  The heating of ions and electrons due to turbulent dissipation plays a
crucial role in the thermodynamics of the solar wind and other plasma
environments. Using magnetic field and thermal plasma observations from the
first two perihelia of the Parker Solar Probe (PSP), we model the relative
heating rates as a function of radial distance, magnetic spectra, and plasma
conditions, enabling us to better characterize the thermodynamics of the inner
heliosphere. We employ the Howes et al. 2008 steady-state cascade model, which
considers the behavior of turbulent, low-frequency, wavevector-anisotropic,
critically balanced Alfv\'enic fluctuations that dissipate via Landau damping
to determine proton-to-electron heating rates $Q_p/Q_e$. We distinguish
ion-cyclotron frequency circularly polarized waves from low-frequency
turbulence and constrain the cascade model using spectra constructed from the
latter. We find that the model accurately describes the observed energy
spectrum from over 39.4 percent of the intervals from Encounters 1 and 2,
indicating the possibility for Landau damping to heat the young solar wind. The
ability of the model to describe the observed turbulent spectra increases with
the ratio of thermal-to-magnetic pressure, $\beta_p$, indicating that the model
contains the necessary physics at higher $\beta_p$. We estimate high magnitudes
for the Kolmogorov constant which is inversely proportional to the non-linear
energy cascade rate. We verify the expected strong dependency of $Q_p/Q_e$ on
$\beta_p$ and the consistency of the critical balance assumption.
