Carnot Cycle (Carnot Refrigeration Cycle)

• A cycle that operates in reverse, transferring heat from a cold body to a hot body using external work.### The Carnot Cycle
• The Carnot cycle is a thermodynamic cycle that uses a refrigerant to transfer heat from a colder body to a hotter body.
• The cycle consists of four stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
• The reverse Carnot cycle is the basis for most refrigeration systems, including household refrigerators and freezers, industrial chillers, and cryogenic coolers.

The Inequality of Clausius

• The inequality of Clausius states that (dQ/T) = 0, where dQ is the amount of heat transferred and T is the temperature at which the heat transfer occurs.
• The inequality indicates that in a reversible process, the integral is equal to zero (S = Q/T), while in an irreversible process, the integral is less than zero (S > Q/T).
• The inequality is a statement of the second law of thermodynamics, which dictates that the total entropy of an isolated system will always increase over time.

Entropy

• Entropy is a measure of the amount of disorder, randomness, or uncertainty in a system.
• Entropy can be thought of as a measure of the amount of energy in a system that is unavailable to do work.
• Entropy is typically denoted by the symbol "S" and is measured in units of joules per kelvin (J/K).
• Entropy is a state function, meaning that only the change in entropy (S) is important, not the absolute value.
• Entropy can be related to the number of possible microstates in a system, with higher entropy corresponding to a larger number of possible microstates.

Principle of Increase of Entropy

• The principle of increase of entropy states that the total entropy of an isolated system will always increase over time, except in reversible processes.
• Entropy always increases over time in a closed system, remains constant in a reversible process, and never decreases spontaneously in an isolated system.
• The principle has far-reaching implications, including energy degradation, disorder and randomness, and irreversibility.

Explore the limitations of the first law of thermodynamics and learn about the principles of energy conservation. This quiz covers the basics of the second law of thermodynamics and its applications.