Proof of Work (PoW)algorithms are primarily used to demonstrate that sufficient computational resources have been expended by a participant to validate transactions and add them to the blockchain. In PoW, miners compete to solve a cryptographic puzzle, which requires significant computational power. This effort helps secure the network by making it prohibitively expensive for any individual or group to alter the blockchain's history.

Key Details:

Mechanism of PoW: The essence of PoW is to prove that a certain amount of computational work has been performed. This “work” is measured by the effort miners invest in solving the cryptographic puzzle. The process requires miners to find a nonce that, when hashed with the block’s data, results in a hash that meets the network's difficulty requirements.

Security and Integrity: By proving computational work, PoW ensures that miners cannot simply fabricate or alter transactions without a significant investment of resources. This mechanism deters attacks and makes blockchain networks resistant to tampering and double-spending.

Association with Bitcoin Mining: Although PoW is often associated with Bitcoin mining (as miners expend computational resources to validate and record transactions), its broader purpose is to establish a cost for participation in the network, ensuring that all entries to the blockchain are trustworthy and secure.

Therefore, PoW is best described as a mechanism for proving that adequate computational resources have been expended, aligning with the correct answer B.