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Chapter Eleven: Thermodynamics

11.1 Introduction

The study of thermodynamics focuses on the thermal properties of matter and the principles governing the transfer and conversion of thermal energy. Thermodynamics plays a crucial role in various applications, from industrial engines to biological processes. An example of thermodynamic principles in action includes rubbing palms together, which generates heat through friction, and the steam engine, which converts heat energy into mechanical work. Key concepts such as heat, temperature, work, internal energy, and entropy serve as foundational components in the subject, leading to a comprehensive understanding of thermal systems and processes.

11.2 Thermal Equilibrium

A system is deemed to be in thermodynamic equilibrium when macroscopic variables—pressure, volume, and temperature—do not exhibit any changes over time. Two essential setups illustrate thermal interactions:

• Adiabatic Wall: This wall allows no heat transfer between systems, maintaining separation of their equilibrium states.

• Diathermic Wall: Allows heat to flow between systems until they reach thermal equilibrium, resulting in equal temperatures.

11.3 Zeroth Law of Thermodynamics

This law states that if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. The zeroth law establishes a foundation for measuring temperature, as it implies that temperature is a variable that indicates thermal equilibrium quality among various systems.

11.4 Heat, Internal Energy, and Work

Temperature serves as a critical indicator of warmth and facilitates the flow of heat from regions of higher temperature to those with lower temperature.

• Internal Energy (U): Defined as the total energy associated with the molecular constituents of a system, which includes kinetic and potential energy but excludes any macroscopic movement.Heat and work are viewed as different modes of energy transfer; heat is specifically defined as energy in transit due to temperature differences, while internal energy represents a state variable characteristic of the energy contained by a system.

11.5 First Law of Thermodynamics

The law of conservation of energy is summarized as follows:[ \Delta Q = \Delta U + \Delta W ]Where:

• ( \Delta Q ) = Heat supplied to the system

• ( \Delta W ) = Work performed by the system

• ( \Delta U ) = Change in internal energy of the systemThe change in heat and work is path-dependent; however, the change in internal energy only depends on the initial and final states of the system, reflecting its intrinsic properties.

11.6 Specific Heat Capacity

Heat capacity is described by the equation:( S = \frac{\Delta Q}{\Delta T} ),where ( S ) is the heat capacity. The specific heat capacity (( s )) is defined as ( s = \frac{S}{m} ), with ( m ) representing the mass. The molar specific heat (( C )) is expressed through the equation: ( C = \frac{Q}{\mu \Delta T} ), where ( \mu ) is the number of moles.These definitions are crucial for understanding how different substances respond to heat energy when undergoing temperature changes.

11.7 Thermodynamic State Variables and Equation of State

State variables are used to characterize the conditions of equilibrium states within a thermodynamic system, specifically: pressure, volume, and temperature. Equilibrium conditions present unique characteristics distinct from classical mechanics.An important relationship, the equation of state, for ideal gases is given by:( PV = \mu RT ),where ( R ) is the universal gas constant. This equation allows predictions about gas behavior under varying conditions.

11.8 Thermodynamic Processes

• 11.8.1 Quasi-static Process: This involves an infinitely slow transformation, keeping the system in thermal and mechanical equilibrium with its surroundings throughout the change.

• 11.8.2 Isothermal Process: During isothermal transformations, the product of pressure and volume remains constant (( PV = constant )). The internal energy of an ideal gas remains unchanged in this process as temperature is constant.

• 11.8.3 Adiabatic Process: In this scenario, no heat is exchanged with the surroundings. The internal energy decreases proportionately to the work performed by the gas. The relation governing adiabatic processes follows the equation: ( PV^\gamma = constant ) (where ( \gamma ) is the heat capacity ratio).

• 11.8.4 Isochoric Process: Here, the volume remains constant; thus, the work done is zero. All the heat transferred leads to changes in the internal energy of the system.

• 11.8.5 Isobaric Process: This process signifies constant pressure. The work performed is directly related to changes in internal energy and heat exchange.

• 11.8.6 Cyclic Process: The system undergoes changes and eventually returns to its original state, resulting in ( \Delta U = 0 ) (no net change in internal energy).

11.9 Second Law of Thermodynamics

This law introduces essential limitations to thermal processes:

• Kelvin-Planck Statement: States that no heat engine can convert all thermal energy completely into work without transferring some heat to a cold reservoir.

• Clausius Statement: Emphasizes that heat cannot spontaneously flow from colder to hotter bodies.

11.10 Reversible and Irreversible Processes

Natural processes are typically irreversible due to dissipative effects such as friction and viscosity, making them less efficient.On the other hand, reversible processes are idealized, quasi-static interactions without any dissipative factors, representing a theoretical benchmark for efficiency.

11.11 Carnot Engine

The Carnot engine exemplifies an idealized reversible engine that operates between two temperatures, ( T_1 ) and ( T_2 ).The Carnot cycle includes two isothermal processes alongside two adiabatic processes, demonstrating maximum theoretical efficiency expressed by:[ \eta = 1 - \frac{T_2}{T_1} ]

Summary Points

• The Zeroth Law establishes the fundamental concept of temperature.

• Internal energy encompasses various molecular energies while excluding overall directional motion.

• The First Law introduces a framework based on the conservation of energy in thermodynamics.

• Specific heat varies and depends notably on the type of thermodynamic process occurring.

• The Equation of State links different key state variables, showcasing the relationship between pressure, volume, and temperature for gases.

• Quasi-static processes are crucial for maintaining equilibrium and define specific thermodynamic transformations.

• The Second Law restricts the feasibility of processes, showcasing the inherent inefficiencies present in real-world thermodynamic applications.

• The Carnot engine offers insight into theoretical limits of efficiency and the principles governing practical thermodynamic engines.