Step 1: Understanding the Concept:
Porosity is the void fraction in a bed.
The bed height changes with porosity.
Step 2: Key Formula or Approach:
Volume of solids is constant: (1 - \(\epsilon_1\)) \(\times\) H\(_1\) = (1 - \(\epsilon_2\)) \(\times\) H\(_2\).
Step 3: Detailed Explanation:
\(\epsilon_1\) = 0.5, \(\epsilon_2\) = 0.75, H\(_1\) = 10 cm.
(1 - 0.5) \(\times\) 10 = (1 - 0.75) \(\times\) H\(_2\).
0.5 \(\times\) 10 = 0.25 \(\times\) H\(_2\).
5 = 0.25 H\(_2\).
H\(_2\) = 5 0.25 = 20 cm.
Thus, the final bed height is 20 cm.
Step 4: Final Answer:
The final bed height is 20 cm.
Hence, the correct option is (B).