International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2529

Full Length Research Paper

Studies on equalities and inequalities of heat, work and ratio of work to temperature

Chengshu Jin
  • Chengshu Jin
  • School of Food and Pharmaceutical Engineering, Suihua University, Suihua, Heilongjiang Province 152061, China.
  • Google Scholar

  •  Received: 04 April 2017
  •  Accepted: 22 August 2017
  •  Published: 16 September 2017


This research investigates relationships between resistances with heat and work. It is completely proven that the ratio of work to temperature for the realistic process is no less than that for the reversible process. The equalities and inequalities on the heat, work and ratio of work to temperature could be applied to the gravitational field and chemical reactions. The relationships between path functions and state functions are studied in the chemical reactions. Some criteria for spontaneous directions have been suggested such as the equalities and inequalities on the heat, work, and ratio of work to temperature, except the Clausius inequality and must be ordinarily obeyed in the spontaneous process.

Key words: First law of thermodynamics, Clausius inequality, thermodynamic functions, chemical reactions, gravitational field, resistances, ratio of work to temperature.


The first law of thermodynamics was as a result applying the conservation of energy to thermodynamics (Sandler and Woodcock, 2010). The Carnot theorem could be proven by the second law of thermodynamics. The Clausius inequality was derived from the Carnot theorem (Atkins and Paula, 2014; Nieto et al., 2011; Lee et al., 2015). In the gravitational field and chemical reactions, relations between the entropy or free energy with the kinetic, gravitational potential, and electrical energy was studied (DeVoe, 2013; Gislason and Craig, 2013; de Abreu and Guerra, 2012). The equalities and inequalities in regard to the work and ratio of work to temperature between the reversible process and irreversible process are  entirely  denied  and  neglected  in  the   fundamental theory; hence, they are seldom researched yet. The motion path of solids and liquids is only affected by external force, which is different from the gas. The application of the scopes of Clausius inequality will be enhanced by the equalities and inequalities on the work and the ratio of work to temperature.
In a reversible process, the first law of thermodynamics is given by:
Complete derivation of the inequality on the ratio of work to temperature from the Clausius inequality
The Clausius inequality can be rewritten as follow:
where p is the pressure, V is the volume, R is the gas constant, and n is the amount of substance. Because 




The author has not declared any conflict of interests.


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