3. The specific Helmholtz Free energy \( f \) is related to the specific internal energy \( u \) as:\[ f(T, \alpha) = u - Ts \]where the "natural variables" of \( f \) are temperature and specific volume.a. Expand the differential of \( f \) in terms of partial derivatives with respect to the natural variables of \( f \).b. Using the result from a. and applying the 1st Law of Thermodynamics, what are \( \left( \frac{\partial f}{\partial \alpha} \right)_T \) and \( \left( \frac{\partial f}{\partial T} \right)_\alpha \)?c. From the equality of mixed partial derivatives, show that \[ \left( \frac{\partial p}{\partial T} \right)_\alpha = \left( \frac{\partial s}{\partial \alpha} \right)_T \]

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Answered: 3. The specific Helmholtz Free energy f…

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