Carnot Heat Engine with a Variable Generalized Chaplygin Gas
Observational evidences suggest that the Universe is accelerating and the cosmological Chaplygin gas model is one of the most reasonable explanations of this phenomena. This model allows to simulate the dark energy in the cosmic fluid and has a great application in the study of the fundamental theories of physics and cosmology. Several independent observations indicate that the greater part of the total energy density of the universe is in the form of a dark energy and the rest in the form of non-baryonic cold dark matter particles, but which have never been detected. In this paper, following usual procedure has been extended the work of Panigrahi and Chatterjee (2016) for a variable generalized Chaplygin gas and has been studied the thermodynamical behavior for a Carnot engine using the thermal equations of state for the pressure and internal energy as function of temperature and volume for this type of gas. It has been derive an expression for the thermal efficiency of Carnot heat engine that depends on the limits of maximum and minimal temperature imposed on the cycle and of an exponent associated with the equation of state of variable generalized Chaplygin gas. Depending on the value of the exponent is recovered the expression for the efficiency of a Carnot cycle in an ideal gas as a particular case of this work.
Variable Generalized Chaplygin Gas, Dark Energy, Thermal Equation of State, Carnot Heat Engine, Thermal Efficiency
A G Reiss et al, Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astron. J. 116, 1009-1038, 1998.
R Amanullah et al, Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union 2 Compilation, Astrophy. J. 716, 712-738, 2010.
A Kamenschick, U Moschella, V. Pasquier, An alternative to quintessence, Phys. Lett. B511, 265-268, 2001.
D. N. Spergel et al. (WMAP Collaboration), First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters, Astrophys. J. Suppl. 148, 175, 2003.
D. N. Spergel et al. (WMAP Collaboration), Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology Astrophys. J. Suppl. 170, 377, 2007.
D. Panigrahi, S. Chatterjee, Viability of Variable Generalised Chaplygin gas -a thermodynamical approach, Gen. Rel. Grav, 49 (3), 35, 2017.
Y. S. Myung, Thermodynamics of Chaplygin gas, Astrophys. Space Sci, 335, 561-564, 2011.
D. Panigrahi, Thermodynamical behaviour of the variable Chaplygin gas, Int. J. Mod. Phys. D24, No. 5, 1550030, 2015.
H. S. Leff, Teaching the photon gas in introductory physics, Am. J. Phys, 70, 792-797, 2002.
M. Malaver, Carnot engine model in a Chaplygin gas, Research Journal of Modeling and Simulation, 2 (2), 42-47, 2015.
H. Lee, Carnot cycle for photon gas? Am. J. Phys, 69, 874-878, 2001.
R. Dickerson, Molecular Thermodynamics, W. A. Benjamin, Inc, Menlo Park, California, ISBN: 0-8053-2363-5, 1969.
L. Nash, Elements of Classical and Statistical Thermodynamics, Addison- Wesley Publishing Company, Inc, Menlo Park, California, 1970.
C. M. Bender, D. C. Brody, B. K. Meister, Quantum mechanical Carnot engine, Journal of Physics A: Mathematical and General, 33 (24), 4427, 2000.
K. Wark, D, Richards, Termodinámica, McGraw-Hill Interamericana, Sexta Edición, ISBN: 84-481- 2829-X, 2001.
M. Malaver, Thermodynamical analysis for a variable generalized Chaplygin gas, World Scientific News, 66, 149-162, 2017.