Chapter 5 - The Second Law of Thermodynamics

Chapter 5: The Second Law of Thermodynamics

• The second law of thermodynamics dictates the direction of a thermodynamic process.
• The first law (conservation of mass and energy) does not dictate the direction.
• Only spontaneous processes are allowed.
• The second law provides a guiding principle to determine whether a process can occur thermodynamically
• Irreversible processes are those where the initial condition cannot be restored spontaneously, but require external means.
• Irreversible processes include heat transfer with a finite temperature difference, unrestrained expansion of gas/liquids, spontaneous chemical reaction, and mixing of matter.

Learning Outcomes

• Explain key concepts of the second law, other statements of the second law, internally reversible process, and the Kelvin temperature scale.
• List important irreversibilities (e.g., heat transfer via finite temperature differences, unrestrained expansion).
• Evaluate power cycles and refrigeration and heat pump cycles using corollaries of sections 5.6.2 and 5.7.2, alongside equations 5.9-5.11.
• Describe the Carnot cycle.
• Apply the Clausius inequality as expressed by Eq. 5.13.

Aspects of the Second Law of Thermodynamics

• Conservation of mass and energy principles indicate the disposition of mass and energy in a process, but do not tell us if the process is possible.
• The second law tells us which processes are thermodynamically feasible.
• The second law has various aspects: predicting process direction, establishing equilibrium conditions, determining the best theoretical performance of cycles, engines, and other devices, and quantitatively evaluating factors that preclude optimal performance. 

Motivation

• The first law is a mathematical statement of energy conservation (Q – W = ΔU).
• The first law does not specify the direction of a process.
• Consider processes involving heat transfer between hot and cold bodies, the natural direction is from hot to cold.

Allowable Processes

• Process I (work done on system): work input, heat output from the system.
• Process II (heat transfer to system): heat input, work output from the system.
• Process I is spontaneous, II is not.

Aspects of the Second Law (cont.)

• The second law, unlike the first, establishes preferred directions for processes.
• Some processes are allowed while others are disallowed by the second law, even though they satisfy the first (conservation) law.

Kelvin-Planck Statement

• It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of work to its surroundings while receiving energy by heat transfer from a single thermal reservoir.
• Any engine cannot have 100% thermal efficiency.
• Thermal efficiency (η) must be less than 100%.

Entropy Statement

• Entropy is an extensive property.
• Entropy is unlike mass and energy, which are conserved. Entropy is produced whenever non-idealities are present. 
• It is impossible for a system to operate in a way that destroys entropy.

Entropy Statement (mathematical interpretation)

• The change in entropy of a system within a time interval equals the net amount of entropy transferred across the system boundary during the time interval plus the net entropy produced by the system within the time interval.
• The entropy production is never negative. The process is possible only if the entropy production is positive or zero.

Irreversibilities

• Actual processes are different from idealized ones because of non-idealities, called irreversibilities.
• Common irreversibilities include heat transfer through finite temperature differences, unrestrained expansion, spontaneous chemical reaction, mixing of matter, friction, electric current flow through a resistance, magnetization/polarization with hysteresis, and inelastic deformation.

Irreversible and Reversible Processes

• A process is irreversible if irreversibilities are present within the system and/or its surroundings.
• All actual processes are irreversible.
• A process is reversible if no irreversibilities are present.
• An internally reversible process is a quasi-equilibrium process.

Example: Internally Reversible Process

• Water evaporating within a piston-cylinder: a sequence of equilibrium states exists during the phase change. The heat transfer to the water is an irreversibility in the surroundings (external).

Analytical Form of the Kelvin-Planck Statement

• For a system undergoing a thermodynamic cycle, the net work cannot be positive (W_cycle ≤ 0) if it communicates thermally with a single reservoir only.

Applications to Power Cycles Interacting with Two Thermal Reservoirs

• For a system undergoing a power cycle while communicating thermally with two thermal reservoirs the thermal efficiency is given by
  η= Wcycle / QH = 1 – Qc / QH. (Eq. 5.4).

Carnot cycle

• The Carnot cycle provides a specific example of a reversible engine between two thermal reservoirs.
• The cycle involves two adiabatic and two isothermal processes.

Carnot Refrigeration Heat Pump Cycles

• If a Carnot power cycle is reversed, this is equivalent to a refrigeration or heat pump cycle with the same magnitudes of heat transfers but opposite directions.
• Coefficients of performance (COP) for such cycles are:
• Carnot refrigeration: βmax = Tc / (Th - Tc) (Eq. 5.10)
• Carnot heat pump: γmax = Th / (Th - Tc) (Eq. 5.11)

Clausius Inequality

• The Clausius inequality is applicable to any cycle, regardless of the body(ies) from which the system receives energy during a heat transfer.
• The mathematical form of Clausius Inequality is: ∮(δQ/T) ≤ 0

Example Use of Clausius Inequality

• The Clausius inequality can be used to determine if a cycle is reversible, irreversible, or impossible.
• Calculations involving heat transfer and temperatures are used.

Maximum Performance Measures for Cycles

• Thermal efficiency of an irreversible cycle is always less than the thermal efficiency of the reversible cycle.
• Coefficient of performance of an irreversible refrigeration/heat pump cycle is always less than the coefficient of performance of the reversible equivalent.

Kelvin Temperature Scale

• Defined using reversible cycles as their basis.
• The ratio of heat transfers is equal to the inverse ratio of the Kelvin temperatures of the hot and cold reservoirs