  Energy supply sources for the heating process in the slow solar wind remain
unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to
study this issue. Recently, PSP observations have found that the slow solar
wind experiences stronger heating inside 0.24 au. Here for the first time we
measure in the slow solar wind the radial gradient of the low-frequency breaks
on the magnetic trace power spectra and evaluate the associated energy supply
rate. We find that the energy supply rate is consistent with the observed
perpendicular heating rate calculated based on the gradient of the magnetic
moment. Based on this finding, one could explain why the slow solar wind is
strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25
au. This finding supports the concept that the energy added from the
energy-containing range is transferred by an energy cascade process to the
dissipation range, and then dissipates to heat the slow solar wind. The related
issues for further study are discussed.
