In supercooled liquids structural relaxation shows up as a frequency d
ependence of mechanical and thermal properties such as the adiabatic b
ulk modulus, K-s, shear modulus, G, expansion coefficient, alpha(p), a
nd isobaric specific heat, c(p). Whereas K-s and G can be measured dir
ectly, we claim this is difficult for c(p). Near the glass transition
where c(p) differs significantly from the isochoric specific heat, c(v
), and G approaches K-s, heat transport is no longer adequately descri
bed by the heat diffusion equation but by four coupled thermoviscoelas
tic equations. Thus the effective specific heat obtained by specific h
eat spectroscopy can differ from c(p). We present specific heat spectr
oscopy data on 1,2,4-butanetriol obtained in an approximate spherical
symmetric geometry. In this geometry the effect of the thermomechanica
l coupling can be calculated. The thermal wavelength can be varied fro
m much greater to much smaller than the sample size. Thus the novel me
thod comprises both the homogeneous and inhomogeneous methods. In the
homogeneous limit, we, as a good approximation, obtain the pure c(p).
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