  The first law of thermodynamics restates the law of conservation of energy.
It partitions the change in energy of a system into two pieces, heat and work.
While there is no ambiguity to define heat and work in classical
thermodynamics, their classification in the quantum regime is not that obvious.
Thus, the first law of thermodynamics becomes problematic in the quantum
regime. However, recent studies have shown if contribution of quantum coherence
is considered to the change of internal energy of the system, the first law of
thermodynamics can be extended to the quantum domain. Here we investigate the
new version of first law of thermodynamics for some quantum transformations by
using two-level atomic system under non-dissipative channel. In our work we
achieve a novel result that quantum coherence can be transformed into heat, and
the heat can dissipate into the environments.
