Discussion
Statement of Reynolds Transport Theorem is given below with three blanks.
The rate of change of ________ extensive property can be calculated by summing the rate of change of the amount of same property in the ________ and the rate at which the property is ________ the surface of the control volume.
Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?
Answer: A
The blanks are system, control volume, exiting.
The Reynolds transport theorem links a system, a fixed collection of matter, to a control volume, a fixed region of space:
\[ \begin{aligned} \frac{dB_{sys}}{dt} &= \frac{d}{dt}\int_{CV} \rho b\,dV \\ &+ \int_{CS} \rho b\,(\vec{V} \cdot \vec{n})\,dA \end{aligned} \]
The left side is the rate of change of the system's extensive property; the first term on the right is the rate of change inside the control volume; the last term is the net rate at which the property leaves (exits) through the control surface, since \(\vec{n}\) points outward.
Swapping system and control volume reverses the theorem's meaning, and 'entering' would give the wrong sign for the flux term.
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