The surface of an iron component is to be hardened by carbon. The diffusion coefficient of carbon in iron at $1000^\circ C$ is given to be $3 \times 10^{–11} m^2/s.$ If the penetration depth of carbon in iron is desired to be 1.0 mm. the hardening process must take at least (a) 1.10 h (b) 1.47 h (c) 1.86 h (d) 2.50 h (e) 2.95 h

A rubber object is in contact with nitrogen $(N_2)$ at 298 K and 250 kPa. The solubility of nitrogen gas in rubber is $0.00156 kmol/m^3 \cdot bar.$ The mass density of nitrogen at the interface is(a) $0.049 kg/m^3$ (b) $0.064 kg/m^3$ (c) $0.077 kg/m^3$ (d) $0.092 kg/m^3$ (e) $0.109 kg/m^3$

Nitrogen gas at high pressure and 298 K is contained in a 2−m × 2−m × 2−m cubical container made of natural rubber whose walls are 4 cm thick. The concentration of nitrogen in the rubber at the inner and outer surfaces are $0.067 kg/m^3$ and $0.009 kg/m^3,$ respectively. The diffusion coefficient of nitrogen through rubber is $1.5 \times 10^{-10} \mathrm{m}^{2} / \mathrm{s}.$ The mass flow rate of nitrogen by diffusion through the cubical container is(a) $8.24 \times 10^{-10} \mathrm{kg} / \mathrm{s}$ (b) $1.35 \times 10^{-10} \mathrm{kg} / \mathrm{s}$ (c) $5.22 \times 10^{-9} \mathrm{kg} / \mathrm{s}$ (d) $9.71 \times 10^{-9} \mathrm{kg} / \mathrm{s}$ (e) $3.58 \times 10^{-8} \mathrm{kg} / \mathrm{s}$

A steel pot, with conductivity of 50 W/m K and a 5-mm-thick bottom, is filled with 15$^{\circ} \mathrm{C}$ liquid water. The pot has a diameter of 20 cm and is now placed on an electric stove that delivers 500 W as heat transfer. Find the temperature on the outer pot bottom surface, assuming the inner surface is at 15$^{\circ} \mathrm{C}$.

A prototype composite material is formed and hence has an unknown modulus. An experiment is performed consisting of forming it into a cantilevered beam of length 1 m and $I=10^{-9} \mathrm{m}^{4}$ with a 6-kg mass attached at its end. The system is given an initial displacement and found to oscillate with a period of 0.5 s. Calculate the modulus E.

Consider a rubber plate that is in contact with nitrogen gas at 298 K and 250 kPa. Determine the molar and mass density of nitrogen in the rubber at the interface.

For the absorption of a gas (like carbon dioxide) into a liquid (like water) Henry’s law states that partial pressure of the gas is proportional to the mole fraction of the gas in the liquid–gas solution with the constant of proportionality being Henry’s constant. A bottle of soda pop $\left(\mathrm{CO}_{2}-\mathrm{H}_{2} \mathrm{O}\right)$ at room temperature has a Henry’s constant of 17,100 kPa. If the pressure in this bottle is 120 kPa and the partial pressure of the water vapor in the gas volume at the top of the bottle is neglected, the concentration of the $CO_2$ in the liquid $H_{2}O$ is (a) $0.003 mol-CO_2/mol$ (b) $0.007 mol-CO_2/mol$ (c) $0.013 mol-CO_2/mol$ (d) $0.022 mol-CO_2/mol$ (e) $0.047 mol-CO_2/mol$

What are two ways of reducing the negative aspects associated with using absorption costing to evaluate the performance of a plant manager?

A shell-and-tube heat exchanger with 1-shell pass and 14-tube passes is used to heat water in the tubes with geothermal steam condensing at $120^\circ C$ $(h_{fg} = 2203 kJ/kg)$ on the shell side. The tubes are thin-walled and have a diameter of 2.4 cm and length of 3.2 m per pass. Water $(c_p = 4180 J/kg \cdot K)$ enters the tubes at $22^\circ C$ at a rate of 3.9 kg/s. If the temperature difference between the two fluids at the exit is $46^\circ C,$ determine (a) the rate of heat transfer, (b) the rate of condensation of steam, and (c) the overall heat transfer coefficient.

