This paper presents an abbreviated method for estimating exergy destruction in a heat exchanger, requiring only black-box data of the exchanger’s inputs and outputs, and eliminating part of the mathematical difficulties associated with the calculations. A well-known model for temperature distributions in an exchanger is adapted for this case, and is used to distinguish between the contributions of the three major causes of the total exergetic loss: heat transfer, fluid friction and energy dissipation to the surroundings. This provides insight into the relative importance of the three, allowing for identification of potential improvements to a given design.

The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.

Although CO ${}_2$ as refrigerant is well known for having the lowest global warming potential (GWP), and commercial domestic heat pump water heater systems exist, its long expected wide spread use has not fully unfolded. Indeed, CO ${}_2$ poses some technological difficulties with respect to conventional refrigerants, but currently, these difficulties have been largely overcome. Numerous studies show that CO ${}_2$ heat pump water heaters can improve the coefficient of performance (COP) of conventional ones in the given conditions. In this study, the performances of transcritical CO ${}_2$ and R410A heat pump water heaters were compared for an integrated nearly zero-energy building (NZEB) application. The thermodynamic cycle of two commercial systems were modelled integrating experimental data, and these models were then used to analyse both heat pumps receiving and producing hot water at equal temperatures, operating at the same ambient temperature. Within the range of operation of the system, it is unclear which would achieve the better COP, as it depends critically on the conditions of operation, which in turn depend on the ambient conditions and especially on the actual use of the water. Technology changes on each side of the line of equal performance conditions of operation (EPOC), a useful design tool developed in the study. The transcritical CO ${}_2$ is more sensitive to operating conditions, and thus offers greater flexibility to the designer, as it allows improving performance by optimising the global system design.