An x-ray beam of wavelength A undergoes first-order reflection (Bragg law diffraction) from a crystal when its angle of incidence to a crystal face is

$$23 ^ { \circ }$$

, and an x-ray beam of wavelength 61 pm undergoes third-order reflection when its angle of incidence to that face is

$$60 ^ { \circ }$$

. Assuming that the two beams reflect from the same family of reflecting planes, find (a) the interplanar spacing and (b) the wavelength A.

Large amounts of $^{65} {\mathrm{Zn}}$ are produced in copper exposed to accelerator beams. While machining contaminated copper, a physicist ingests $50.0\ \mu \mathrm{Ci}$ of $^{65} {\mathrm{Zn}}.$ Each $^{65} {\mathrm{Zn}}$ decay emits an average $\gamma$-ray energy of 0.550 MeV, 40.0% of which is absorbed in the scientist’s 75.0-kg body. What dose in mSv is caused by this in one day?

For the beams and loadings shown, assume that $E I=$ $5.0 \times 10^6 \mathrm{kip}-\mathrm{in}^2{ }^2$ is constant for each beam. (a) For the beam in , determine the concentrated upward force $P$ required to make the total beam deflection at $B$ equal to zero (i.e., $v_B=0$ ). (b) For the beam in Figure P11.29b, determine the concentrated moment $M$ required to make the total beam slope at $C$ equal to zero (i.e., $\theta_C=0$ ).

Complete the truth table for the given statement by filling in the required columns. $\sim p \wedge p$.

$$\begin{matrix} \text{p} & \text{}{\sim p} & \text{}{\sim p \wedge p}\\ \text{T} & \text{ } & \text{ }\\ \text{F} & \text{ } & \text{ }\\ \end{matrix}$$

A long, cylindrical, electrical heating element of diameter $D=10 \mathrm{~mm}$, thermal conductivity $k=240 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$, density $\rho=2700 \mathrm{~kg} / \mathrm{m}^3$, and specific heat $c_p=900 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of $27^{\circ} \mathrm{C}$ and $10 \mathrm{~m} / \mathrm{s}$, respectively.

(a) Neglecting radiation, estimate the steady-state surface temperature when, per unit length of the heater, the power dissipation is $1000 \mathrm{~W} / \mathrm{m}$.

(b) If the heater is activated from an initial temperature of $27^{\circ} \mathrm{C}$, estimate the time required for the surface temperature to come within $10^{\circ} \mathrm{C}$ of its steady-state value.

Accountants at Warner Co. use worksheets similar to the one shown in Exhibit 5-13, on page 209. In the company's most current year-end worksheet, the amounts transferred from the adjusted trial balance columns to the balance sheet and income statement columns are as follows:

$$\begin{array}{|cc} \text { Total amount transferred to the credit column of the balance sheet } & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots \$ 410,000 \\ \text {Total amount transferred to the debit column of the balance sheet } & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots 540,000 \\ \text { Total amount transferred to the credit column of the income statement. } & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots 380,000\\ \end{array}$$

b. What was the total amount transferred from the adjusted trial balance columns to the debit column of the income statement?

For the following exercise,

Express the equation for the hyperbola as two functions, with $y$ as a function of $x$. Express as simply as possible. Use a graphing calculator to sketch the graph of the two functions on the same axes.

$$\frac{y^2}{9}-\frac{x^2}{1}=1$$

If

$$A=\left[\begin{array}{rr} 1 & -3 \\ -3 & 5 \end{array}\right] \text { and } A B=\left[\begin{array}{rr} -3 & -11 \\ 1 & 17 \end{array}\right]$$

, determine the first and second columns of B.

When you receive a chest x-ray at a hospital, the x-rays pass through a set of parallel ribs in your chest. Do your ribs act as a diffraction grating for x-rays?
(a) Yes. They produce diffracted beams that can be observed separately.
(b) Not to a measurable extent. The ribs are too far apart
(c) Essentially not The ribs are too close together.
(d) Essentially not. The ribs are too few in number.
(e) Absolutely not. X-rays cannot diffract.

