Review Sheet for Thermodynamics 1: Basic Laws | Phys 627, Study notes of Physics

Download Review Sheet for Thermodynamics 1: Basic Laws | Phys 627 and more Study notes Physics in PDF only on Docsity! Review of Thermodynamics. 1: Basic Laws L06 What is Thermodynamics? • Idea: The macroscopic counterpart to statistical mechanics, initially developed phe- nomenologically, gradually developed into a coherent framework, and now providing the observational context in which to verify many of the predictions of statistical mechanics. • Plan: Recall the main definitions and relationships of thermodynamics, without men- tioning statistical mechanics; The connection between the two will be established later. Variables and State of a Thermodynamical System • Energy: Thermodynamics boils down to a theory of what happens to energy in various situations, and many of the most interesting situations are ones in which energy is the only relevant macroscopic conservation law. • Extensive variables: The state of a thermodynamic system in equilibrium can be specified by assigning the values of a set of extensive variables (S, ~x), where S is the entropy (see below) and ~x quantities that may include V , {Ni}, Q, ~M , ~p, ~L, ... One equation of state for the system expresses E as a function of (S, ~x). • Intensive variables: Each extensive variable has a conjugate intensive one. Examples are (S, T ) and, for the ~x, the pairs (V,−p), (Ni, µi), (Q,Φ), ( ~M, ~B), etc. Intensive variables play an important role in equilibrium, and each one of them can replace its conjugate one to give a new complete set of state variables. • Other equations of state: Once values for a complete set of state variables are specified, values for all other variables can be obtained using equations of state (e.g., p = p(T, V )). • Typical task: For thermodynamics, finding the change in the value of any state variable after some transformation. For statistical mechanics, and in this course, one of the main tasks is to derive the equations of state from models of the microscopic interactions. Zeroth Law of Thermodynamics • Statement: If system A is in equilibrium (thermal, mechanical, chemical, ...) with systems B and C, then systems B and C are in equilibrium with each other. • Remark: This law amounts to the possibility of establishing universal scales for the corresponding intensive quantities. It has a statistical justification, as we will see soon. First Law of Thermodynamics • Statement: The law of conservation of energy, which can be taken to be a definition of heat exchanged, written as dE = δQ+ δW , where the work δW may have a contribution from each of the intensive-extensive pairs, δW = ~f · d~x . For example, −p dV , f dL, µdN ; the quantity ~f is called a generalized force. • Remark: This equation can be taken as a definition of δQ. Second Law of Thermodynamics • Statement: There exists an extensive quantity S(E, ~x), normally taken to be a mono- tonically increasing function of E (but there are exceptions!), such that, if A 7→ B is an adiabatic transformation between accessible states, then ∆Sadiabatic ≥ 0. • Remark: This implies that, for a reversible process, ∆S = 0. It also allows us to rewrite the first law in a convenient form.