An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1-2 Isentropic compression from 100 kPa and $22^{\circ} \mathrm{C}$ to 600 kPa, 2-3 v = constant heat addition to 1500 K, 3-4 Isentropic expansion to 100 kPa, 4-1 P = constant heat rejection to initial state. (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency.

Johnstown Foundry, Inc., with several major plants, is one of the largest makers of cast-iron water and sewer pipes in the U.S. In one of the nation's most dangerous industries, Johnstown is perhaps one of the most unsafe, with four times the injury rate of its six competitors combined. Its worker death rate is six times the industry average. In a recent 7-year period, Johnstown's plants were also found to be in violation of pollution and emission limits 450 times.

Workers who protest dangerous work conditions claim they are "bull's-eyed"-marked for termination. Supervisors have bullied injured workers and intimidated union leaders. Line workers who fail to make daily quotas get disciplinary actions. Managers have put up safety signs after a worker was injured to make it appear that the worker ignored posted policies. They doctor safety records and alter machines to cover up hazards. When the government investigated one worker's death recently, inspectors found the Johnstown policy "was not to correct anything until OSHA found it."

Johnstown plants have also been repeatedly fined for failing to stop production to repair broken pollution controls. Three plants have been designated "high-priority" violators by the EPA. Inside the plants, workers have repeatedly complained of blurred vision, severe headaches, and respiratory problems after being exposed, without training or protection, to chemicals used in the production process. Near one Pennsylvania plant, school crossing guards have had to wear gas masks; that location alone has averaged over a violation every month for 7 years. Johnstown's "standard procedure," according to a former plant manager, is to illegally dump industrial contaminants into local rivers and creeks. Workers wait for night or heavy rainstorms before flushing thousands of gallons from their sump pumps.

Given the following scenarios, what is your position, and what action should you take?

You are Johnstown's banker.

A turboprop aircraft propulsion engine operates where the air is at 8 psia and $-10^{\circ} \mathrm{F},$ on an aircraft flying at a speed of 600 ft/s. The Brayton cycle pressure ratio is 10, and the air temperature at the turbine inlet is $940^{\circ} \mathrm{F}.$ The propeller diameter is 10 ft and the mass flow rate through the propeller is 20 times that through the compressor. Determine the thrust force generated by this propulsion system. Assume ideal operation for all components and constant specific heats at room temperature.

An air-standard dual cycle has a compression ratio of 18 and a cutoff ratio of $1.1$. The pressure ratio during the constant volume heat addition process is 1.1. At the beginning of the compression, $P_1=90\ \mathrm{kPa}, T_1=18^{\circ} \mathrm{C}$, and $V_1=0.003 \mathrm{~m}^3$. If the isentropic compression, efficiency is $85$ percent and the isentropic expansion efficiency is $90$ percent, find the power produced by this cycle when it is executed $4000$ times per minute. Use constant specific heat at room temperature.

The dissolution of $\mathrm{CaCl}_2(s)$ in water is exothermic, with $\Delta H_{\text {adin }}=-81.3 \mathrm{~kJ} / \mathrm{mol}$. If you were to prepare a $1.00 \mathrm{~m}$ solution of $\mathrm{CaCl}_2$ beginning with water at $25.0^{\circ} \mathrm{C}$, what would the final temperature of the solution be in ${ }^{\circ} \mathrm{C}$ ? Assume that the specific heats of both pure $\mathrm{H}_2 \mathrm{O}$ and the solution are the same, $4.18 \mathrm{~J} /(\mathrm{K} \cdot \mathrm{g})$.

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at $40^{\circ} \mathrm{C}$ at a rate of $850 m^3/min$ and leaves the turbine at $650^\circ C.$ Using variable specific heats for air and assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine (a ) the net power output, (b ) the back work ratio, and (c) the thermal efficiency.

Why do you think businesses offer discounts if the invoice is paid early? Do you think it is always to the purchaser's advantage to pay early?

• Explain your reasoning.
• Show your understanding of mathematics in an organized manner.
• Use charts, graphs, and diagrams in your explanation.
• Show the solution in more than one way or relate it to other situations.
• Investigate beyond the requirements of the problem.

Consider the following specific heats of metals.

$$\begin{array}{ll}\text { Metal } & \text { Specific Heat } \\ \text { copper } & 0.385 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) \\ \text { magnesium } & 1.02 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) \\ \text { mercury } & 0.138 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) \\ \text { silver } & 0.237 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\end{array}$$

Four 25-g samples, one of each metal, and four insulated containers with identical water volumes, all start out at room temperature. Now suppose you add exactly the same quantity of heat to each metal sample. Then you place the hot metal samples in different containers of water (that all have the same volume of water). Which of the answers below is true? a. The water with the copper will be the hottest. b. The water with the magnesium will be the hottest. c. The water with the mercury will be the hottest. d. The water with the silver will be the hottest. e. The temperature of the water will be the same in all the cups.

