A thermally insulated, closed copper vessel contains water at `15^@C`. When the vessel is shaken vigorously for 15 minuts, the temperature rises to `17^@C`. The mass of the vessel is 100 g and that of the water is 200 g. The specific heat capacities of copper and water are `420(J)/(kg-K)` and `4200(J)/(kg-K)` resprectively. Neglect any thermal expansion.
(a) How much heat is transferred to the liquid vessel system?
(b) How much work has been doen on this system?
(c ) How much is the increase in internal energy of the system?

Explanation

(a) No heat is transferred, here temperature increases due to work. (The temperature can be increased by supplying heat or by doing work. Heat and work are equivalent.)
(b) `DeltaW=(m_(C)s_(C)+m_(omega)s_(omega))(Deltatheta)`
`=(0.1xx420+0.2xx4200)(17-15)`
`=1764J`
(c ) `DeltaU=DeltaW=1764J`