Transcritical
cycles are a successful and probed system in engineering
practices, particularly in refrigeration. Therefore, their optimization
is a critical factor in the design, control, and operation in order
to maximize the coefficient of performance (COP) and to find the optimal
pressure operating conditions. Often, this labor is faced using empirically
based correlations, which are limited by their origin and the configuration
of the cycle. In this regard, this work is devoted to the development
of a rigorous and general framework in order to characterize the behavior
and performance of a simple transcritical refrigeration cycle. An
accurate mathematical expression for the COP depending on the compressor
efficiency and the properties of the working fluid is presented. The
expression proposed has no approximations and is relevant to any model
depending on the Helmholtz variable group, being easy to combine with
any equation of state (EOS), regardless of its complexity. From this
expression, it is possible to derive a simple control function for
transcritical refrigeration cycles. As an example, the expression
is combined with the Span–Wagner EOS, presenting a comprehensive
application for a transcritical cycle using CO
2
and N
2
O as working fluids.