Rhapsody tells us that things will work exactly as you would expect. You queue up you music from the library of over 32 million songs, then cast them to your television. Since Rhapsody purchased Napster in 2011, support for Chromecast is also added to the Android app.
If you're a user of either service, you'll want to check for your update at Google Play. If you want to give them a look, the download links are below.