Two black holes can merge to create a bigger black hole, thus increasing the entropy of the universe. Alternatively, they can be used as two heat reservoirs from which work can be extracted. We discuss a process during which two black holes are transformed into one while the total entropy is kept as constant. The resulting black hole has a smaller mass than the total mass of the input black holes and the mass difference is converted into work. Although the process will probably not be used within the next 1011 yr for energy production, we can speculate that it might be an energy source for those who might inhabit our universe after that. We discuss the basic thermodynamics of the proposed system.
REFERENCES
1.
S.
Frautschi
, “Entropy in an expanding universe
,” Science
217
, 593
–599
(1982
).2.
L. M.
Krauss
and G. D.
Starkman
, “Life, the universe, and nothing: Life and death in an ever-expanding universe
,” Astron. J.
531
, 22
–30
(2000
).3.
J. D.
Bekenstein
, “Black holes and entropy
,” Phys. Rev. D
7
, 2333
–2346
(1973
).4.
A simple estimate is based on the assumption that a person consumes about 2000 kcal ≈107 J in food per day for about 75 yr and dissipates most of it as heat at ≈300 K.
5.
This estimate is based on the incoming power 103 W of solar radiation per square meter multiplied by the illuminated area of ≈1.3 × 1014 m2. The age of the Earth is ≈5 × 109 yr so that the total received energy is about 2 × 1034 J. The same amount of energy is released as heat at the Earth ’s surface temperature of ≈300 K, yielding the entropy increase of ≈1032 J/K. The ratio of outcoming/incoming numbers of photons is equal to the ratio of the solar and Earth temperatures (≈5000/300 ≈17, using the same numbers as in Ref. 1). As stressed in Ref. 1, the dominant parameter characterizing the entropy is the number of particles carrying energy, because the entropy is linearly proportional to this number and depends only logarithmically on other parameters.
6.
The estimate is based on the solar power of ≈4 × 1026 W multiplied by its age of ≈5 × 109 yr, corresponding to ≈5 × 1043 J of released energy. If we divide it by the solar surface temperature ≈5 × 103 K, we obtain the entropy estimate of ≈1040 J/K. The number of created photons follows from the ratio of released nuclear energy per particle ≈7 MeV to the energy of a visible photon ≈1 eV, corresponding to the solar surface temperature.
7.
E.
Schrödinger
, What is Life? The Physical Aspect of the Living Cell
(Cambridge U. P.
, Cambridge
, 1944
).8.
S. W.
Hawking
, “Black holes and thermodynamics
,” Phys. Rev. D
13
, 191
–197
(1976
).9.
S. W.
Hawking
, “The quantum mechanics of black holes
,” Sci. Am.
236
(1
), 34
–40
(1977
).10.
O.
Kaburaki
and I.
Okamoto
, “Kerr black holes as a Carnot engine
,” Phys. Rev. D
43
, 340
–345
(1991
).11.
Deng
Xi-Hao
and Gao
Si-Jie
, “Reversible Carnot cycle outside a black hole
,” Chin. Phys. B
18
, 927
–932
(2009
).12.
D. N.
Page
, “Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole
,” Phys. Rev. D
13
, 198
–206
(1976
).13.
B. R.
Parker
and R. J.
McLeod
, “Black-hole thermodynamics in an undergraduate thermodynamics course
,” Am. J. Phys.
48
, 1066
–1070
(1980
).14.
P. S.
Custodio
and J. E.
Horvath
, “Thermodynamics of black holes in a finite box
,” Am. J. Phys.
71
, 1237
–1241
(2003
).15.
T.
Opatrn
ý, “The maser as a reversible heat engine
,” Am. J. Phys.
73
, 63
–68
(2005
).16.
P.
Anninos
, R. H.
Price
, J.
Pullin
, E.
Seidel
, and W.-M.
Suen
, “Head-on collision of two black holes: Comparison of different approaches
,” Phys. Rev. D
52
, 4462
–4480
(1995
).© 2012 American Association of Physics Teachers.
2012
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.