The problem here is that there is really no such thing as an "average desktop". There are a lot of factors that influence this, and just "averaging them out" doesn't really work. Your university may have very fancy modern power-efficient desktops that can use less than 20W idling, or it may have six year old power-hungry behemoths that use well over 100W idling. Who knows? You can't just say "ah, so the average must be about 60W", as that may not reflect reality at all (this is why "averaging it out" almost never works).
Some factors that influence this include:
- Power usage of the components (du'h), especially the CPU and video card (if any).
- Efficiency of the power supply (PSU); typical PSUs sit in the ~70% efficiency range, but some people put a 800W PSU for a 150W computer, which will drastically reduce the power efficiency. Really good (and usually expensive) PSUs are >90%.
- Operating system and configuration; there are quite a few tricks you can do in some operating systems, and older operating systems may not be able to take advantage of some power-saving features. On my laptop I managed to get about one hour of extra battery life by frobbing with various settings.
- The programs running on the computer. A computer is rarely 100% "idle"; there are various maintenance tasks that are done to keep the computer running (e.g. keep the computer clock running, listening for new emails, etc.). Typically this should use a negligible amount of processing power, but this is in no way guaranteed. I know of some programs that will use >20% CPU just by being open (not even doing anything).
- BIOS settings; sometimes things like C-states (which will make the CPU to go a "light sleep mode" when not used) are turned off by default (why? who knows...)
The best and only sure way to figure out how much electricity this will cost your university is to get a power meter (the kind that you can stick between the wall socket and any appliance) and measure it. This will probably still only give you a rough estimate as your university will probably have a bunch of different computers models in use.
All of that being said, the absolute best case scenario you can get with modern components is probably around 10W, but it's almost certainly higher than that since most people don't buy the extra power-efficient components. The "realistic best case" is more like 20W, based on my experience of recently buying a power-efficient desktop and measuring its idle usage.
In the end I guess it depends on your definition of "very little energy". Is 20W times n computers "very little energy"? I'll leave that for the reader to decide...