  The specific heat is frequency dependent in highly viscous liquids. By
solving the full one-dimensional thermo-viscoelastic problem analytically it is
shown that, because of thermal expansion and the fact that mechanical stresses
relax on the same time scale as the enthalpy relaxes, the plane thermal-wave
method does not measure the isobaric frequency-dependent specific heat
c_p(omega). This method rather measures a "longitudinal" frequency-dependent
specific heat, a quantity defined and detailed here that is in-between
c_p(omega) and c_v(omega). This result means that no wide-frequency
measurements of c_p(omega) on liquids approaching the calorimetric glass
transition exist. We briefly discuss consequences for experiment.
