When turning instant soup into liquid soup, how can I optimise dissolution?

Add the water incrementally. It's probably enough to add just a bit, stir, then add the rest, but you can break it up a bit more if that doesn't work.

A clump of powder or a lump of paste won't dissolve easily into water, but it's easy enough to add a little water to it and thin it out. So the idea is to work your way up from powder to paste to thinner paste to liquid. This is a good idea for all kinds of things where you start with a powder or a thick paste, not just instant soup.

From chemistry we know that dissolving is affected by temperature, pressure, surface area, and agitation.

• temperature: are you using a hot water dispenser that isn't hot enough? If you have access to a microwave, you could use it for a minute or so.
• pressure: not really applicable here if you're making instant soup in a mug
• surface area: the powder granules need to be as small as possible, but you won't have much control over this since this is a prepackaged instant soup, unless you want to mill them down into smaller particles at home and repackage them. Break up the large clumps of soup powder when they come out of the packet. You'll also need to need to maximize the contact area between the soup and the water via constant stirring as the water is added.
• agitation: see previous for stirring technique

An option:

1. use a heavy ceramic mug
2. fill with half the water called for
3. bring to a rolling boil (ie. bubbles) in a microwave
4. carefully stir in the package mix
5. to lower the temp to something palatable, I add tepid tap water to very hot water in the mug

A bonus side effect, since the mug was heated quite a bit, it keeps to soup warmer longer.

Stir to the bottom of the cup or mug immediately after (or while) pouring and use boiling-hot water. In my experience, which is mostly with the same brand, this clumpy paste will only form if you wait too long to stir or use water that's too cold.

I'm sure some of the other tips given here will work with enough time and effort but I'd like to respect the "Minute Soup" tagline and avoid turning instant soup preparation into high art. I've had fool-proof results with this on a dozen different types of soup.

If you're at work and have the good fortune of having one of those large coffee machines that also dispenses (boiling) hot water, the pressure of the water coming from the faucet will typically be enough.

Shaken, not stirred... -James Bond

For dissolving solids into liquids, agitation beats stirring every time.

Whenever I make instant "just add boiling water" soup/noodles/whatever with a powdered base, I do so in a vessel that can be closed with a tight seal so I can shake the water and ingredients together instead of stirring them. I haven't seen a trace of undissolved base since I switched to this method instead of stirring in a bowl like I used to.

There are multitudes of Tupperware-like containers (or a thermos if the soup is really just liquid) that one can use for this, though my personal preference is to use an insulated food jar which I keep at my office for this very purpose.

Of course it goes without saying that a bit of common sense care should be taken when opening the container, as there will be a slight pressure that has built up inside from the steam.

I find that waiting is often the key. Add you powder, then your boiling water, stir a little (no need to go crazy), then add your noodles. Cover the mug with a heavy object you don't mind getting wet (or touching your food) like a plastic plate. Wait 5-10 minuets. Stir a little bit to get an even temperature. Enjoy soup.

By covering the mug your keeping the "heat" in. The insulation of the mug does most the work, but by not letting the steam escape you cut off a large source of heat dissipation. Just don't seal it air tight. That will make a fun, but messy, explosion. Stick something on top, don't use a lid.