Consider a non-ideal gas that follows the Van der Waals equation of state: RT a v-b...

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Consider a non-ideal gas that follows the Van der Waals equation of state: RT a v-b 22 P = Where p is the pressure, T the temperature, v the specific volume, R the universal gas constant, and a and b two constants that are to be considered known. a) Show that the internal pressure 7 of this gas is given by the relation: π = (5%) b) Show that α du = c₂dT + 2 dv where u is the specific internal energy and co the specific heat under constant volume. (5%) c) Explain exactly how the expression that you got for the differential of internal energy in question (b) differs from the corresponding one for ideal gas (5%) and under what condition(s) the relation of question (b) can be approximated acceptably by the one of the ideal gas. (5%) Consider a non-ideal gas that follows the Van der Waals equation of state: RT a v-b 22 P = Where p is the pressure, T the temperature, v the specific volume, R the universal gas constant, and a and b two constants that are to be considered known. a) Show that the internal pressure 7 of this gas is given by the relation: π = (5%) b) Show that α du = c₂dT + 2 dv where u is the specific internal energy and co the specific heat under constant volume. (5%) c) Explain exactly how the expression that you got for the differential of internal energy in question (b) differs from the corresponding one for ideal gas (5%) and under what condition(s) the relation of question (b) can be approximated acceptably by the one of the ideal gas. (5%)