  This Letter reports the first observational estimate of the heating rate in
the slowly expanding solar corona. The analysis exploits the simultaneous
remote and local observations of the same coronal plasma volume with the Solar
Orbiter/Metis and the Parker Solar Probe instruments, respectively, and relies
on the basic solar wind magnetohydrodynamic equations. As expected, energy
losses are a minor fraction of the solar wind energy flux, since most of the
energy dissipation that feeds the heating and acceleration of the coronal flow
occurs much closer to the Sun than the heights probed in the present study,
which range from 6.3 to 13.3 solar radii. The energy deposited to the
supersonic wind is then used to explain the observed slight residual wind
acceleration and to maintain the plasma in a non-adiabatic state. As derived in
the Wentzel-Kramers-Brillouin limit, the present energy transfer rate estimates
provide a lower limit, which can be very useful in refining the
turbulence-based modeling of coronal heating and subsequent solar wind
acceleration.
