I despise the smell of litter boxes. Even when cleaned well, the smell of cat litter can be overwhelming. It's ok if you live in a large house where you can dedicate a utility room, garage, or basement to the litter box. In an apartment, it is often impossible to keep a litter box out of smells reach.
For that reason, I made this simple litter box exhaust, which draws a small amount of air out of a covered litter box, and blows it outside. The computer fan draws just enough air to keep odors from escaping the box. The hot/cold air loss to the exterior seemed to be pretty minimal, because there is no noticeable change in heating/cooling costs. It works so well that people would be surprised that there were cats in the apartment.
The computer fan is rated at 0.13A, so it could easily be run off batteries being charged from a small solar panel outside. This instructable shows how to do just that: https://www.instructables.com/id/The-Amazing-Solar-Powered-Fan-A-Green-Gadget/
Cats are generally freaked out by noise and weird stuff in the litter box. The fan is so quite, and far enough away from the litter box, that the cats did not care in the least bit. They were actually a little curious as to the dryer hose sticking in the box.
I built this system years ago, but was prompted to put it up after seeing this: http://hackaday.com/2008/09/16/hack-your-littler-box/
The bathroom fan seems like overkill, especially considering the fact that they cannot leave it on all the time.
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Step 1: Materials
2. Plastic dryer hose
3. Sheet of Lexan
4. 2 Plastic cups that fit about 3/4 of the way into the dryer hose
5. Outdoor electrical junction box (which computer fan fits inside of)
8. 12 Volt wall power adapter
Step 2: Fan Box Construction
1. Cut a square hole in the bottom of the box to accommodate the size of the fan.
2. The fan is mounted to the back using screws at the corners of the hole.
3. Since the back of the box will be facing the exterior, a screen is placed across the hole to prevent the entry of bugs.
4. A circle is cut in the cover of the electrical box (fan box) to accommodate one of the plastic cups.
5. Cut the bottom off the plastic cup, and push the cup through the hole of the electrical box cover. Glue in place.
Step 3: Mount Fan Box in Window
1. Cut a piece of Lexan to the appropriate size to fit in the window.
2. Cut a square hole in the Lexan. The hole should be the same size as the hole that was cut in the electrical box. I only cut 3 sides of the hole, bending the center piece out to create a mini awning to protect the fan from rain, etc.
3. Screw the electrical box to the Lexan window.
4. Mount the Lexan and fan box assembly in the window. (The pictures below show it with the dryer hose already installed)
Step 4: Install Dryer Hose on Fan Box
Step 5: Install Dryer Hose in Litter Box
2. Pass the end of the dryer hose into the hole in the box.
3. From the inside, push the plastic cup into the dryer hose. Push far enough to wedge it tightly.
4. I covered the top of the cup with a screen to try to keep cat hair out of the fan. You could also use a filter, because the dust still goes through the screen. But the dust never damaged the fan, and computer fans are cheap.
Step 6: Power It Up, and Test It Out
Hope this improves your air quality, and leads to a healthier life. Enjoy!