Q: Can i connect my mid 2010 27 inch iMac to my tv using the mini display port and get full sound.

Hello Camerman,

Thank you for the question.  The model of your iMac does support multichannel audio through the Mini DisplayPort:

These Apple computers supply multichannel audio (up to 8 channels) and video signals over Mini DisplayPort:

• MacBook Pro (Retina, 13-inch, Late 2012 and later) 1
• MacBook Pro (Retina, 15-inch, Early 2013)
• MacBook Pro (Retina, Mid 2012)1
• Mac mini (Mid 2010 and later)1
• Mac Pro (Mid 2010)
• MacBook (Mid 2010 and later)
• MacBook Pro (Mid 2010 and later)
• MacBook Air (Late 2010 and later)
• iMac (Late 2009 and later)

You can find the full article here:

About Mini DisplayPort to HDMI adapters

http://support.apple.com/kb/HT4241

Thank you for using Apple Support Communities.

Best,

Sheila M.