Explain to your friend, who is skeptical about energy quantization, the simple evidence provided by distinct colors you sec when you hold a CD (serving as a diffraction grating) near a fluorescent light. It may be helpful to contrast this evidence with the spectrum produced by an incandescent light, which relies on heating a filament to produce a rather nonspecific blackbody spectrum.

During a cold winter day, wind at 55 km/h is blowing parallel to a 4-m-high and 10-m-long wall of a house. If the air outside is at $5^\circ C$ and the surface temperature of the wall is $12^\circ C,$ determine the rate of heat loss from that wall by convection. What would your answer be if the wind velocity was doubled?

Exhaust gases from a manufacturing plant are being discharged through a 10-m tall exhaust Stack with outer diameter of 1 m, wall thickness of 10 cm, and thermal conductivity of $40 W/m \cdot K.$ The exhaust gases are discharged at a rate of 1.2 kg/s, while temperature drop between inlet and exit of the exhaust Stack is $30 ^\circ C,$ and the constant pressure specific heat of the exhaust gasses is $1600 J/kg \cdot K.$ On a particular day, the outer surface of the exhaust Stack experiences radiation with the surrounding at $27 ^\circ C,$ and convection with the ambient air at $27 ^\circ C$ also, with an average convection heat transfer coefficient of $8 W/m^2 \cdot K.$ Solar radiation is incident on the exhaust Stack outer surface at a rate of $150 W/m^2,$ and both the emissivity and solar absorptivity of the outer surface are 0.9. Assuming steady one-dimensional heat transfer, (a) obtain the Variation of temperature in the exhaust Stack wall and (b) determine the inner surface temperature of the exhaust Stack.

Starting with an energy balance on a volume element, obtain the two-dimensional transient implicit finite difference equation for a general interior node in rectangular coordinates for T(x, y,t) for the case of constant thermal' conductivity and no heat generation.

Consider laminar flow over a flat plate. Will the friction coefficient change with distance from the leading edge? How about the heat transfer coefficient?

Crude oil at $22^\circ C$ enters a 20-cm-diameter pipe with an average velocity of 20 cm/s. The average pipe wall temperature is $2^\circ C.$ Crude oil properties are as given below. Calculate the rate of heat transfer and pipe length if the crude oil outlet temperature is $20^\circ C.$

$$\begin{matrix} \text{T} & \rho & \text{K} & \mu & C_p\\ ^\circ C & kg/m^3 & W/m \cdot K & mPa \cdot s & kJ/kg \cdot K\\ \text{2.0} & \text{900} & \text{0.145} & \text{60.0} & \text{1.80}\\ \text{22.0} & \text{890} & \text{0.145} & \text{20.0} & \text{1.90}\\ \end{matrix}$$

You want to test two strains of E. coli for sensitivity to the DNA damaging agent, MMS (methyl methanesulfonate), an alkylating agent that methylates specific bases in DNA. After treating cells with a range of doses of MMS (by incubating the cells with MMS in liquid culture for various times), you plate the cells on a solid media to count survivors (given below). Plot the data for the two strains (percent survival vs. time of MMS exposure). Which strain is more sensitive to MMS? (Note that to count single colonies, you would have to serial-dilute the culture. For this example, we will ignore the serial dilution step.)

$$\begin{matrix} & \text{0 MIn} & \text{5 Min } & \text{10 Min}\\\text{Strain} & \text{in MMS} & \text{in MMS} & \text{in MMS}\\\text{Strain A} & \text{254} & \text{251} & \text{249}\\\text{Strain B} & \text{325} & \text{253} & \text{189}\\\end{matrix}$$

A 150-mm diameter and 1-cm long vertical rod has water flowing across its outer surface at a velocity of 0.5 m/s. The water temperature is uniform at $40^\circ C,$ and the rod surface temperature is maintained at $120^\circ C.$ Under these conditions are the natural convection effects important to the heat transfer process?

Consider the Newton’s method iteration. (a) Use initial vector $x_0 = (1.4, 10)$ and calculate the successive approximations $x_1, x_2, x_3,$ etc. To what solution of the system of equations do the approximations converge? (b) Repeat part (a) with $\mathbf{x}_{0}=(1.3,10)$. (c) We saw that (4, 5) was a solution of the given system of equations. Is (1.3, 10) closer to (4, 5) or to the limiting point of the sequence you calculated in part (b)? (d) Comment on your observations in part (c). What do these observations suggest about howeasily you can use the initial vector $x_0$ to predict the value of $\lim _{k \rightarrow \infty} \mathbf{x}_{k}$ (assuming that the limit exists)?

(a) Show that the angle of recoil of the target particle relative to the incident direction of the scattered particle is simply $\Phi=\frac{1}{2}(\pi-\Theta)$. (b) It is observed that in elastic scattering the scattering cross section is isotropic in terms of $\Theta$. What are the corresponding probability distributions for the scattered energy of the incident particle, E$_{1}$, and for the recoil energy of the target particle, E$_{2}$?

A certain electric circuit has a resistor and a capacitor. The capacitor is initially charged to 100 V. When the power supply is detached, the capacitor voltage decays with time as shown in the following data table. Find a functional description of the capacitor voltage v as a function of time t.

Water at 40$^{\circ} \mathrm{F}$ is to flow through a 1$\frac{1}{2}$-in: schedule 40 steel pipe. The outside surface of the pipe is to be insulated with a 1-in.-thick layer of 85% magnesia and a 1-in.-thick layer of packed glass wool, k = 0.022 Btu/h ft $^{\circ} \mathrm{F}$. The surrounding air is at 100$^{\circ} F$. a. Which material should be placed next to the pipe surface to produce the maximum insulating effect?b. What will be the heat flux on the basis of the outside pipe surface area? The convective heat-transfer coefficients for the inner and outer surfaces are 100 and 5 Btu/h ft $^{\circ} \mathrm{F}$, respectively.

A steel control rod is 5.5 ft long and must not stretch more than 0.04 in. when a 2-kip tensile load is applied to it. Knowing that $E=29 \times 106$ psi, determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load.

The stream function for an incompressible, two dimensional flow field is $\psi=3 x^{2} y+y$. For this flow field, sketch several streamlines.