Pressurized water ( \(p_{\text {in }}=10 \mathrm{bar}, T_{\text {in }}=110^{\circ} \mathrm{C}\) ) enters the bottom of an \(L=12\)-m-long vertical tube of diameter \(D=110 \mathrm{~mm}\) at a mass flow rate of \(\dot{m}=1.5 \mathrm{~kg} / \mathrm{s}\). The tube is located inside a combustion chamber, resulting in heat transfer to the tube. Superheated steam exits the top of the tube at \(p_{\text {out }}=7 \mathrm{bar}, T_{\text {out }}=600^{\circ} \mathrm{C}\). Determine the change in the rate at which the following quantities enter and exit the tube:

(a) the combined thermal and flow work,

(b) the mechanical energy, and

(c) the total energy of the water. Also,

(d) determine the heat transfer rate, \(q\).