Intake temperature and compressor capacity For a given compressor and speed, the delivered capacity (mass flow rate) will be __________ when the intake air temperature is at its lowest value.

Introduction / Context:
Compressor capacity in mass terms depends directly on inlet air density. Since density is inversely related to absolute temperature at a given pressure, lowering the intake temperature increases density and thus mass flow for a fixed volumetric flow capability.

Given Data / Assumptions:

• Same compressor geometry and rotational speed.
• Same inlet pressure; variable inlet temperature.
• Performance within surge/choke limits.

Concept / Approach:
Mass flow m_dot = rho * V_dot. For ideal gas at fixed pressure, rho = p / (R * T). Decreasing T increases rho, hence increases m_dot for the same volumetric throughput. Therefore, the capacity is highest when the intake air is coldest.

Step-by-Step Solution:
Fix volumetric flow (machine-limited) and inlet pressure.Use rho = p / (R * T): lowering T raises rho.Compute m_dot = rho * V_dot: higher rho yields higher mass flow.So capacity is highest at the lowest intake temperature.

Verification / Alternative check:
Corrected mass flow definitions in turbomachinery use inlet total temperature precisely to normalize such effects; cooler inlets show higher actual mass flow.

Why Other Options Are Wrong:
“Lowest” contradicts the density relationship; “unchanged” ignores ideal gas behavior; “indeterminate” is false because the dependence is clear and monotonic under the stated constraints.

Common Pitfalls:
Confusing volumetric capacity with mass capacity; volumetric flow may be similar, but mass capacity changes with density.

Final Answer:
highest