- Title Pages
- Dedication
- Acknowledgements
- 1 How to use this book(†)
- 2 Introducing thermodynamics
- 3 A survey of thermodynamic ideas
- 4 Some general knowledge
- 5 Mathematical tools
- 6 Zeroth law, equation of state
- 7 First Law, internal energy
- 8 The Second Law and entropy
- 9 Understanding entropy
- 10 Heat flow and thermal relaxation
- 11 Practical heat engines
- 12 Introducing chemical potential
- 13 Functions and methods
- 14 Elastic bands, rods, bubbles, magnets
- 15 Modelling real gases
- 16 Expansion and flow processes
- 17 Stability and free energy
- 18 Reinventing the subject
- 19 Thermal radiation
- 20 Radiative heat transfer
- 21 Chemical reactions
- 22 Phase change
- 23 The Third Law
- 24 Phase change, nucleation, and solutes
- 25 Continuous phase transitions
- 26 Self-gravitation and negative heat capacity
- 27 Fluctuations
- 28 Thermoelectricity and entropy flow
- A Electric and magnetic work
- B More on natural variables and free energy
- C Some mathematical results
- Bibliography
- Index

# Self-gravitation and negative heat capacity

# Self-gravitation and negative heat capacity

- Chapter:
- (p.375) 26 Self-gravitation and negative heat capacity
- Source:
- Thermodynamics
- Author(s):
### Andrew M. Steane

- Publisher:
- Oxford University Press

The basic thermodynamics of self-gravitating systems is explained. First the virial theorem is introduced, and it is shown that a gravitating cloud bound by its own gravity is unstable, and each region of such a cloud has a negative heat capacity. The Jean’s length is obtained by a simple argument. Black holes and Hawking radiation are discussed. The area theorem and Penrose process are sketched, and the formulae for temperature and entropy of a black hole are given. Black hole evaporation is described.

*Keywords:*
Self-gravitation, negative heat capacity, virial theorem, Jean’s length, area theorem, Penrose process, Hawking radiation, black hole temperature, black hole entropy

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- Title Pages
- Dedication
- Acknowledgements
- 1 How to use this book(†)
- 2 Introducing thermodynamics
- 3 A survey of thermodynamic ideas
- 4 Some general knowledge
- 5 Mathematical tools
- 6 Zeroth law, equation of state
- 7 First Law, internal energy
- 8 The Second Law and entropy
- 9 Understanding entropy
- 10 Heat flow and thermal relaxation
- 11 Practical heat engines
- 12 Introducing chemical potential
- 13 Functions and methods
- 14 Elastic bands, rods, bubbles, magnets
- 15 Modelling real gases
- 16 Expansion and flow processes
- 17 Stability and free energy
- 18 Reinventing the subject
- 19 Thermal radiation
- 20 Radiative heat transfer
- 21 Chemical reactions
- 22 Phase change
- 23 The Third Law
- 24 Phase change, nucleation, and solutes
- 25 Continuous phase transitions
- 26 Self-gravitation and negative heat capacity
- 27 Fluctuations
- 28 Thermoelectricity and entropy flow
- A Electric and magnetic work
- B More on natural variables and free energy
- C Some mathematical results
- Bibliography
- Index