Critical Temperature and Pressure:
The critical temperature of the refrigerant must be as high as possible above the condensing temperature to have a superior heat transfer at a stable temperature. If it is not taken care of, then we shall have excessive power consumption through the refrigeration system.
The critical pressure must be positive and moderate. A very high pressure shall make the system bulky and heavy while in case of very low pressures, there is a chance of air leaking into the refrigerating system.
Specific Heat:
The specific heat of the liquid must be as small as possible. It ensures that the irreversibilities connected with throttling are small and there is superior sub cooling of the liquid. Alternatively, the specific heat of vapour must be high to have less superheating of the vapour.