(a) The heat capacity at \(1 \mathrm{~atm}\) pressure of solid magnesium in the temperature range of 0 to \(560^{\circ} \mathrm{C}\) is given by the expression

\[ C_{P}=6.2+1.33 \times 10^{-3} T+6.78 \times 10^{4} T^{-2} \mathrm{cal} / \mathrm{deg} \text {-g-atom } \]

Determine the increase of entropy, per \(\mathrm{g}\)-atom, for an increase of temperature from \(300 \mathrm{~K}\) to \(800 \mathrm{~K}\) at \(1 \mathrm{~atm}\) pressure.

(b) A steam turbine developing \(34 \mathrm{~kW}\) receives steam at 15 bar with an internal energy of \(2720 \mathrm{~kJ} / \mathrm{kg}\), specific volume of \(0.17 \mathrm{~m}^{3} / \mathrm{kg}\) and velocity of \(110 \mathrm{~m} / \mathrm{s}\). Steam is exhausted from turbine at 0.1 bar with internal energy \(2177 \mathrm{~kJ} / \mathrm{kg}\), specific volume \(15 \mathrm{~m}^{3} / \mathrm{kg}\) and velocity \(320 \mathrm{~m} / \mathrm{s}\). The heat loss over the surface of the turbine is \(20 \mathrm{~kJ} / \mathrm{kg}\). Neglecting change in potential energy, determine (i) Work done per \(\mathrm{kg}\) of steam (ii) Steam flow through the turbine in \(\mathrm{kg} / \mathrm{h}\).