  We have measured the specific heat of crystals of (Ca1-xSrx)3Ru2O7 using ac-
and relaxation-time calorimetry. Special emphasis was placed on the
characterization of the Neel (TN=56 K) and structural (Tc = 48 K) phase
transitions in the pure, x=0 material. While the latter is believed to be first
order, detailed measurements under different experimental conditions suggest
that all the latent heat (with L ~ 0.3 R) is being captured in a broadened peak
in the effective heat capacity. The specific heat has a mean-field-like step at
TN, but its magntitude (Delta cP ~ R) is too large to be associated with a
conventional itinerant electron (e.g. spin-density-wave) antiferromagnetic
transition, while its entropy is too small to be associated with full ordering
of localized spins. The TN transition broadens with Sr substitution while its
magnitude decreases slowly. On the other hand, the entropy change associated
with the Tc transition decreases rapidly with Sr substitution and is not
observable for our x=0.58 sample.
