On the Sackur–Tetrode equation in an expanding universe

S.H. Pereira

Universidade Federal de Itajubá, Campus Itabira, Rua São Paulo, 377–35900–373, Itabira, MG, Brazil, e–mail: saulopereira@unifei.edu.br

Recibido el 5 de abril de 2010 ]]> Aceptado el 2 de febrero de 2011

Abstract

In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an ideal gas confined to a constant volume V. In particular the Sackur–Tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen.

Keywords: Expanding universe; ideal gas; Sackur–Tetrode equation.

Resumen

En el presente trabajo investigamos las propiedades termodinámicas que son satisfechas por un universo en expansión, el cual es lleno por un gas ideal monoatómico. Se prueba que las ecuaciones para la densidad de la energía, la densidad de la entropía y el potencial químico son las mismas que las de un gas ideal, el cual se encuentra confinado en un volumen V. En particular, la ecuación de Sackur–Tetrode, para la entropía del gas ideal continua siendo válido en el caso de un universo en expansión, siempre que el valor constante que representa la entropía del universo actual sea escogido adecuadamente.

Descriptores: Universo en expansión; gas ideal; ecuación de Sackur–Tetrode.

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Acknowledgements

I am grateful to Juan C.Z. Aguilar for reading the manuscript and to CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnologico, brazilian research agency, for the financial support, process number 477872/2010–7.

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