An instrumentation package has a spherical outer surface of diameter D=100 mm and emissivity $\varepsilon=0.25$. The package is placed in a large space simulation chamber whose walls are maintained at 77 K. If operation of the electronic components is restricted to the temperature range $40 \leq T \leq 85^{\circ} \mathrm{C}$, what is the range of acceptable power dissipation for the package? Display your results graphically, showing also the effect of variations in the emissivity by considering values of 0.20 and 0.30.

An overhead 25-m-long, uninsulated industrial steam pipe of 100-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?

Consider a circuit element, with terminals a and b, that has $v_{ab} = −12 \ V$ and $i_{ab} = 3 \ A$. Over a period of 2 seconds, how much charge moves through the element? If electrons carry the charge, which terminal do they enter? How much energy is transferred? Is it delivered to the element or taken from it?

Pressurized water $\left(p_{\mathrm{in}}=10 \text { bar, } T_{\mathrm{in}}=110^{\circ} \mathrm{C}\right)$ enters the bottom of an L=10-m-long vertical tube of diameter D=100 mm at a mass flow rate of m=1.5 kg/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 $p_{\mathrm {out }}=7 \mathrm { bar }$, $T_{\mathrm{out}}=600^{\circ} \mathrm{C}$. 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. Hint: Relevant properties may be obtained from a thermodynamics text.

Liquid oxygen, which has a boiling point of 90 K and a latent heat of vaporization of 214 kJ/kg, is stored in a spherical container whose outer surface is of 500-mm diameter and at a temperature of $-10^{\circ} \mathrm{C}$. The container is housed in a laboratory whose air and walls are at $25^{\circ} \mathrm{C}$. (a) If the surface emissivity is 0.20 and the heat transfer coefficient associated with free convection at the outer surface of the container is $10 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, what is the rate, in kg/s, at which oxygen vapor must be vented from the system? (b) Moisture in the ambient air will result in frost formation on the container, causing the surface emissivity to increase. Assuming the surface temperature and convection coefficient to remain at $-10^{\circ} \mathrm{C}$ and $10 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively, compute the oxygen evaporation rate (kg/s) as a function of surface emissivity over the range $0.2 \leq \varepsilon \leq 0.94$.

Air at $40^{\circ} \mathrm{C}$ flows over a long, 25-mm-diameter cylinder with an embedded electrical heater. In a series of tests, measurements were made of the power per unit length, $P^{\prime}$, required to maintain the cylinder surface temperature at $300^{\circ} \mathrm{C}$ for different free stream velocities V of the air. The results are as follows:

$$\begin{matrix} \text{Air velocity, V(m/s)} & \text{1} & \text{2} & \text{4} & \text{8} & \text{12}\\ \text{Power, }{P^{\prime}(\mathrm{W} / \mathrm{m})} & \text{450} & \text{658} & \text{983} & \text{1507} & \text{1963}\\ \end{matrix}$$

(a) Determine the convection coefficient for each velocity, and display your results graphically. (b) Assuming the dependence of the convection coefficient on the velocity to be of the form $h=C V^{n}$, determine the parameters C and n from the results of part (a).