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1)For the above problem find the time for the benzene level to fall by 2 cm

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1)For the above problem find the time for the benzene level to fall by 2 cm. The specific gravity of benzene is 0.874. For this condition find the mole-fraction profile of benzene in the vapor phase and compare your answer with the linear approximation (which would be the prediction of the low-flux model).

2)Benzene is contained in an open beaker of height 6 cm and filled to within 0.5 cm of the top. The temperature is 298 K and the total pressure is 1 atm. The vapor pressure of benzene is 0.131 atm under these conditions, and the diffusion coefficient is 9.05 × 10−6 m2 /s. Find the rate of evaporation based on (a) the low-flux model, (b) exact solutions, and (c) the low-flux model corrected for the drift flux. 

3)Derive an expression for the fall in the liquid level during evaporation using a quasi-steadystate approach. Show that dH dt = MA ρL NA where NA is the instantaneous rate of evaporation, i.e., based on the current height of the vapor space H. Verify the following expression for the height change:H2 − H2 0 = 2 MA ρL DACyA,sFt where F is the drift correction factor. In this expression we assume that the bulk mole fraction of A is zero.

4)Verify that the concentration profile in a slab is linear, whereas that in a hollow cylinder is logarithmic, and for a spherical shell it is an inverse function of r for the three geometries in Fig. 10.1. Also verify the expressions for the numbers of moles transported across the system, WA.

5)The Antoine constants for water are A = 8.071 31, B = 1730.63, and C = 233.426 in the units of mm Hg for pressure and ?C for temperature. Convert this to a form where pressure is in Pa and temperature is in K. Also rearrange the Antoine equation to a form where temperature can be calculated explicitly. This represents the boiling point at that pressure. What is the boiling point of water at Denver, CO (the so-called mile-high city)?

6)The Henry’s-law constants for O2 and CO2 are reported as 760.2 l· atm/mol and 29.41 l· atm /mol. What is the form of Henry’s law used? Convert to values for the other forms shown in the text.Given the Antoine constants for a species, can you calculate the heat of vaporization of that species?

7) At a point in a methane reforming furnace we have a gas of the composition 10% CH4, 15% H2, 15% CO, and 10% H2O by moles. Find the mass fractions and the average molecular weight of the mixture.

Express the Henry’s-law constants reported in Table 8.1 as Hi,pc and Hi,cp.

8)Apply the lumped model for cooling of a solid in the form of (i) a long slab and (ii) a long cylinder. Also apply the modified lumped model shown in the text, and show what correction is needed for the simple lumped model for an assumed quadratic variation in temperature of the solid.

9) A porous solid is in the shape of a hollow sphere and has temperatures of Ti and To at the radii of ri and ro, respectively. Find an expression for the heat loss from the sphere. In order to reduce the heat loss, a gas is blown through the porous hollow sphere at a velocity of v0. Derive an expression for the reduction in heat loss from this system.

10) For the linear generation, use the Robin condition at the surface rather than the Dirichlet condition used in the text. Derive an expression for the temperature profile, the maximum temperature, and the stability condition.Verify the solutions in the text for the temperature distribution in a square slab with constant generation of heat. Generate illustrative contour plots for the temperature profiles.

11) Consider heat conduction with generation in a slab and a sphere geometries. Derive the solution similar to Eq. (8.18) for slab and sphere cases. For all three cases (slab, cylinder, and sphere) find the heat flow from the surface to the fluid and show that the results satisfy an overall heat balance.