Answer
No. Yes. Positive.
Work Step by Step
In this case, the increase in temperature of the liquid proves that energy has been given to the system. A well-insulated container proves that no heat transfer can take place between the liquid and the outside environment. Therefore, the energy that led to the temperature increase should have come from work being done on the system.
The irregular stirring means work is being done on the system. The irregular stirring implies that the force being applied to the liquid was variable and thus the work being done on the system was changing in accordance with the change in force.
Because the temperature of the liquid rose, the internal energy of the system has increased implying a positive ∆U.
No work is done by the system since the whole liquid is the system and there are no external forces. The work was done on the system by the stirring mechanism.
It is important that the stirring is irregular because it means that work done is variable and some energy is lost and thus the process is not reversible.
