This question is about a key design parameter used to characterize the performance of air pollution control equipment such as cyclones, electrostatic precipitators, and baghouses.
Step 1: Recall the collection efficiency curve. Any particulate control device has a collection (or removal) efficiency that varies with particle size, generally increasing as particle size increases, and this relationship is plotted as an efficiency-versus-size curve for the device.
Step 2: Define the specific size referenced in the question. The particle size at which the device removes exactly 50 percent of the particles entering it is a standard reference point on this curve, used to compare the performance of different control devices. This particular size is called the cut size, often written as \(d_{50}\).
Step 3: Distinguish from the other terms. Mean size and median size describe the central tendency of a particle size distribution in the incoming dust stream itself, not a performance metric of the control device. Mode size refers to the most frequently occurring particle size in a distribution. None of these three relate to a 50 percent removal efficiency threshold of the equipment.
Step 4: Conclude. Since the term specifically describes the particle diameter collected at 50 percent efficiency by the device, the correct term is cut size, option (C).