Introduction to Power Plant

Second Law of Thermodynamics

Kelvin-Planck Statement

• A device cannot completely and continuously convert heat into work.

• Heat is not entirely convertible into work on a continuous basis; this means that during a cycle, some heat must be rejected as low-grade heat after work has been completed.

• Unavailable Energy: The portion of heat that cannot be converted to work must be rejected.

• Although energy is conserved, availability is not, and the availability of a system always decreases.

• Thermal efficiency of a heat engine must be less than 100%.

• Carnot Cycle: Represents an ideal heat engine providing the maximum thermal efficiency.

Clausius Statement

• It is impossible to construct a device that operates in a cycle producing no effect other than the transfer of heat from a cooler body to a hotter body.

• This statement complements the Kelvin-Planck statement and asserts the limits of energy transformation.

• A device can transfer heat from the low-temperature reservoir but cannot do work without an external energy source.

Concept of Reversibility

• Introduced by Sadi Carnot, this concept deals with the idealization where processes can be reversed, restoring the system back to its original state without loss of energy.

• An irreversible process in a cycle means the entire cycle cannot be reversed.

• Four significant sources of irreversibility:

  • Friction: Mechanical work dissipated into heat (e.g., gears, bearings).

  • Heat Transfer: Heat moves from higher to lower temperatures without external assistance, leading to irreversibility.

  • Throttling: Uncontrolled expansion processes where no work is done during heat transfer.

  • Mixing: Mixing fluids leads to a loss of availability and is irreversible without external energy input.

Entropy

• Introduced primarily through Claude Shannon, entropy is a measure of disorder or irreversibility in a system.

• Units of Entropy: Commonly represented by Btu/(degree Rankine) or J/K.

• Entropy is mathematically represented:

  • For reversible processes:

    • ( dW = P dV )

    • Equivalent for heat can be expressed as: ( dQ = T dS )

• The area under a process curve in a T-S diagram represents heat transfer, analogous to the area under the curve in a P-V diagram representing work.

• Increased irreversibility leads to an increase in system entropy, impacting work availability and efficiency.

• The concept emphasizes that in every isolated system, entropy continuously increases toward a maximum, which aligns with the universe's trend toward equilibrium and disorder.

Second Law of Thermodynamics

Kelvin-Planck Statement

• Definition: A fundamental principle stating that no device can completely and continuously convert heat into work without some losses.

• Significance: Implies that during a thermodynamic cycle, a part of the input heat must be dissipated as low-grade heat once work has been extracted. This unavoidable loss leads to inefficiencies in heat engines.

• Unavailable Energy: Refers to the portion of heat energy that is incapable of being transformed into work, underscoring the limits of energy conversion processes.

• Conservation vs. Availability: While the first law of thermodynamics ensures energy conservation, the second law emphasizes that the availability, or utility of energy, continuously depletes within a system.

• Thermal Efficiency: The thermal efficiency of any heat engine must always fall below 100%, establishing a benchmark for evaluating engine performance.

Carnot Cycle

• Explanation: Idealized model of a heat engine cycle that serves as a standard for measuring the maximum efficiency achievable by any engine performing in such a manner under reversible processes.

• Importance: Provides a fundamental understanding of how energy can be converted and the theoretical limits on efficiency.

Clausius Statement

• Definition: Complements the Kelvin-Planck statement, articulating that it is impossible to design a device that solely transfers heat from a cooler body to a hotter one without the input of work from an external source.

• Implications: This limitation constrains the efficiency and operation of all thermal systems and machines that involve heat transfer processes.

Concept of Reversibility

• Origin: Introduced by Sadi Carnot, this concept revolves around the idea that ideal processes can be reversed without any net energy loss, cycling the system back to its initial state.

• Irreversible Processes: Acknowledges that real-world processes lead to irreversible changes, culminating in energy dissipation and cycle inefficiencies.

• Sources of Irreversibility: Four major sources include:

  1. Friction: Energy loss as mechanical work gets converted to thermal energy in systems with moving components like gears and bearings.

  2. Heat Transfer: Natural heat flow from hot to cold bodies without any work input, leading to energy dissipation.

  3. Throttling: Expansion of gas or fluid through a valve without performing work, resulting in dissipative heat transfer.

  4. Mixing: Combining different fluids results in loss of potential energy, rendering the process irreversible without external work to separate them again.

Entropy

• Definition: Primarily introduced in thermodynamic discussions through Claude Shannon, entropy quantifies the level of disorder or randomness in a system, reflecting how energy is distributed across different states.

• Units of Measurement: Frequently measured in units like Btu/(degree Rankine) or J/K, highlighting its quantitative aspect.

• Mathematical Representation: In the context of thermodynamic processes, for reversible interactions:

  • Work: ( dW = P dV )

  • Heat exchange: ( dQ = T dS )

• T-S Diagram Analogy: The area under the curve in a Temperature-Entropy (T-S) diagram corresponds to heat transfer, just as the area under the Pressure-Volume (P-V) diagram represents work done in the process.

• Impact of Irreversibility: Increasing irreversibility leads to the heightened entropy of a system, consequently depleting available energy for work and diminishing the operational efficiency of thermodynamic systems.

• Universal Trends: The second law of thermodynamics establishes that in any isolated system, entropy will perpetually grow, moving towards a state of greater disorder and reinforcing the overall trend in the universe towards equilibrium.