Step 1: Understanding sillimanite isograds.
- An isograd marks the first appearance of a new metamorphic index mineral during progressive metamorphism.
- In pelitic rocks, the sillimanite isograds are reached during high-temperature metamorphism.
- The first sillimanite isograd usually appears when staurolite and muscovite break down to produce sillimanite, garnet, and biotite.
- The second sillimanite isograd involves the breakdown of muscovite in the presence of quartz to form sillimanite and K-feldspar.
Step 2: Checking the given reactions.
- (A) Muscovite + Quartz → Sillimanite + K-feldspar + H$_2$O
This is the classic dehydration reaction marking the second sillimanite isograd.
- (B) Staurolite + Quartz → Garnet + Sillimanite + H$_2$O
This is a breakdown reaction but corresponds to an earlier isograd, not the second sillimanite one.
- (C) Staurolite + Muscovite + Quartz → Garnet + Biotite + Sillimanite + H$_2$O
This is associated with the first sillimanite isograd.
- (D) Kyanite → Sillimanite
This represents an Al$_2$SiO$_5$ polymorphic transformation, not the second sillimanite isograd.
Step 3: Final Answer.
Hence, the correct reaction for the second sillimanite isograd is:
\[
\boxed{\text{Muscovite + Quartz = Sillimanite + K-feldspar + H$_2$O}}
\]