Unformatted text preview: S = 5 2 kN + kN ln ² V (2 π mkT ) 3 / 2 Nh 3 ³ 8.13 Application to other systems Thermodynamics can be applied to other systems than gases and liquids. To do this the term d W = pdV has to be replaced with the correct work term, like d W rev =Fdl for the stretching of a wire, d W rev =γ dA for the expansion of a soap bubble or d W rev =BdM for a magnetic system. A rotating, noncharged black hole has a temparature of T = ¯ hc/ 8 π km . It has an entropy S = Akc 3 / 4¯ h κ with A the area of its event horizon. ±or a Schwarzschild black hole A is given by A = 16 π m 2 . Hawkings area theorem states that dA/dt ≥ . Hence, the lifetime of a black hole ∼ m 3 ....
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 Spring '10
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 Thermodynamics, Energy, Black hole, kN ln, kN + kN, gi exp

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