# Specific heat of a heavy ion plasma

1. Dec 15, 2011

### rosewc

I am surprised by the result when I estimate the specific heat of the plasma produced by heavy ion collisions in the LHC:
C(plasma) ~= 2e5 J/(g-K) (Details below.)
This is ~1e6 times greater than C(lead)=0.13 J/(g-K) (1).
Did I make a mistake? If not, can the physics experts who read this explain why the specific heat is so high? (Extra degrees of freedom, ...?)

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Estimate of specific heat of a heavy ion plasma at LHC:
C = energy added/(mass*change in temperature)

Energy of a heavy-ion collison at LHC = 1150 TeV (2).
Energy = 1150 TeV * 1.6e-7 J/TeV = 1.8e-4 J

Mass:
Mass = 2 x 206 nuceons x 1.66e-24 g/nucleon = 6.8e-22 g

Temperature:
Heavy ion plasma temp at LHC exceeds 100,000 X solar core temp (3).
Temp>=1.6e7 K *1e5 = 1.6e12 K

C = energy added/(mass*change in temperature)
C = 1.7e5 J/(g-K)

(1) http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html
(2) http://cdsweb.cern.ch/record/1165534/files/CERN-Brochure-2009-003-Eng.pdf, p.21.
(3) Ibid., p.25.

2. Dec 15, 2011