Why was the second weapon in the Manhattan project never tested?

The second weapon developed during the Manhattan Project, known as the "Fat Man" bomb, was not tested before its use because the project prioritized practical deployment over further testing. The first successful test of an atomic bomb, codenamed "Trinity," demonstrated the weapon's effectiveness, leading to the decision to use the Fat Man and the "Little Boy" bomb without conducting an additional test. This approach aimed to expedite the end of World War II and maximize the psychological impact on Japan.