Refrigeration performance metric: The coefficient of performance (COP) is defined as useful refrigeration divided by net work. COP is dimensionless. The units of which of the following are the same as COP?

Introduction / Context:
Performance indices help compare cycles irrespective of absolute scale. The coefficient of performance (COP) is widely used for refrigerators and heat pumps. Recognizing that COP is a ratio of like units prevents dimensional mistakes in calculations and reporting.

Given Data / Assumptions:

• COP = refrigeration effect / net work.
• Both numerator and denominator have energy units (e.g., kJ) per cycle or power units (e.g., kW) for steady operation.
• Therefore, COP is dimensionless.

Concept / Approach:

Since COP is a ratio of two energy (or power) quantities, the units cancel. None of the listed dimensional quantities (kinematic viscosity, work, temperature, pressure) are unitless; hence, none share the same units as COP. This mirrors thermal efficiency for power cycles, which is also dimensionless.

Step-by-Step Solution:

Verification / Alternative check:

Handbooks list COP without units (e.g., COP = 3.2), confirming the dimensionless nature.

Why Other Options Are Wrong:

Kinematic viscosity has units of m^2/s, work has joules, temperature has kelvin, pressure has Pa. These cannot match a dimensionless COP.

Common Pitfalls:

Reporting COP with energy units attached; confusing COP with EER (which uses Btu/hr per W but is still a ratio convertible to dimensionless via constants).

Final Answer:

none of these