Is it work or heat? One student of mine has found one question in a book of thermodynamics (1st year university level).

Work or Heat? You grab a bottle of juice and shake it thoroughly.
  Is this an example of a work or a heat interaction? Recall that work can be
  described with mechanical or electromagnetic variables.

My opinion is that we should first define the system. If we take the juice as our system, there is no work done by the system;  nor on the system since the system boundaries do not move.
There is not heat neither that transverse the system boundary.
Am I correct?
On a second thought, I think that we should define the bottle and its content as the system. Then we have clearly a work done on the system.
Is there any contradiction? What am I missing here?
 A: Even if the system is the juice only, the walls of the bottle are moving and exerting forces on the juice.  So you have forces applied through displacements.  This is clearly work.  The mechanical work that the walls of the bottle do on the juice is soon dissipated by the viscous friction in the fluid, which converts the mechanical work into internal energy of the juice (i.e., small temperature rise).  If the bottle is insulated (effectively), there is no heat transfer involved.
A: You are doing work on the juice. 
Let the juice and the bottle be the system. Lets say the bottle is glass (rigid) or if plastic when you shake the bottle you don't squeeze it. There are several types of work that you can do. One is boundary work which expands or contracts the boundary (bottle). This doesn't apply. There is also stirrer work which increases the temperature. This was the basis of the famous Joule experiment that proved the equivalency of heat and work.
Although this normally involves stirring the contents of the bottle with a paddle wheel that is in the bottle increasing the temperature of the contents, shaking the contents also does work on the contents. In addition to what @David White pointed out, shaking the contents creates viscous friction within the juice, raising its temperature.
Of course there is also the possibility of heat transfer from your hand to the juice if the juice is at a lower temperature than your hand.
Hope this helps. 
