why is my aircondition compressor does not have cool copper piped?
The small line actually get hot. An air conditioner doesn't add cool. It removes heat from the room.
Your compressor compresses the freon to high pressure. When the pressure increases, the temperature goes up so the exist line will be hot. On the other side, the suction line will be at a lower temperature and for most compressors, the temp of that line should be in the 40-60's range depending on the ambient and indoor conditions. If it is also hot or very warm, then your A/C has a significant problem and should be evaluated by a professional. I would get into details but some of the solutions require an EPA license in the US.