Google can get some eyeballs out of the effort by having more Google-apps users so this effort be somewhat self-supporting but more importantly, it serves Google's strategic goals.

Keep in mind that with the web constantly growing and constantly improving, Google doesn't need a new business model - being the entrance to the greatest show on earth will work for a long time now. Google today mostly needs to fend off outside monopolists who would aim to seize the whole thing by taking control of one or another choke-points. And having an OS to challenge MS is important here - even if the OS only takes minority share, keeping MS honest is important. Moreover, if all those other companies don't make monopoly profits, they won't have extra cash to throw at Google.

To get to a Google prompt, a user needs: 1) A PC 2) An operating system 3) A web browser 4) An Internet Connection from an ISP

The OS can potentially control search engine choice. Ditto with the browser and the ISP. Notice that Google has challenged monopolistic behavior in steps 2-4 by now (wireless venture, Chrome, Chrome OS). PC architecture is already mostly open so Google doesn't have to do anything there - but Google does build PCs!