  We have investigated the effect of Yb substitution on the Pauli limited,
heavy fermion superconductor, CeCoIn$_5$. Yb acts as a non-magnetic divalent
substituent for Ce throughout the entire doping range, equivalent to hole
doping on the rare earth site. We found that the upper critical field in
(Ce,Yb)CoIn$_5$ is Pauli limited, yet the reduced (H,T) phase diagram is
insensitive to disorder, as expected in the purely orbitally limited case. We
use the Pauli limiting field, the superconducting condensation energy and the
electronic specific heat coefficient to determine the Wilson ratio ($R_{W}$),
the ratio of the specific heat coefficient to the Pauli susceptibility in
CeCoIn$_5$. The method is applicable to any Pauli limited superconductor in the
clean limit.
