The present paper derives an expression for the change in internal energy and enthalpy of the black holes using first law of thermodynamics and showing that the change in internal energy and enthalpy are the manifestations of same thing at constant pressure and volume. The paper also shows that the spinning black holes with spin a * 1 → do not radiate energy and mass of the black hole becomes infinity for zero surface gravity.

Mahto et al. gave an expression for the change in enthalpy and internal energy with corresponding change in the radius of the event horizon of black holes of spin parameter a* = 1 (2013). On the basis of this research work, we have proposed an expression for the change in the internal energy and enthalpy of the spinning black holes to assume spin parameter a* = 1/2 and calculated their values for different test spinning black holes existing in XRBs.

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Aims: To derive an expression for change in entropy of spinning black holes on the basis of the model for the energy of spinning black holes ( Mahto et al. 2011a) & the model for entropy change ( Mahto et al. 2011b) and then calculate their values for different test spinning black holes. Study Design: Data for the mass of black holes have collected from the research paper entitled :Super massive Black Holes in Galactic Nuclei: Past Present & Future Research(2005), Space Science Reviews by L. Ferrarese & H. Ford and Black holes in Astrophysics(2005), New Journal Physics by R. Narayan. The data for black hole constant for spinning black holes () is taken from the paper entitled: Study of Schwarzschild radius with reference to the spinning black holes. Bulletin of Pure and Applied Sciences (2011a). Place and Duration of Study: Department of Physics, Marwari College Bhagalpur and University Department of Physics, T.M.B.U. Bhagalpur, between December 2013 and March 2014. Methodology: A theoretical based work using Laptop to calculate the calculation for change in entropy of different test spinning black holes at Marwari College Bhagalpur and the residential research chamber of the first author. Results: The calculation shows that the change in entropy of spinning black holes of the rest masses for stellar – mass black holes (M ~ 5 ­ 20 Mʘ) in X-ray binaries is to J/K and for the super massive black holes (M ~ 106 – 109.5 Mʘ) in active galactic nuclei is to J/K. The nature of the graph for XRBs is the same to the Hawking entropy with the event horizon and straight line for AGN which confirms the validity of equations and . Conclusion: The change in energy and entropy of black holes are mainly dependent on the mass and independent of their event horizons.