In a dairy operation, milk at a flow rate of 250 L/h and a cow-body temperature of $38.6^{\circ} \mathrm{C}$ must be chilled to a safe-to-store temperature of $13^{\circ} \mathrm{C}$ or less. Ground water at $10^{\circ} \mathrm{C}$ is available at a flow rate of $0.72 \mathrm{m}^{3} / \mathrm{h}$. The density and specific heat of milk are $1030 \mathrm{kg} / \mathrm{m}^{3}$ and $3860 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$, respectively. (a) Determine the UA product of a counterflow heat exchanger required for the chilling process. Determine the length of the exchanger if the inner pipe has a 50-mm diameter and the overall heat transfer coefficient is $U=1000 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. (b) Determine the outlet temperature of the water. (c) Using the value of UA found in part (a), determine the milk outlet temperature if the water flow rate is doubled. What is the outlet temperature if the flow rate is halved?

A long nickel alloy (ASTM B335) cylindrical rod is used as a component in high-temperature process equipment. The rod has a diameter of $5 \mathrm{~cm}$; its thermal conductivity, specific heat, and density are $11 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, 380 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$, and $9.3 \mathrm{~g} / \mathrm{cm}^3$, respectively. Occasionally, the rod is submerged in hot fluid for several minutes, where the fluid temperature is $500^{\circ} \mathrm{C}$ with a convection heat transfer coefficient of $440 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. The ASME Code for Process Piping limits the maximum use temperature for ASTM B335 rod to $427^{\circ} \mathrm{C}$ (ASME B31.32014). If the initial temperature of the rod is $20^{\circ} \mathrm{C}$, how long can the rod be submerged in the hot fluid before reaching its maximum use temperature?

Base your answers to question on the following diagram and data tables.

The diagram represents a light source located equal distance from two air-filled metal cans. One can is shiny, and the other is black. Both cans were heated for 10 minutes. The lamp was removed, and both cans were allowed to cool for 10 minutes. Temperature readings of the cans' $^{\prime}$ interiors were recorded each minute for the 20 minutes of heating and cooling. The data tables show these temperatures. A graph is provided to allow you to plot the given data and to assist you in answering the questions.

$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Lamp On } & & & & & & & & & & & \\ \hline \text { Time (min) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Temperature of Shiny Can }\left({ }^{\circ} \mathrm{C}\right) & 20 & 20 & 21 & 22 & 23 & 24 & 24.5 & 25 & 25.5 & 26 & 26.5 \\ \hline \text { Temperature of Black Can }\left({ }^{\circ} \mathrm{C}\right) & 20 & 21 & 23 & 25 & 27 & 28.5 & 29.5 & 30.5 & 31 & 31.5 & 32 \\ \hline \text { Lamp Off } & & & & & & & & & & & \\ \hline \text { Time (min) } & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & \\ \hline \text { Temperature of Shiny Can }\left({ }^{\circ} \mathrm{C}\right) & 26.5 & 26 & 25.5 & 25 & 24.5 & 24 & 24 & 23.5 & 23.5 & 23 & \\ \hline \text { Temperature of Black Can }\left({ }^{\circ} \mathrm{C}\right) & 31.5 & 31 & 30.5 & 29.5 & 28.5 & 27.5 & 26.5 & 25.5 & 25 & 24.5 & \\ \hline \end{array}$$

How would the specific heat of the iron in the cans compare to the specific heat of the dry air in the cars?

What rows or columns or matrices do you multiply to find (a) the third column of AB? (b) the first row of AB? (c) the entry in row 3, column 4 of AB? (d) the entry in row 1, column 1 of CDE?

Glucose is used as fuel in the body according to the reaction

$$\begin{aligned} \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6(a q)+6 \mathrm{O}_2(g) \rightarrow 6 \mathrm{CO}_2(g) & +6 \mathrm{H}_2 \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}} & =-2802.5 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \end{aligned}$$

During a fever, body temperature rises to about $39^{\circ} \mathrm{C}$. How many grams of glucose must be burned to raise the temperature of the body from a normal temperature of $36.8^{\circ} \mathrm{C}$ to $39.0^{\circ} \mathrm{C}$ for an 82-kilogram person? Assume that all the energy released as heat from the combustion of glucose is used to heat the body. Assume also that the heat capacity per gram (specific heat) of the body is that of water.