Refrigerator falls in Class 11, lighting & appliances, and depending on what exactly you sell it can also fall in Class 39 or Class 37 or Class 7. Everything below is read from the USPTO's own list of accepted descriptions, not from an opinion about where it belongs.
Searching the USPTO Trademark ID Manual for refrigerator returns 110 accepted descriptions, and most of them sit in Class 11. The manual is the list of identifications the office has already approved, so wording taken from it is pre-approved and settles the class at the same time.
The class follows from the identification you write, so "what class am I in" is really "what exactly do you sell". How the class system works covers the rest.
Lighting, heating, cooling, cooking, or plumbing equipment.
51 accepted descriptions in the manual mention refrigerator. For example:
You transport, ship, store, or arrange travel for people or goods.
13 accepted descriptions in the manual mention refrigerator. For example:
You build, install, clean, or repair things like buildings, vehicles, or equipment.
12 accepted descriptions in the manual mention refrigerator. For example:
Machines, power tools, motors, or engines (other than for land vehicles).
8 accepted descriptions in the manual mention refrigerator. For example:
Refrigerator appears in 4 classes because what you make, what it is made of and the service of selling it are separate classes. Pick the descriptions above that match what you actually do.
Making refrigerator is Class 11; a shop or online store that sells it is retail store services (Class 35), and a business that does both files in both.
Apparatus for lighting, heating, cooking and cooling. The test against Class 21 is electricity: electric kettles are here and non-electric kettles are there. Candles give light but count as fuel, so they are Class 4.
The class decides what a registration covers; it does not decide whether the name is available. Relatedness is judged on the identifications, so a conflict can sit in a class you never looked at: the same name in a different industry.
Check whether your name is clear for refrigerator Searches the live USPTO register, including sound-alike and meaning-alike names. First search $2, then $5.Refrigerator sits in Class 11, lighting & appliances. That is where the USPTO's own ID Manual puts it: 51 accepted descriptions mentioning refrigerator fall in Class 11. Depending on exactly what you sell it can also fall in Class 39 or Class 37 or Class 7.
You file in every class you actually use the mark in, and the USPTO charges its fee per class. Selling a product and also running an online store for it is two classes, not one. Filing in classes you do not use is worse than filing in too few: an application has to be supported by real use or a genuine intent to use.
No. The class decides what a registration covers. Availability turns on whether someone already holds a similar mark for related goods, and relatedness is judged on what the identifications say rather than on the class number, so marks in different classes can still conflict.
Not what you sell? Search the class finder for your own wording, or browse all 45 classes.