NO
Heat and work are related. Work can be completely converted into heat, but the reverse is not true: heat energy cannot be wholly transformed into work energy. Scientists and engineers have been able to exploit the principles of thermochemistry to develop technologies ranging from hot/cold packs to gasoline powered combustion engines.
For a closed system, the change in internal energy (∆U) is related to heat (Q) and work (W) as follows:
ΔU=Q+W
This means that the total energy within a system is affected by the sum of two possible energy transfers: heat and work.
THEY ARE NOT EQUAL