i molecuiar dimamics calculations, it is easy to obtain u and h from averaging energies of arrangements of atoms representative of a given temperature斗however, even if all the atomic positions are known, there is still no way to directly calculate s, f or g. one eeds to know all possible arrangements prove that gt ot in a molecular dynamics calculation, the temperature is raised from ti to t2, at constant pressure and the heat capacity is c a bt). find an expression forfial gibbs free energy in terms of its initial value, the initial enthalpy (h gi) and cp. 2. prove the general result that the van der wals equation for one mole of diatoe fluid is given by 3. show that the heat capacity at coustant volume of a van der waals fluid depends only on the temperature. 2 4. using the previous results, and the fact that in the low pressure limit the van der waals fluid energy must be the same as the ideal gas, prove that the molar internal energy of a diatomic van der waals fluid is given by and hence show that cu is the same for the ideal gas and van der waals fluid. explain the physical reason for why the coustant a appears in this equation, but not the constant b 5. sketch the p, t phase diagram for the van der waals fluid. calculate the isothmal bulk modulus by differen- tiating the van der waals equation in terms of v and t, give conditions for the differential to be negative, and explain what would actually happen to a van der waals fuid under such conditins 6. show that the change in entropy when one mole of a van der waals find converts from (to, w) to(t, v) is