Question 2.10: Show that Eq. (2.28) reduces to Eq. (2.3) for the case of a ...

The second term of Eq. (2.28) is omitted in the absence of flowing streams:

\frac{d(mU)_{CV} }{dt}  = \dot{Q} + \dot{W}

Integration over time gives

\Delta (mU)_{CV} = \int_{t_{1} }^{t_{2}}{\dot{\varrho}  dt} + \int_{t_{1} }^{t_{2}}{\dot{W}dt}

or

\Delta U^{t} =Q + W

The Q and W terms are defined by the integrals of the preceding equation.

Note here that Δ indicates a change over time, not from an inlet to an outlet.

One must be aware of its context to discern its meaning.