Step 1: Understanding the Question:
The question asks to match four types of powder density, true density, granule density, bulk density, and bulkiness, to the method or relation used to determine each one.
Step 2: Key Formula or Approach:
Each density type differs in what volume it counts as part of the powder: true density excludes all pores, granule density includes only the pores inside each particle, and bulk density includes both the internal pores and the gaps between particles. Bulkiness is simply the reciprocal of bulk density.
\[ \text{Bulkiness} = \frac{1}{\rho_{bulk}} \]
Step 3: Detailed Explanation:
True density needs a method that reaches into every internal pore of the solid, which is why a Helium Pycnometer is used, helium is a small enough gas molecule to fill even the finest voids. Granule density only needs to exclude the spaces between separate particles, not the pores inside each one, and mercury, which does not wet or penetrate fine pores under ordinary conditions, is used for this in the mercury displacement method. Bulk density is measured the simplest way, by pouring a known mass of powder into a graduated cylinder and reading its volume, since this naturally includes the air gaps between particles. Bulkiness follows directly as the reciprocal of that bulk density value.
Step 4: Final Answer:
The correct matching is I-(R) Helium Pycnometer, II-(S) mercury displacement method, III-(Q) graduated cylinder method, IV-(P) reciprocal of bulk density.