  In the present work, we have reported the temperature dependent thermopower
($\alpha$) behavior of La$_{0.75}$Ba$_{0.25}$CoO$_{3}$ compound in the
temperature range 300-600 K. Using the Heikes formula, the estimated value of
$\alpha$ corresponding to high-spin configuration of Co$^{3+}$ and Co$^{4+}$
ions is found to be $\sim$$16$ $\mu$V/K, which is close to the experimental
value, $\sim$13 $\mu$V/K, observed at $\sim$600 K. The temperature dependent TE
behavior of the compound is studied by combining the WIEN2K and BoltzTrap code.
The self consistency field calculations show that the compound have
ferromagnetic ground state structure. The electronic structure calculations
give half metallic characteristic with a small gap of $\sim$50 meV for down
spin channel. The large and positive value for down spin channel is obtained
due to the unique band structure shown by this spin channel. The temperature
dependent relaxation time for both the spin-channel charge carriers is
considered to study the thermopower data in temperature range 300-600 K. An
almost linear values of $\tau_{up}$ and a non-linear values of $\tau_{dn}$ are
taken into account for evaluation of $\alpha$. By taking the temperature
dependent values of relaxation time for both the spin channels, the calculated
values of $\alpha$ using two current model are found to be in good agreement
with experimental values in the temperature range 300-600 K. At 300 K, the
calculated value of electrical conductivity by using the same value of
relaxation time, i.e. 0.1 $\times $10$^{-14}$ seconds for spin-up and 0.66
$\times $10$^{-14}$ seconds for spin-dn channel, is found to be equal to the
experimentally reported value.
