An overhead 25 -m-long, uninsulated industrial steam pipe of \(100-\mathrm{mm}\) diameter is routed through a building whose walls and air are at \(25^{\circ} \mathrm{C}\). Pressurized steam maintains a pipe surface temperature of \(150^{\circ} \mathrm{C}\), and the coefficient associated with natural convection is \(h=10\) \(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The surface emissivity is \(\varepsilon=0.8\).

(a) What is the rate of heat loss from the steam line?

(b) If the steam is generated in a gas-fired boiler operating at an efficiency of \(\eta_{f}=0.90\) and natural gas is priced at \(C_{g}=\$ 0.02\) per MJ, what is the annual cost of heat loss from the line?