To determine the metamorphic facies of a pelitic rock consisting of cordierite, garnet, K-feldspar, and sillimanite, we need to understand the conditions under which these mineral assemblages are stable.
- The granulite facies represents high-temperature and moderate to high-pressure metamorphic conditions. It is characterized by the presence of minerals such as orthopyroxene in mafic rocks, or, as in this case, the assemblage cordierite + garnet + K-feldspar + sillimanite in pelitic rocks.
- Under granulite facies conditions, temperature typically exceeds approximately 700°C, and such conditions lead to dehydration reactions that produce these minerals in the rock.
- Among the options provided:
- Granulite: Suitable for the given mineral assemblage due to high-temperature conditions.
- Eclogite: Generally associated with high-pressure, low-temperature conditions, typically containing omphacite and garnet in mafic rocks, not typical for the minerals provided.
- Greenschist: Characterized by low-grade metamorphism, typically involving chlorite and actinolite, unsuitable for high-temperature minerals like sillimanite and K-feldspar.
- Blueschist: Metamorphic facies defined by high-pressure, low-temperature conditions, with minerals like glaucophane, not typical for the given assemblage.
Therefore, based on mineral stability and metamorphic conditions, the correct answer is Granulite.