Can the vacuum of space be used to sterilize equipment?
Supposing that washing dishes and sterilizing medical equipment could be expensive to do in space, would a viable option be to expose dishes, scalpels, silverwear etc to the vacuum of space? Would the combination of "vacuum" and radiation from the sun be enough to kill enough of the bacteria and other things? If not for medical equipment, perhaps enough for eating utensils?
No.
Simple washing and sterilization (almost always?) starts with a physical process to remove dirt and reduce the bioload. Anything caked-on protects anything underneath, in most cases.
Space is full of porous dust, it could be poisonous, radioactive, or even contain biomaterial. Cleaning and then exposing to unknown dust goes against the principles of cleaning.
In most cases heat is a necessary part of sterilization, though there are exceptions. Methods utilizing heat, such as the majority of loads sterilized in the laboratory setting, involves sterilization at 121.1°C/250°F for 30-90 minutes.
If your load contains items that are sensitive to heat the default cycle temperature of 121.1°C/250°F may be too hot and you might need to consider a lower temperature. Using lower sterilization temperatures will result in longer sterilization times. This can be calculated by using the F0 relationship: $Fo = time * 10^{(\text{Temp_Celcius} \, - \, 121.1)/10}$.
Operation of an airlock involves some costs: maintenance, risk, electricity, loss of a bit of oxygen, time. You'll need to use the airlock twice as often to put objects outside and retrieve them as opposed to simple ejection.
Sterilization for each type of object has what is called "cycle development", a procedure designed to reproduce a desired result, to clean to a specified level. See: "How to Validate an Autoclave: Sterilization Cycle Development". There is a recipe that must be followed, simply doing what amounts to 'hanging everything out on the clothesline' is a random method that would provide random results; better to simply dispose of things in most cases.
No doubt there are specific cases where sticking stuff outside would work, using search tools turns up nothing supporting the idea. NASA doesn't do it. Afterwards you would need to clean off the radioactive dust in a sterile manner. It's probably cheaper to litter and let it burn up in the atmosphere.
On a base (on the moon or a planet) cleaning and reuse becomes more cost effective. Cleaning with gravity is different than without. Similarly utensils and dishes are not usable in zero gravity.
Currently NASA is investigating using 'heating trash compactors' that make disks out of the trash which will be tested as additional radiation shielding.
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