Step 1: Understanding the process.
Limestone (CaCO\(_3\)) is decomposed to produce lime (CaO) and carbon dioxide (CO\(_2\)) in the blast furnace, which is essential for the extraction of iron. The decomposition of limestone occurs at a temperature of around 1200 K. Step 2: Analyzing the options. (A) 1500 K: Incorrect. The temperature for decomposition is typically lower than 1500 K. (B) 2000 K: Incorrect. This temperature is too high for the decomposition of limestone. (C) 1200 K: Correct. Limestone decomposes efficiently at around 1200 K. (D) 500 K: Incorrect. The temperature is too low for the decomposition process. Step 3: Conclusion.
The correct answer is (C) 1200 K.