Exact forms for the thermodynamic functions of linear adsorbates in one dimension are presented in the lattice gas description of localized adsorption with multisite occupancy. A modified form of the adsorption isotherm for linear adsorbates on heterogeneous substrates is proposed, by introducing the rigorous expression for the Helmholtz free energy of the adlayer on a homogeneous one-dimensional lattice into the multisite occupancy model proposed by Nitta et al. (1984). Comparisons between the original and modified isotherms and Monte Carlo simulations for dimers and 4-mers on heterogeneous surfaces with two type of sites are carried out. Fitting of the adsorption isotherm to experimental data for CO, N-2, and O-2 on zeolites 5A and 10X is performed and discussed as well.