What type of air system operates using hot compressor bleed air on some turbine aircraft?

The correct response highlights the function of the ram air cycle cooling unit, which specifically relies on the use of hot compressor bleed air in turbine aircraft. This system utilizes the high-temperature bleed air extracted from the engine's compressor stages to operate the cooling cycle.

The ram air cycle cooling unit works by using the hot bleed air to drive a turbine, which in turn compresses ambient air, allowing it to cool. This process capitalizes on the principles of thermodynamics to provide efficient cabin cooling. In many turbine aircraft designs, relying on this method allows for a simplified air conditioning system that uses existing engine systems for cabin temperature control.

The other options pertain to different systems that either do not utilize hot compressor bleed air or serve different functions altogether. The cold air supply system would not rely on any heat source from the engine's bleed air, the chemical oxygen generator system serves to provide supplemental oxygen in emergencies and does not involve cooling, and the vapor-cycle cooling unit employs refrigerants instead of bleed air for its cooling process. Each of these systems has unique purposes and functionalities that distinguish them from the ram air cycle cooling unit.