Help in understanding first way of changing the state of system

There is a statement in my book:



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> THERMODYNAMICS
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> ***One way***: We do some mechanical work, say $\pu{1 kJ},$ by rotating a set of small paddles and thereby churning water. Let the new state be called $\mathrm{В}$ state and its temperature, as $T\_\mathrm{B}.$ It is found that $T\_\mathrm{B} > T\_\mathrm{A}$ and the change in temperature, $\Delta T = T\_\mathrm{B} - T\_\mathrm{A}.$ Let the internal energy of the system in state $\mathrm{B}$ be $U\_\mathrm{B}$ and the change in internal energy, $\Delta U = U\_\mathrm{B} - U\_\mathrm{A}.$
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By rotating a small set of peddles, let us say we do mechanical work of $\pu{1 kJ}.$ Let the new state then be $\mathrm{B}$ and $\mathrm{A}$ as initial state.


It is found that $T\_\mathrm{B} > T\_\mathrm{A}.$ Let internal energy of system be $U\_\mathrm{B}.$


They say that $\Delta U = U\_\mathrm{B} - U\_\mathrm{A}.$ Do we assume $T\_\mathrm{A} = 0?$


We know $\Delta U = q + W.$ So, is $q = T\_\mathrm{B} - T\_\mathrm{A}?$


Should we say that work, i.e $W\_\mathrm{A} = 0$ and same for $W\_\mathrm{B} = \pu{1 kJ}?$


What is the difference in saying $\Delta U$ as internal energy and amount of mechanical work?


