The mass of an isolated black hole where J = 0 and Q = 0 is 1 0 5 M ⊙ .The black hole evaporates through Hawking radiation over a long period of time and reaches a mass of 1 0 3 M ⊙ . The change in temperature of the black hole can be expressed to three significant figures as a b c × 1 0 − 1 3 K . What is the value of a b c ?
Due to approximation of constants and potential rounding errors, we accept a 2% range of answers for this problem.
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Temperature T h of black hole is given by:
T h = 8 π G M k b ℏ c 3
Where:
M is mass of black hole.
c is speed of light.
k b is the Boltzmann constant.
ℏ is Planck's constant divided by 2 π
G is the universal gravitational constant.
In the question, M ⊙ represents mass of our sun.
Just substitute and subtract to arrive at answer.
Source: Wikipedia
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Δ T = 1 6 π 2 G k B h c 3 ( M 1 − M 0 1 ) ≈ 1 . 2 2 7 × 1 0 2 3 × ( M 1 − M 0 1 )
where M stands for the final mass of the BH and M 0 stands for the initial mass of the BH.