The exhaust gases of an automotive engine leave the combustion chamber and enter a 8-ft-long and 3.5-in-diameter thin-walled steel exhaust pipe at $800^{\circ} \mathrm{F}$ and 15.5 psia at a rate of 0.05 lbm/s. The surrounding ambient air is at a temperature of $80^{\circ} \mathrm{F},$ and the heat transfer coefficient on the outer surface of the exhaust pipe is $3 \quad \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot^{\circ} \mathrm{F}.$ Assuming the exhaust gases to have the properties of air, determine (a) the velocity of the exhaust gases at the inlet of the exhaust pipe and (b) the temperature at which the exhaust gases will leave the pipe and enter the air.

The passenger compartment of a minivan traveling at 70 mph can be modeled as a 3.2 -ft-high, 6-ft-wide, and 12 -ftlong rectangular box whose walls have an insulating value of $R-3$ (i.e., a wall thickness-to-thermal conductivity ratio of $\left.3 \mathrm{~h} \cdot \mathrm{ft}^2{ }^{\circ} \mathrm{F} / \mathrm{Btu}\right)$. The interior of a minivan is maintained at an average temperature of $70^{\circ} \mathrm{F}$ during a trip at night while the outside air temperature is $90^{\circ} \mathrm{F}$.

The average heat transfer coefficient on the interior surfaces of the van is $1.2 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^2{ }^{\circ} \mathrm{F}$. The air flow over the exterior surfaces can be assumed to be turbulent because of the intense vibrations involved, and the heat transfer coefficient on the front and back surfaces can be taken to be equal to that on the top surface. Disregarding any heat gain or loss by radiation, determine the rate of heat transfer from the ambient air to the van.

A 40-cm-thick brick wall $(k = 0.72 W/m \cdot K,$ and $\alpha = 1.6 \times 10^{–6} m^2/s)$ is heated to an average temperature of $18^{\circ} \mathrm{C}$ by the heating system and the solar radiation incident on it during the day. During the night, the outer surface of the wall is exposed to cold air at $-3^{\circ} \mathrm{C}$ with an average heat transfer coefficient of $20 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ determine the wall temperatures at distances 15, 30, and 40 cm from the outer surface for a period of 2 h.

A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate coming off a furnace at $820^{\circ} \mathrm{C}$ is to be quenched in an oil bath $\left(c_p=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)$ at $185^{\circ} \mathrm{C}$. The metal sheet is moving at a steady velocity of $20 \mathrm{~m} / \mathrm{min}$, and the oil bath is $9 \mathrm{~m}$ long. Taking the convection heat transfer coefficient on both sides of the plate to be $860 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$, find the temperature of the sheet metal when it leaves the oil bath. Also, determine the required rate of heat removal from the oil to keep its temperature constant at $45^{\circ} \mathrm{C}$.

Hot carbon dioxide exhaust gas at 1 atm is being cooled by flat plates. The gas at $220^{\circ} \mathrm{C}$ flows in parallel over the upper and lower surfaces of a 1.5-m-long flat plate at a velocity of 3 m/s. If the flat plate surface temperature is maintained at $80^{\circ} \mathrm{C},$ determine (a) the local convection heat transfer coefficient at 1 m from the leading edge, (b) the average convection heat transfer coefficient over the entire plate, and (c) the total heat flux transfer to the plate.

A refrigerator removes 1.5 Btu from the cold space rising 1 Btu work input. How much energy goes into the kitchen, and what is its coefficient of performance?

Do you think a heat pump system will be more cost-effective in New York or in Miami? Why?

A Brayton cycle with a pressure ratio of 12 operates with air entering the compressor at 13 psia and $20^\circ F,$ and the turbine at $1000^{\circ} \mathrm{F}.$ Calculate the net specific work produced by this cycle treating the air as an ideal gas with (a) constant specific heats at room temperature and (b) variable specific heats.

A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate ($\rho$ = 7854 kg/m^3 and $c_{p}$ = 0.434 kJ/kgK) coming off a furnace at 820$^\circ{}$C is to be quenched in an oil bath at 45$^\circ{}$C to a temperature of 51.1$^\circ{}$C. If the metal sheet is moving at a steady velocity of 10 m/min, determine the required rate of heat removal from the oil to keep its temperature constant at 45$^\circ{}$C. Answer: 4368 kW

Find the solution of $y^{\prime \prime}+x y^{\prime}+y=0$ that satisfies y(0) = 1 and $y^{\prime}(0)=0$.

Do you find Brooks's support for his central idea convincing? Why or why not?

What excuse do Macbeth and Lady Macbeth give for his behavior at the banquet?

Joaquin needed to find the maximum value of $y=-x^{2}+4 x-1$ but was stuck. "No problem," said Thao. "The parabola opens downward so just complete the square to find the vertex. They-value of the vertex will be the maximum." "I know that," said Joaquin. "The problem is that it is $-x^2$." "Mmm ... what ifwe multiply everything by -1? Can we now complete the square?" a. Multiply the equation by -1 so you have -y = .... b. Complete the square on the right side. c. Multiply the equation by -1 so you are back to y = .... d. Identify the vertex and the maximum value.

Top-It-Off Incorporated makes numerous lids for a variety of containers. Some of the most popular lids they produce are circular lids for oil drums and other cylindrical containers. Although the lids are ordered by the diameter of the circle, the price is set by the amount of metal used. Top-It-Off needs to set up a price structure that relates the weight of a lid to its diameter. Below is a list of weights for the standard size lids currently produced.

$$\begin{matrix} \text{Diameter of lid (in)} & \text{Weight of metal (lbs)}\\ \text{10} & \text{3.9}\\ \text{12} & \text{5.7}\\ \text{16} & \text{10.1}\\ \text{20} & \text{15.7}\\ \text{24} & \text{22.6}\\ \text{30} & \text{35.3}\\ \text{36} & \text{50.9}\\ \text{40} & \text{62.8}\\ \end{matrix}$$

a. The company analyst needs to find a good model for the weight as a function of the diameter. Use your calculator to create a scatterplot of your data and sketch the results. b. The data appears to have only a slight curve. Based on the scatterplot alone, you may think a linear model would be a good fit. Use your calculator to find the equation of the LSRL. Add this line to the sketch from part (a). c. Make a residual plot for your model. What conclusion can you draw about your linear model? d. What is the correlation coefficient? Write a sentence about R-squared in context.