The Reynolds transport theorem for mass is
$$\frac{dm_{sys}}{dt} = \frac{dm_{cv}}{dt} - \dot{m_{in}} + \dot{m_{out}}$$
My question is the term $\frac{dm_{sys}}{dt}$ always zero. Since this is the change in mass of the system and by definition mass cannot be transferred to or from a system, that is, its always the case that $$m_{sys} = constant$$.
That is where the conservation of mass principle for a control volume (cv) comes from that $$\frac{dm_{cv}}{dt} = \dot{m_{in}} - \dot{m_{out}}$$ as however the mass changes in the cv it is accounted for by the mass which entered or left since mass cannot appear in the cv out of nowhere.
All this seems to fall apart if the system term is not zero. So is mass just a special case of it always being zero, or are there cases that its not? For other properties, if forexample applying the reynolds transport theorem to energy, the system term should not be zero since the energy of the system can still change through other means such as heat or work.
