Which of the following equations describes the work done by environment, as it pushes mass elements through the boundary? (qm is mass flow rate, p is pressure, v is specific volume, w is velocity)

Question

Which of the following equations describes the work done by environment, as it pushes mass elements through the boundary? (qm is mass flow rate, p is pressure, v is specific volume, w is velocity)

BlackTom AI · Accepted Answer

The question asks: Which of the following equations describes the work done by the environment as it pushes mass elements through the boundary? (qm is mass flow rate, p is pressure, v is specific volume, w is velocity)

First, note that the problem is about open-system (control volume) analysis, where mass crosses the boundary and the surrounding environment performs flow work on the incoming or outgoing stream.

In open-system thermodynamics, the flow work (also called boundary work associated with mass transfer) associated with moving a mass flow across a boundary is given per unit time by the product of pressure, specific volume, and mass flow rate: Wdot_flow = p · v · qm. Here:
- p is the pressure at the boundary,
- v is the specific volume of the fluid (v = V/m for the stream), and
- qm is the mass flow rate (kg/s).
Multiplying these quantities yields the rate at which work is done by the environment to push the mass through the boundary.

Given that the prompt states the correct option is d. qm · p · v, this aligns with the standard expression for flow work rate in open-system analysis.

Since the list of answer options is not provided in the data (the field answer_options is empty), I cannot comment on the specific reasoning for each of the other hypothetical options. In general:
- Any option missing the p or v factor would underrepresent the flow work, since both boundary pressure and specific volume directly contribute to the energy needed to move the mass across the boundary.
- An option replacing qm with a velocity term w or incorporating incorrect units would signal a misunderstanding of work rate in this context, as work rate must have units of energy per time (e.g., Watts) and p·v·qm has the correct units for flow work rate.

In summary, the expression p · v · qm correctly captures the environment’s work rate on mass crossing a boundary in an open system, and the form d. qm · p · v matches that standard result.

BH20A0720 Engineering Thermodynamics - Blended teaching 2.9.2024-15.12.2024 Quiz 3

Which of the following equations describes the work done by environment, as it pushes mass elements through the boundary? (qm is mass flow rate, p is pressure, v is specific volume, w is velocity)

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Which of the following equations describes the work done by environment, as it pushes mass elements through the boundary? (qm is mass flow rate, p is pressure, v is specific volume, w is velocity)

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