I have installed these Webapps in my Ubuntu 12.10: Facebook, GMail, YouTube and they work fine. However while launching the website from the corresponding Webapp, it always opens in a new window of my default browser. Is there any way by which I can make them to open in a new tab instead of a new window?
There is a nice workaround for Firefox. Install the Tab Mix plus add-on and check "Enable Single Window Mode" in its options.
From what I understand opening the Web Apps as new tabs instead of new windows is not currently supported, on the Canonical blog they explained the rationale as;
At OSCON today, Mark Shuttleworth revealed Ubuntu Web Apps, a new feature due to land in October’s Ubuntu 12.10 release. It will enable Ubuntu users to run online applications like Facebook, Twitter, Last.FM, Ebay and GMail direct from the desktop. Making web applications behave like their desktop counterparts improves the user experience dramatically; it’s faster and it reduces the proliferation of browser tabs and windows that can quickly make a desktop unmanageable.
Of course you can drag the open web app to your browser and there is will sit like any other tab (I have done this while testing with Chromium) but I am not aware of a way to open it with that behaviour by default.
This bug was posted on launchpad.net here.