Wayne Myrvold: Thermodynamics: The Basics

The speaker begins by reflecting on the audience's familiarity with thermodynamics, questioning how many have taken related courses and how well they recall the material. They admit to gaps in their own understanding from previous studies, suggesting that thermodynamics concepts can be elusive. The speaker aims to clarify logical relations better than a standard textbook, also touching on the idea that thermodynamics foundations might be less clear-cut than commonly believed.

The speaker continues by discussing the basic principles of thermodynamics, highlighting the common experience of confusion during learning, especially with statistical mechanics. They introduce the concept of 'minus first law' or the equilibrium principle, which states that an isolated system will spontaneously reach a unique equilibrium state. The talk also covers the zeroth law of thermodynamics, which involves the idea of thermal contact and the transitive nature of thermal equilibrium, leading to the definition of temperature equivalence.

The paragraph delves into the first law of thermodynamics, which is essentially the law of conservation of energy. It discusses the concepts of kinetic and potential energy, work done on or by a system, and heat transfer. The speaker explains that energy can be transferred as work (when compressing or expanding a gas) or as heat (through thermal contact). The first law is presented in both its integral and differential forms, emphasizing the state function of internal energy and the non-state nature of heat transfer.

The speaker explores the second law of thermodynamics, focusing on the limitations it imposes on the use of energy. They mention Lord Kelvin's statement about the impossibility of deriving mechanical effect from a single heat source below the temperature of the coldest surrounding object. The discussion highlights the importance of temperature differences for heat engines and the concept of time asymmetry in thermodynamic processes.

This paragraph examines the time asymmetry inherent in the second law of thermodynamics and its various formulations. The speaker discusses the Kelvin-Planck and Clausius statements, emphasizing their temporal asymmetry and the conditions under which they hold. They also touch on the historical context of these laws, including the consideration of 'inanimate material agency' and the philosophical implications of excluding intelligent agents from thermodynamic systems.

The speaker introduces the concepts of reversible and irreversible processes, using the Carnot cycle as an example of a reversible process. They explain that quasi-static reversible processes can be used to define state functions like entropy. The paragraph also discusses the challenges in defining heat and work in thermodynamics and the distinction between them, especially in the context of kinetic theory versus thermodynamics.

The speaker discusses the establishment of temperature scales, particularly the absolute or Kelvin scale, derived from the efficiency of reversible heat engines. They then connect this to the ideal gas temperature scale, which is defined by the product of pressure and volume for an ideal gas. The paragraph explores the relationship between these two temperature scales and how they can be used to define each other.

The speaker delves into the Carnot cycle, a reversible cycle used in thermodynamics, and its implications for understanding entropy. They explain that the integral of heat over temperature around any cycle is zero, leading to the definition of entropy as a state function. The Carnot cycle's efficiency is related to the temperatures of the heat reservoirs, providing a connection between the ideal gas temperature and the absolute thermodynamic temperature.

This paragraph discusses the foliation of state space in thermodynamics, where isotherms and adiabats form a coordinate system for the state space. The speaker explains that the assumption of non-intersecting adiabats and isotherms filling the state space is crucial for defining entropy as a state function. They also touch on the implications of this assumption for the existence of a state function that remains constant along adiabatic paths.

The speaker emphasizes that entropy is a state function, meaning its value depends only on the current state of the system, not on the path taken to reach that state. They discuss the importance of this property for entropy, especially in the context of reversible and irreversible processes. The paragraph also addresses the challenges in defining entropy and the assumptions underlying its definition.

The speaker returns to the second law of thermodynamics, discussing its implications for entropy. They explain that for any process, reversible or not, the change in entropy will be non-decreasing, which is a statement of the second law. The paragraph also touches on the concept of quasi-static processes and how they relate to the state space representation of thermodynamic systems.

The speaker explores the equivalence of the Kelvin and Clausius statements of the second law of thermodynamics. They discuss the background assumptions required for these formulations to be considered equivalent, including the positivity of absolute temperatures. The paragraph also mentions the implications of negative absolute temperatures in certain physical systems, such as spin systems with inverted populations found in lasers.

The speaker briefly touches on the third law of thermodynamics, which deals with the behavior of systems as temperature approaches absolute zero. They mention that the entropy of a system approaches a constant value, often interpreted as zero, which provides a natural zero point for entropy. The paragraph also discusses the quantum mechanical basis for the third law and its implications for substances with negative absolute temperatures.