Hawking Radiation:
A Violation of the Zeroth Law of Thermodynamics
Spring 2018 Meeting of the APS New England Section
March 16-17, 2018
Suffolk University,
Boston, MA
Pierre-Marie Robitaille
Department of Radiology
The Ohio State University
Columbus, Ohio 43210


Zeroth Law of Thermodynamics
A ↔ B and B ↔ C
Then...
A↔C
But the law also implies that temperature is an intensive property.
The temperature of an object cannot depend
on extensive properties which in combination do not yield
an intensive property.


Intensive versus Extensive Properties
Intensive Properties Extensive Properties
Temperature Mass
Pressure Energy
Density Enthalpy
Concentration Entropy
Specific Volume Volume
Color Heat Capacity
Some properties are neither intensive nor extensive
(e.g. radius of a sphere, area of a sphere)


Intensive versus Extensive Properties
The concept of intensive and extensive properties is so
important that Peter Landsberg wanted to establish it as
The 4th Law of thermodynamics
P.T. Landsberg, Thermodynamics with Quantum Statistical
Illustrations, Interscience Publishers, New York, 1961, p. 142.


Equations: Intensive versus Extensive Properties
“If one side of an equation is extensive (or intensive),
then so must be the other side”
S.G. Canagaratna
Intensive and Extensive Properties: Underused Concepts,
J. Chem. Educ., 1992, v. 69, no. 12, 957-963.


Ideal Gas Law (P in terms of intensive properties)


Entropy of a Black Hole


Hawking Temperature