An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1-2 Isentropic compression from 100 kPa and $22^\circ C$ to 600 kPa. 2-3 v = constant heat addition to 1500 K.
3-4 Isentropic expansion to 100 kPa. 
4-1 P = constant heat rejection to initial state (a)  Show the cycle on P-v and T-s diagrams. (b)  Calculate the net work output per unit mass. (c)  Determine the thermal efficiency.

Portions of orbital diagrams representing the groundstate electron configurations of certain elements are shown here. Which of them violate the Pauli exclusion principle? Which violate Hund's rule?

a) $\boxed{\upharpoonleft |\upharpoonleft|\upharpoonleft \upharpoonright~}$

b) $\boxed{\upharpoonleft |\upharpoonleft \upharpoonright| \downharpoonright~}$

c) $\boxed{\upharpoonleft |\upharpoonleft\downharpoonright| \upharpoonleft~}$

d) $\boxed{\upharpoonleft \downharpoonright | ~~~~| \upharpoonleft |\upharpoonleft |\upharpoonleft ~}$

e) $\boxed{ \upharpoonleft |\upharpoonleft |\upharpoonleft | \downharpoonright |\upharpoonleft\downharpoonright~}$

f) $\boxed{ \upharpoonleft\downharpoonright|\upharpoonleft\downharpoonright|\downharpoonleft \downharpoonright |\upharpoonleft\downharpoonright | \upharpoonleft\downharpoonright~}$

Let $(S, \leqslant)$ and $\left(S^{\prime} , \leqslant^{\prime}\right)$ be two partially ordered sets. $(S, \leqslant)$ is isomorphic to $\left(S^{\prime}, \leqslant^{\prime}\right)$ if there is a bijection $f: S \rightarrow S^{\prime}$ such that for x, y in S, $x<y \rightarrow f(x)<^{\prime} f(y)$ and $f(x)<^{\prime} f(y) \rightarrow x<y.$ a. Show that there are exactly two nonisomorphic, partially ordered sets with two elements (use diagrams). b. Show that there are exactly five nonisomorphic, partially ordered sets with three elements. c. How many nonisomorphic, partially ordered sets with four elements are there?

S.B. is a $17$-year-old man who lost control of his sport utility vehicle and struck a tree. Witnesses reported he was not restrained, and his face hit the windshield on impact. When paramedics arrived, S.B. was responsive but confused, had significant facial swelling, and complained of pain in his right wrist and left forearm. The paramedics initiated cervical spine precautions, strapped him to a backboard, started oxygen at $15 \mathrm{~L} / \mathrm{min}$ via a nonrebreather mask, and started a 16 -gauge IV with $0.9 \%$ normal saline. His vital signs were $120 / 75,125,36$, and $\mathrm{SaO}_2 94 \%$. On arrival to the local emergency department (ED) 5 minutes later, his VS were $110/62$, $110$ regular, $28$ to $32$ and shallow, and $\mathrm{SaO}_2 99 \%$. An additional 16-gauge IV was inserted and the following labs were drawn: CBC, type and crossmatch, complete metabolic panel, PT/ PTT INR, and alcohol level. The trauma physician completed a head-to-toe assessment and found the following:

Physician Note

Obeys commands, responds to voice but not oriented to time or place. Generalized facial edema with full-thickness $2$-cm cheek laceration and bilateral mandibular depressed fractures. Blood behind left tympanic membrane, edema with slight discoloration over left mastoid process. Clear drainage coming from the left nare. Mid to upper chest contusions without crepitus, breath sounds clear. Abdomen slightly firm but not tender. Catheterized for $500$ mL clear yellow urine; negative for blood, glucose, ketones. Positive deformity of right wrist and diffuse tenderness of left lower forearm.

How would you test S.B. for evidence of cerebrospinal fluid (CSF) leakage?

A block of mass $m_{1}=2.00 \mathrm{kg}$ and a block of mass $m_{2}=6.00 \mathrm{kg}$ are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of $\theta=30.0^{\circ}$. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley.

Presented with recordings of a pair of people of the same sex speaking the same phrase, can a listener determine which speaker is taller simply from the sound of their voice? Twenty four young adults at Washington University listened to 100 pairs of speakers, and within each pair were asked to indicate which of the two speakers was the taller. Here are the number correct (out of 100) for each of the 24 participants:

$$\begin{array}{llllllllllll} 65 & 61 & 67 & 59 & 58 & 62 & 56 & 67 & 61 & 67 & 63 & 53 \\ 68 & 49 & 66 & 58 & 69 & 70 & 65 & 56 & 68 & 56 & 58 & 70 \end{array}$$

Researchers believe that the key to correct discrimination is contained in a particular type of sound produced in the lower airways or the lungs, known as subglottal resonances, whose frequency is lower for taller people. Despite the masking of these resonances by other voice sounds, researchers wondered whether the information they contained could still be heard by listeners and used to identify the taller person.

(a) Make two stemplots, with and without splitting the stems. Which plot do you prefer and why?

(b) Describe the shape, center, and variability of the distribution. Are there any outliers?

(c) If the experimental subjects are just guessing which speaker is taller, they should correctly identify the taller person about 50% of the time. Does this data support the researchers, conjecture that there is information in a person's voice to help identify the taller person? Why or why not?