Entropy & Work Done: Understanding Reversible Heating/Stirring

[pukb]

There is a container containing water (state 1) which is being stirred. There is a temperature rise (state 2) due to stirring. It is required to find out change in entropy of the system if the process is reversible. Since, there is no heat transfer there would be no change in entropy due to external work. But the argument is, if the same state (state 2) is reached by reversible heating of the fluid instead of stirring, there would be some change in entropy. Since entropy is a state function, it would mean that there is a change in entropy while stirring also.
How does one understand this?

 

[grimm]

( in my opinion ) whenever, there is a change in temperature, there will be a change in entropy.

The second low of thermodynamics, says it's right that the change of the system and the surrounding is zero only because it's a reversible process (ideal).

Sorry for my poor English.