  Tuning the energy density of matter at high pressures gives rise to exotic
and often unprecedented properties, e.g., structural transitions,
insulator-metal transitions, valence fluctuations, topological order, and the
emergence of superconductivity. The study of specific heat has long been used
to characterize these kinds of transitions, but their application to the
diamond anvil cell (DAC) environment has proved challenging. Limited work has
been done on the measurement of specific heat within DACs, in part due to the
difficult experimental setup. To this end we have developed a novel method for
the measurement of specific heat within a DAC that is independent of the DAC
design and therefore readily compatible with any DACs already performing high
pressure resistance measurements. As a proof-of-concept, specific heat
measurements of the MgB2 superconductor were performed, showing a clear anomaly
at the transition temperature (Tc), indicative of bulk superconductivity. This
technique allows for specific heat measurements at higher pressure than
previously possible.
