  We revisit the problem of work extraction from a system in contact with a
heat bath to a work storage system, and the reverse problem of state formation
from a thermal system state in single-shot quantum thermodynamics. A physically
intuitive and mathematically simple approach using only elementary majorization
theory and matrix analysis is developed, and a graphical interpretation of the
maximum extractable work, minimum work cost of formation, and corresponding
single-shot free energies is presented. This approach provides a bridge between
two previous methods based respectively on the concept of thermomajorization
and a comparison of subspace dimensions. In addition, a conceptual
inconsistency with regard to general work extraction involving transitions
between multiple energy levels of the work storage system is clarified and
resolved. It is shown that an additional contribution to the maximum
extractable work in those general cases should be interpreted not as work
extracted from the system, but as heat transferred from the heat bath. Indeed,
the additional contribution is an artifact of a work storage system
(essentially a suspended "weight" that can be raised or lowered) that does not
truly distinguish work from heat. The result calls into question the common
concept that a work storage system in quantum thermodynamics is simply the
quantum version of a suspended weight in classical thermodynamics.
