Where will the exhaust air go?

All that hot air has to go somewhere. In a window unit it automatically goes outside. With portable air conditioners you get a hose that vents to the outside similar to your clothes dryer hose setup.

There are window kits constructed of plastic or foam for windows that slide up or down (they won't work for casement windows that open to the outside). The kit has a rubber edged receptacle for the hose and sliders to take up the rest of the window opening or you can use a kit that allows venting through a wall, again like your dryer hook-up.

This venting hose should be short and fairly straight to get optimum cooling. Insulate it as well, if it is not short, to keep the heat from migrating back into the room.