B3 (a) Derive the Maxwell relation as (ӘР av ar where S is the entropy, V is the volume, T is the temperature, and P is

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B3 (a) Derive the Maxwell relation as (ӘР av ar where S is the entropy, V is the volume, T is the temperature, and P is the pressure. [10 Marks] (). V (F), т V N (b) (i) Consider the central equation of thermodynamics and the result of Q. B3 (a). Show that for any gas a E ӘР =T P. av at where E is the total internal energy of the gas. (ii) One mole of a van der Waals gas has an equation of state given by RT V-6 V2 where a and b are constants. Find (), for the van der Waals gas. (iii) The gas of Q. B3 (b)(ii) undergoes an isothermal expansion to three times its initial volume of 1m. Calculate the change in internal energy of the gas noting that a = 0.3640 J m mol-2, and b = 4.267 x 10-5mmol- [10 Marks) a P = (2