B1. Reversible Carnot Refrigeration Cycle

A device-independent upper bound on chiller thermodynamic performance can be established by considering an idealized reversible thermodynamic cycle. Usually called a Carnot refrigeration cycle, it comprises 4 reversible branches, as portrayed in Figures 2.1 and 2.2:

1. Work W is input, adiabatically compressing the refrigerant and raising its temperature.

2. The refrigerant rejects heat Q _hot isothermally to a hot reservoir at temperature T _hot.

3. The refrigerant is expanded adiabatically.

4. Heat Q _cold is removed from the cold reservoir at temperature T _cold by isothermal transfer to the refrigerant.

Figure 2.1: Schematic of the reversible Carnot refrigeration cycle.

Figure 2.2: Temperature-entropy ( T- S) plot for the Carnot refrigeration cycle. The heat rejection and heat removal branches are isothermal (horizontal lines), while the compression and expansion branches are isentropic (vertical lines). The area enclosed within the solid rectangle is the work input to the cycle, W. The area of the dotted-line (lower) rectangle is the cooling energy produced. Note that the direction for the refrigeration cycle is anti-clockwise, in contrast to the clockwise direction for heat engine operation.

The refrigerant then returns to the compression stage and the cycle is repeated. Because the compression and expansion branches are adiabatic and non-dissipative ( i.e. isentropic), because all heat transfers are isothermal to or from an infinite reservoir, and because no loss mechanisms (irreversibilities) are introduced, the Carnot refrigeration cycle ensures that the maximum cooling energy is...