  Heat capacity measurements using the ac steady state method are often
considered difficult to provide absolute accuracy. By adjusting the working
frequency to maintain a constant phase and using the phase information to
obtain the heat capacity, we have found that it is possible to achieve good
absolute accuracy. Here we present a thermodynamic study of a ~ 2.6 {\mu}g Pb
superconducting crystal to demonstrate the newly opened capabilities. The
sample is measured using a differential membrane-based calorimeter. The
custom-made calorimetric cell is a pile of thin film Ti heater, insulation
layer and Ge_{1-x}Au_{x} thermometer fabricated in the center of two
Si_{3}N_{4} membranes. It has a background heat capacity < 100 nJ/K at 300K,
decreasing to 9 pJ/K at 1 K. The sample is characterized at temperatures down
to 0.5 K. The zero field transition at Tc = 7.21 K has a width \approx 20 mK
and displays no upturn in C. From the heat capacity jump at Tc and the
extrapolated Sommerfeld term we find \DeltaC/{\gamma}Tc = 2.68. The latent heat
curve obtained from the zero field heat capacity measurement, and the
deviations of the thermodynamic critical field from the empirical expression Hc
=Hc(0)[1-(T/Tc)^2] are discussed. Both analyses give results in good agreement
with literature.
