For a device that can run in both cooling and heating modes between the same two reservoirs, the heat quantities per cycle are QH (heat given to the hot reservoir) and QC (heat absorbed from the cold reservoir) while the work input per cycle is W.
(i) Starting from the first law of thermodynamics for one complete cycle, establish a relation between QH, QC and W.
(ii) Using the definitions of the coefficient of performance for a refrigerator and for a heat pump, derive an algebraic expression connecting the two COPs.
(iii) Show that this expression simplifies to a relation of the form COPHP=COPref+1 and explain the significance of the additional unity in practical terms.