3100k is a rather low color temperature for full spectrum (which is usually considered about 5000-7000k). Nevertheless, pepper plants will still grow with lower color temperatures, although they probably won't reach toward the light as much. A much stronger bulb wouldn't hurt either.
Anyway, your peppers should grow fine for most people's gardening purposes, although the setup may not be ideal for growth (which may be a problem if you're just getting started). I don't know exactly how fast they'll grow in that light, but they will grow. However, they should grow a whole lot faster if you put the light closer than seven inches. As close as possible without burning the plants is normally ideal. (One or two inches is great.)
Edit: Your bulb seems to have a spike in the blue end of the spectrum that may not be typical of regular 3100k fluorescent bulbs. This may mean that your light is pretty good overall for plants. Granted, the wavelength of the spike could be somewhat higher, but it's still in the useful range.
I might add here that lower color temperatures are more red and higher ones are more blue. Blue is great for leaf growth. Red is great for flowering. I've found that my lower color temperature bulbs seem to ward off damping off better than high color temperature bulbs, too. Your bulb follows this rule, except for a few spikes here and there, which seem to make this a better bulb.