A wall has inner and outer surface temperatures of 16 and $6^{\circ} \mathrm{C}$, respectively. The interior and exterior air temperatures are 20 and $5^{\circ} \mathrm{C}$, respectively. The inner and outer convection heat transfer coefficients are 5 and $20 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively. Calculate the heat flux from the interior air to the wall, from the wall to the exterior air, and from the wall to the interior air. Is the wall under steady-state conditions?

A concrete wall, which has a surface area of $20 \mathrm{m}^{2}$ and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at $25^{\circ} \mathrm{C}$, and the thermal conductivity of the concrete is $1 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. (a) Determine the heat loss through the wall for outer surface temperatures ranging from $-15^{\circ} \mathrm{C}$ to $38^{\circ} \mathrm{C}$, which correspond to winter and summer extremes, respectively. Display your results graphically. (b) On your graph, also plot the heat loss as a function of the outer surface temperature for wall materials having thermal conductivities of 0.75 and $1.25 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. Explain the family of curves you have obtained.

A furnace for processing semiconductor materials is formed by a silicon carbide chamber that is zone-heated on the top section and cooled on the lower section. With the elevator in the lowest position, a robot arm inserts the silicon wafer on the mounting pins. In a production operation, the wafer is rapidly moved toward the hot zone to achieve the temperature-time history required for the process recipe. In this position, the top and bottom surfaces of the wafer exchange radiation with the hot and cool zones, respectively, of the chamber. The zone temperatures are $T_{h}=1500 \mathrm{K}$ and $T_{c}=330 \mathrm{K}$, and the emissivity and thickness of the wafer are $\varepsilon=0.65$ and d=0.78 mm, respectively. With the ambient gas at $T_{\infty}=700 \mathrm{K}$, convection coefficients at the upper and lower surfaces of the wafer are 8 and $4 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively. The silicon wafer has a density of $2700 \mathrm{kg} / \mathrm{m}^{3}$ and a specific heat of $875 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$. (a) For an initial condition corresponding to a wafer temperature of $T_{w, i}=300 \mathrm{K}$ and the position of the wafer shown schematically, determine the corresponding time rate of change of the wafer temperature, $\left(d T_{w} / d t\right)_{i}$. (b) Determine the steady-state temperature reached by the wafer if it remains in this position. How significant is convection heat transfer for this situation? Sketch how you would expect the wafer temperature to vary as a function of vertical distance.

Consider the motion of the following objects. Assume the x-axis is horizontal, the positive y-axis is vertical, the ground is horizontal, and only the gravitational force acts on the object. A projectile is launched from a platform $20 \mathrm{ft}$ above the ground at an angle of $60^{\circ}$ above the horizontal with a speed of $250 \mathrm{ft} / \mathrm{s}$. Assume the origin is at the base of the platform. Determine the time of flight and range of the object.

Write the symbol for the element: platinum

Determine whether the following statements are true and give an explanation or counterexample.

$| \mathbf { u } \times \mathbf { v } |$ is less than both $|u|$ and $|v|$.

Find all horizontal and vertical asymptotes. $f(x)=\frac{3 x+2}{x-4}$

A particle is in the first excited ( $n=2)$ state of a onedimensional box that has length $L$. (The box has one end at the origin and the other end on the positive $x$ axis.) . Find \left\langle x^2\right\rangle$.

A box of snack-size cracker packs weighs $28 \frac{1}{2}$ ounces. Each snack pack weighs $4 \frac{3}{4}$ ounces. How many snack packs are in the box?

Explain why fluid pressure on a surface is calculated using horizontal representative

What is the pulse deficit if an apical pulse is 112 and the radial pulse is 88?

Sum the series (if they converge).

$$\sum_{k=1}^{\infty} \frac{3^{2 k}+1}{27^k}$$

A $45.0-\mathrm{kg}$ crate is dragged at constant velocity $8.20 \mathrm{~m}$ across a horizontal floor with a rope making a $30^{\circ}$ angle above the horizontal. The coefficient of kinetic friction is $0.250$. Find the work done (a) by friction.

Plate glass at $600^{\circ} \mathrm{C}$ is cooled by passing air over its surface such that the convection heat transfer coefficient is $h=$ $50 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. To prevent cracking, it is known that the temperature gradient must not exceed $15^{\circ} \mathrm{C} / \mathrm{mm}$ at any point in the glass during the cooling process. If the thermal conductivity of the glass is $1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$ and its surface emissivity is $0.8$, what is the lowest temperature of the air that can initially be employed for the cooling? Suppose that the temperature of the air equals that of the surroundings.