The Zeroth Law of Thermodynamics Definition Thermal Equilibrium

The “Zeroth Law” of Thermodynamics

Definition: Thermal Equilibrium: • 2 systems are in thermal equilibrium: If & only if there is no NET flow of heat between them when they are brought into thermal contact. • A system’s Temperature is an indicator of Thermal Equilibrium because, if 2 systems at the same temperature are in thermal contact, There is no net flow of heat between them.

The “Zeroth Law” of Thermodynamics A TA B TB • Consider 3 Objects, A, B C: C TC

The “Zeroth Law” of Thermodynamics A TA B TB C TC • Consider 3 Objects, A, B C: “If A is in thermal equilibrium with B & if B is in thermal equilibrium with C, then A is in thermal equilibrium with C”.

The “Zeroth Law” of Thermodynamics A TA B TB C TC • Consider 3 Objects, A, B C: “If A is in thermal equilibrium with B & if B is in thermal equilibrium with C, then A is in thermal equilibrium with C”. • In terms of system Temperatures: If TA = TB & TB = TC, then TA = TB.

The ZEROTH Law is 1. The main reason that thermometers work! & also 2. The main reason that they are useful!!

A More General Discussion! • As we know, if warm & cold objects are placed in thermal contact, Heat Energy Q flows from the Warm Object to the Cold Object until Thermal Equilibrium is established.

A More General Discussion! • As we know, if warm & cold objects are placed in thermal contact, Heat Energy Q flows from the Warm Object to the Cold Object until Thermal Equilibrium is established. “ 0 th” Law of Thermodynamics “If 2 systems are both in thermal equilibrium with a 3 rd system, they are in thermal equilibrium with each other”

th “ 0 ” Law of Thermodynamics “If 2 systems are both in thermal equilibrium with a 3 rd system, they are in thermal equilibrium with each other” • The property which the 3 systems have in common is known as a Thermometric Parameter, X. • So, generally, The “ 0 th” Law of Thermodynamics is If X 1 = X 2 & X 1 = X 3, then X 2 = X 3.

The “Zeroth” Law of Thermodynamics Example

Another Example of the “Zeroth” Law a) b) C A V A, P A V C, P C B C V B , P B V C, P C “If 2 systems are in thermal equilibrium with a 3 rd system, they are in equilibrium with each other. ” c) A B V A, P A V B , P B

The “ 0 th Law” of Thermodynamics “If 2 systems are in thermal equilibrium with a 3 rd system, they are in thermal equilibrium with each other. ” • For gases, this leads to an Equation of State: q = f(P, V ) where the parameter q (= temperature) characterizes the equilibrium. • Even more useful is the fact that this same value of q also characterizes any other system which is in thermal equilibrium with the first system, regardless of its state.

The 3 rd Law of Thermodynamics • The 3 rd Law of Thermodynamics is a Quantum Mechanical Law that fixes the absolute value of the entropy: S → 0 as T → 0

The 3 rd Law of Thermodynamics • The 3 rd Law of Thermodynamics is a Quantum Mechanical Law that fixes the absolute value of the entropy: S → 0 as T → 0 • Reif’s statement of the 3 rd Law is S → S 0 as T → 0+ with 0+ < ~ 0. 01 K

Corollary to the rd 3 Law: The attainment of a temperature of T=0 K (“Absolute Zero”) is not possible. • The 3 rd Law says that the entropy temperature curves for a fixed external parameter, such as magnetic field, meet at T → 0. • So, it is impossible to reach T = 0 in a finite number of steps.

3 rd Law: Attainment of a temperature of T = 0 K (“Absolute Zero”) is not possible. • This says that the entropy-temperature curves for a fixed external parameter, such as magnetic field, meet at T → 0. So, it is impossible to reach T = 0 in a finite number of steps. Adiabatic Processes Isothermal Processes

Another Statement of rd The 3 Law of Thermodynamics “As T 0, the entropy of a pure substance S 0. ” • In general, we know that S = k. Bln(Ω) • So, as the total system energy approaches its ground quantum mechanical state of energy E E 0, the temperature T 0 & Ω 1 so S 0

The rd 3 Law of Thermodynamics Entropy S = k. Bln(Ω) As T 0 , E E 0, & Ω 1 so S 0 Ordered System Disordered System

The 3 rd Law of Thermodynamics The entropy of a pure substance at T = 0 is S = 0.