A lump of ice with a mass of \(1.5 \mathrm{~kg}\), at an initial temperature of \(T_{1}=260 \mathrm{~K}\) melts at a pressure of 1 bar as a result of heat transfer from the environment. After some time has elapsed, the resulting water attains the temperature of the environment i.e. \(T_{0}=293 \mathrm{~K}\). Calculate the entropy production associated with this process. Take the enthalpy of fusion for water, \(h_{s f}=333.4 \mathrm{~kJ} / \mathrm{kg}\) and the isobaric specific heat capacities of ice and water as \(C_{p, i c e}=2.07 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\) and \(C_{p, w}=4.20 \mathrm{~kJ} / \mathrm{lkg}\) K. Ice melts at \(T_{m}=273.16 \mathrm{~K}\).

(a) Calculate the specific physical exergy of \(\mathrm{CO}_{2}\left(C_{p}=0.8659 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}, R=ight.\) \(0.1889 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K})\) for a state defined by \(p_{1}=0.7 \mathrm{bar}\) and \(T_{1}=268.15 \mathrm{~K}\).

(b) Calculate the molar chemical exergy of \(\mathrm{CO}_{2}\). The partial pressure of \(\mathrm{CO}_{2}\) in the atmosphere is equal to 0.0003 bar. The molar ideal gas constant is \(8.3144 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}\).

(c) Calculate the molar chemical exergy of a mixture of gases with the following composition by volume (or by more): CO-0.15, air-0.85. For the environment take, \(T_{0}=293.15 \mathrm{~K}\) and \(p_{0}=1.0\) bar.