The experimental equilibrium phase diagram of a mixture of linear polystyrene of molecular weight M-omega = 44,000 g/mol and 4-cyano-4'-n-octyl-biphenyl (8CB) is established. The three transitions smectic A-nematic, nematic-isotropic, and isotropic-isotropic are observed. The first two are observed both by optical microscopy and differential scanning calorimetry (DSC) while the isotropic-isotropic transition could be seen only via optical microscopy. Two series of samples with the same compositions were independently prepared and yielded consistent results both by microscopy and DSC. Measurements of sample compositions with less than 50 weight % of 8CB were influenced by the vicinity of the glass transition temperature (T-g) of the polymer in the mixture. This quantity is also determined by DSC as a function of composition. A single T-g is observed, which decreases with composition of the LC. Other thermodynamic quantities such as the enthalpy variations of LC in the nematic-isotropic transition and the fraction of LC contained in the droplets are also considered.