A sound knowledge of thermodynamic properties of sII hydrates is of great importance to understand the stability of sII gas hydrates in petroleum pipelines and in natural settings. Here, we report direct molecular dynamics (MD) simulations of the thermal expansion coefficient, the compressibility, and the specific heat capacity of C3H8, or tetrahydrofuran (THF), in mixtures of CH4 or CO2, in sII hydrates under a wide, relevant range of pressure and temperature conditions. The simulations were started with guest molecules positioned at the cage center of the hydrate. Annealing simulations were additionally performed for hydrates with THF. For the isobaric thermal expansion coefficient, an effective correction method was used to modify the lattice parameters, and the corrected lattice parameters were subsequently used to obtain thermal expansion coefficients in good agreement with experimental measurements. The simulations indicated that the isothermal expansion coefficient and the specific heat capacity of C3H8-pure hydrates were comparable but slightly larger than those of THF-pure hydrates, which could form Bjerrum defects. The considerable variation in the compressibility between the two appeared to be due to crystallographic defects. However, when a second guest molecule occupied the small cages of the THF hydrate, the deviation was smaller, because the subtle guest-guest interactions can offset an unfavorable configuration of unstable THF hydrates, caused by local defects in free energy. Unlike the methane molecule, the carbon dioxide molecule, when filling the small cage, can increase the expansion coefficient and compressibility as well as decrease the heat capacity of the binary hydrate, similar to the case of sI hydrates. The calculated bulk modulus for C3H8-pure and binary hydrates with CH4 or CO2 molecule varied between 8.7 and 10.6 GPa at 287.15K between 10 and 100 MPa. The results for the specific heat capacities varied from 3155 to 3750.0 J kg-1 K-1 for C3H8-pure and binary hydrates with CH4 or CO2 at 287.15K. These results are the first of this kind reported so far. The simulations show that the thermodynamic properties of hydrates largely depend on the enclathrated compounds. This provides a much-needed atomistic characterization of the sII hydrate properties and gives an essential input for large-scale discoveries of hydrates and processing as a potential energy source.