Assume that the equation of state for a certain fluid is given as g = g - (T,P) (for example, this is the case for the IF97 equation of state, but it has also been applied for mixture equations of state like ammonia/water and LiBr/water). Show that all primary properties can be obtained by appropriate differentiation. Derive also the expressions for the specific heats c_P, c_ν , and the speed of sound c.