Tesla Motors assembles the fully electric Model S-85 automobile at its Fremont, California, plant. The standard variable manufacturing cost per vehicle in 2017 is $58,800, which consists of:$

$$\begin{matrix} \text{Direct materials} & \text{\$36.000}\\ \text{Direct manufacturing labor} & \text{\$ 10.800}\\ \text{Variable manufacturing overhead} & \text{\$ 12.000}\\ \end{matrix}$$

$Variable manufacturing overhead is allocated to vehicles on the basis of assembly time. The standard assembly time per vehicle is 20 hours. The Fremont plant is highly automated and has a practical capacity of 4.000 vehicles per months. The budgeted monthly fixed manufacturing overhead is$45 million. Fixed manufacturing overhead is allocated on the basis of the standard assembly time for the budgeted normal capacity utilization of the plant. For 2017, the budgeted normal capacity utilization is 3.000 vehicles per month. Tesla started production of the Model S-85 in 2017. The actual production and sales figures for the first three months of the year are:

$$\begin{matrix} \text{ } & \text{January} & \text{February } & \text{March}\\ \text{Production} & \text{3.200} & \text{2.400} & \text{3.800}\\ \text{Sales} & \text{2.000} & \text{2.900} & \text{3.200}\\ \end{matrix}$$

Franz Holzhausen is SVP of Tesla and director of the Fremont plant. His compensation includes a bonus that is 0.25% of monthly operating income, calculate using absorption costing. Tesla prepare absorption-costing income statements monthly, which include an adjustment for the production-volume variance occuring in that month. There are no variable cost variances or fixed overhead spending variances in the first three months of 2017. The Fremont plant is credited with revenue (net of marketing costs) of $96.000 for the sale of each Tesla S-85 vehicle. 1. Compute (a) the fixed manufacturing cost per unit and (b) the total manufacturing cost per unit. 2. Compute the monthly operating income for January, February, and March under absorption costing. What amount of bonus is paid each month to Franz Holzhausen? 3. How much would the use of variable costing change Holzhausen bonus each month if the same 0.25% figure were applied to variable-costing operating income? 4. Explain the differences in Holzhausen bonuses in requirements 2 and 3. 5. How much would the use of throughput costing change Holzhausen bonus each month if the same 0.25% figure were applied to throughput-costing operating income? 6. What are the different approaches Tesla Motors could take to reduce possible undesirable behavior associated with the use of absorption costing at its Fremont plant?

Does a mass transfer process have to involve heat transfer? Describe a process that involves both heat and mass transfer.

An aluminum plate and a stainless steel plate are pressed against each other at an average pressure of 20 MPa. Both plates have a surface roughness of $2 \mu \mathrm{m}.$ Determine the impact on the temperature drop at the interface if the surface roughness of the plates is increased by tenfold.

A water-soaked 10 cm × 10 cm square sponge is experiencing parallel dry air flow over its surface. The average convection heat transfer coefficient of dry air at $20^\circ C$ flowing over the sponge surface is estimated to be $30 W/m^2 \cdot K,$ and the sponge surface is maintained at $30^\circ C.$ If the sponge is placed under an array of radiant lamps, determine (a) the rate of evaporation of water from the sponge and (b) the net radiation heat transfer rate.

Hydrogen gas at 1 atm is flowing in parallel over the upper and lower surfaces of a 3-m-long flat plate at a velocity of 2.5 m/s. The gas temperature is $120^\circ C$ and the surface temperature of the plate is maintained at $30^\circ C.$ Using the EES (or other) software, investigate the local convection heat transfer coefficient and the local total convection heat flux along the plate. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{m},$ plot the local convection heat transfer coefficient and the local total convection heat flux as functions of x. Assume flow is laminar but make sure to verify this assumption.