A tiny $1 \mu g$ particle is in a 1 cm wide enclosure and takes a year to bounce from one-end to the other and back, (a) How many nodes are there in its enclosure? (b) How would your answer change if the particle were more massive or moving faster?

What does the effectiveness of a heat exchanger represent? Can effectiveness be greater than one? On what factors does the effectiveness of a heat exchanger depend?

“Companies should always make and sell all products whose selling prices exceed variable costs.” Assuming fixed costs are irrelevant, do you agree? Explain.

A system of mass 10 kg and stiffness $1.5 \times 10^4 N/m$ is subject to Coulomb damping. If the mass is driven harmonically by a 90-N force at 25 Hz, determine the equivalent viscous-damping coefficient if the coefficient of friction is 0.1.

“Variable costs are always relevant, and fixed costs are always irrelevant.” Do you agree? Why?

Water is boiled at 1 atm pressure in a 20-cm-internal diameter Teflon-pitted stainless-steel pan on an electric range. If it is observed that the water level in the pan drops by 10 cm in 15 min. determine the inner surface temperature of the pan.

Consider a 20-cm × 20-cm × 20-cm cubical body at 750 K suspended in the air. Assuming the body closely approximates a blackbody, determine (a) the rate at which the cube emits radiation energy, in W and (b) the spectral blackbody emissive power at a wavelength of $4 \mu m.$

A 10-m-long 5-cm-outer-radius cylindrical steam pipe is covered with 3-cm thick cylindrical insulation with a thermal conductivity of $0.05 W/m \cdot K.$ If the rate of heat loss from the pipe is 1000 W, the temperature drop across the insulation is (a) $163^\circ C$ (b) $600^\circ C$ (c) $48^\circ C$ (d) $79^\circ C$ (e) $251^\circ C$

Consider the base plate of a 800 W house hold iron having a thickness of L =0.6 cm, base area of $A = 160 cm^2,$ and thermal conductivity of $k =20 W/m \cdot K,$ The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be $85^\circ C.$ Disregarding any heat loss through the upper part of the iron and taking the nodal spacing to be 0.2 cm,(a) obtain the finite difference formulation for the nodes and (b) determine the inner surface temperature of the plate by solving those equations.

Exposure to high concentration of gaseous ammonia can cause lung damage. To prevent gaseous ammonia from leaking out, ammonia is transported in its liquid state through a pipe $(k = 25 W/m \cdot K, D_{i, pipe} = 2.5 cm, D_{o, pipe} = 4 cm,$ and L = 10 m). Since liquid ammonia has a normal boiling point of $−33.3^\circ C,$s the pipe needs to be properly insulated to prevent the surrounding heat from causing the ammonia to boil. The pipe is situated in a laboratory, where air at $20^\circ C$ is blowing across it with a velocity of 7 m/s. The convection heat transfer coefficient of the liquid ammonia is $100 W/m^2 \cdot K.$ Calculate the minimum insulation thickness for the pipe using a material with $k = 0.75 W/m \cdot K$ to keep the liquid ammonia flowing at an average temperature of $− 35^\circ C,$ while maintaining the insulated pipe outer surface temperature at $10^\circ C.$

Consider the system described by Obtain the transfer function of the system.

$$\left[\begin{array}{c}{\dot{x}_{1}} \\ {\dot{x}_{2}}\end{array}\right]=\left[\begin{array}{rr}{-4} & {-1} \\ {3} & {-1}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}}\end{array}\right]+\left[\begin{array}{l}{1} \\ {1}\end{array}\right] u$$

$$y=\left[\begin{array}{ll}{1} & {0}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}}\end{array}\right]$$

A 1.4-m-diameter spherical steel tank filled with iced water at $0^\circ C$ is buried underground at a location where the thermal conductivity of the soil is $k = 0.55 W/m \cdot K.$ The distance between the tank center and the ground surface is 2.4 m. For ground surface temperature of $18^\circ C,$ determine the rate of heat transfer to the iced water in the tank. What would your answer be if the soil temperature were $18^\circ C$ and the ground surface were insulated?

Aluminum wires, 3 mm in diameter, are produced by extrusion. The wires leave the extruder at an average temperature of $350^\circ C$ and at a linear rate of 10 m/min. Before leaving the extrusion room, the wires are cooled to an average temperature of $50^\circ C$ by transferring heat to the surrounding air at $25^\circ C$ with a heat transfer coefficient of $50 W/m^2 \cdot K.$ Calculate the necessary length of the wire cooling section in the extrusion room.

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.)

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