There are two relationships that are often mistaken for causation. A common response is when some other reason may cause the same result. A confounding variable is when there are other variables that are unknown or unobserved. a. In North Carolina, the number of shark attacks increases when the temperature increases. Therefore, a temperature increase appears to cause sharks to attack. List two or more common responses that could also cause this result. b. A company claims that their weight loss pill caused people to lose 20 pounds when following the accompanying exercise program. List two or more confounding variables that could have had an effect on this claim.

A small circular surface of area $A_1 = 2 cm^2$ located at the center of a 2-m-diameter sphere emits radiation as a blackbody at $T_1 = 1000 K.$ Determine the rate at which radiation energy is streaming through a $D_2$ = 1-cm-diameter hole located (a) on top of the sphere directly above $A_1$ and (b) on the side of sphere such that the line that connects the centers of $A_1$ and $A_2$ makes $45^\circ$ with surface $A_1.$

Consider a cylindrical enclosure whose height is twice the diameter of its base. Find the view factor from the side surface of this cylindrical enclosure to its base surface.

It is desired that the radiation energy emitted by a light source reach a maximum in the blue range $(\lambda=0.47 \mu \mathrm{m}).$ Determine the temperature of this light source and the fraction of radiation it emits in the visible range $(\lambda=0.40-0.76 \mu \mathrm{m}).$

Find the exact value of each expression. Do not use a calculator. $\tan ^{-1}\left[\tan \left(-\frac{3 \pi}{8}\right)\right]$

Consider two identical bodies, one at 1000 K and the other at 1500K. Which body emits more radiation in the shorter-wavelength region? Which body emits more radiation at a wavelength of $20 \mu \mathrm{m} ?$

A thermocouple used to measure the temperature of hot air flowing in a duct whose walls are maintained at $T_w=500 \mathrm{~K}$ shows a temperature reading of $T_{\text {th }}=850 \mathrm{~K}$. Assuming the emissivity of the thermocouple junction to be $\varepsilon=0.6$ and the convection heat transfer coefficient to be $h=75 \mathrm{~W} / \mathrm{m}^2$.K, find the actual temperature of air.

Consider a cylindrical enclosure whose height is twice the diameter of its base. Find the view factor from the side surface of this cylindrical enclosure to its base surface.

Consider a conical enclosure of height h and base diameter D. Determine the view factor from the conical side surface to a hole of diameter d located at the center of the base.

A furnace is shaped like a long semicylindrical duct of diameter $D=15 \mathrm{ft}$. The base and the dome of the furnace have emissivities of $0.5$ and $0.9$ and are maintained at uniform temperatures of $550$ and $1800 \mathrm{~R}$, respectively. Find the net rate of radiation heat transfer from the dome to the base surface per unit length during steady operation.

Consider a cylindrical enclosure whose height is twice the diameter of its base. Determine the view factor from the side surface of this cylindrical enclosure to its base surface.

A horizontal plate is experiencing uniform irradiation on the both upper and lower surfaces. The ambient air temperature surrounding the plate is 290 K with a convection heat transfer coefficient of $30 W/m^2 \cdot K.$ Both upper and lower surfaces of the plate have a radiosity of $4000 W/m^2,$ and the plate temperature is maintained uniformly at 390 K. If the plate is not opaque and has an absorptivity of 0.527, determine the irradiation and emissivity of the plate.

Some experiments are being conducted in a laboratory in which the air temperature is $27^{\circ}\mathrm{C}$ and the atmospheric pressure is 14.3 psia. Determine the density of the air. Express your answers in slugs/ft$^{3}$ and in kg/m$^{3}$.

Find the exact value of each expression. Do not use a calculator. $\sin ^{-1}\left[\sin \left(-\frac{5 \pi}{3}\right)\right]$