2.4 Sign Convention in Thermodynamics
We cannot overemphasize the importance of this since most, if not all, textbooks do not strictly follow the convention. What convention is followed is not important, but the consistent use of it is. For example, Callen (1960) says that all energy in is positive and all energy out is negative, and in that text this is followed consistently whereas most commonly used undergraduate and graduate textbooks do not, as is shown in the bibliography and references of Arnas et al. (2003). Precision is very important, as is mentioned in Obert (1960). In most textbooks, all energy transfer due to a difference of temperature only called heat in is positive and heat out is negative, and all energy transfers due to a potential difference other than temperature called work in is negative and work out is positive giving us HIP to WIN. In all that we will do, this convention will be followed due to its universal and more common usage. For the equivalence of heat to absolute temperature, consider a Carnot cycle, Fig. 2.1. It is made of two reversible adiabatic lines and two reversible, constant temperature heat reservoirs. If the working fluid is considered to be an ideal gas, for simplicity of algebra, then the energy added at TH is given by, for an ideal gas, n mK V
Similarly for the process (d-a),
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