With assumption (3), if small amount of heat rejection pressure increment dP is considered, the decrement of refrigerant enthalpy at gas-cooler outlet becomes increment of specific cooling capacity and the ratio can be represented by Eq. (2) On the other side, the increment of specific compression work per unit increment of the heat rejection pressure is calculated by Eq. (3). With these equations, the new COP for the increased heat rejection pressure can be written as Eq. (4) Additionally, the ratio of increment of cooling capacity to increment of compression work is written in Eq. (5). Finally, as shown in inequality (1), if inequality (6) is satisfied, the new COP is higher as heat rejection pressure is increased.