Scenario: You have a 100GB log file that needs to be sorted lexicographically, but you are operating on a machine with only 8GB of RAM. You cannot simply load the entire file into memory.

Question: Explain why a standard in-memory sort algorithm (like Quicksort or Mergesort operating entirely in RAM) cannot be used in this scenario. Then, describe in detail an External Sort (or External Merge Sort) algorithm that can efficiently sort this 100GB log file using the available 8GB of RAM. Your explanation should cover:

1. In-memory Sort Limitations: Clearly explain why 8GB of RAM is insufficient for a 100GB file, discussing concepts like memory oversubscription, virtual memory, paging, and potential performance issues (e.g., thrashing).
2. External Sort Algorithm - Phase 1 (Splitting and Initial Sort): Describe how the large file is broken down into smaller, manageable chunks. Explain how these chunks are sorted using an in-memory sort and written back to disk as temporary sorted 'runs'. Specify how the size of these chunks relates to the available RAM.
3. External Sort Algorithm - Phase 2 (Merging Sorted Runs): Detail the multi-way merge process. Explain how multiple sorted runs are read from disk, merged, and written to a new temporary file, or directly to the final output. Discuss the 'k-way merge' concept and how the number of runs merged concurrently relates to available RAM and I/O efficiency.
4. Optimizations and Considerations: Briefly mention any potential optimizations (e.g., using a min-heap for the merge phase, buffering I/O, using multiple disks) and critical considerations like disk I/O performance and temporary disk space requirements.