Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
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A CO₂-saturated brine (ionic strength = 2.5 mol/kg, pH = 3, a_H⁺ = 0.01) flows at 2 cm/s through a horizontal tubular reactor (L = 1 m, D = 0.05 m) packed with 5 kg of olivine (Zhuravlev-BET surface area = 30 m²/g). The system operates at 90 °C and 40 bar, and external mass transfer resistance is negligible. The rate-limiting step is electron transfer at the mineral surface, governed by Marcus theory, with λ = 0.75 eV, ΔG° = –0.30 eV, and k₀ = 10⁶ s⁻¹. The Mg²⁺ activity coefficient is γ = 0.76 (from PHREEQC with Pitzer model). For Mg₂SiO₄ + 4 H⁺ → 2 Mg²⁺ + SiO₂(aq) + 2 H₂O, determine the total moles of Mg²⁺ released after 10 minutes at steady state.
In baseball, batters frequently attempt to hit a ball as far as possible. However, baseballs are inelastic with an officially required "coefficient of restitution" CR ≈ 0.55 on ash wood. The coefficient of restitution of a dropped ball iswhere H is the initial drop height, h is the max. height on the rebound, and h ≈ 2πH tan δ for a homogeneous material. Assuming that a baseball is homogeneous and has a storage modulus approximately the same as that of cork (E' = 18.6 MPa), what must the value of the loss modulus E'' be so that the ball is regulation?
The creep strain rate of a polymer (in “Hz”) is given by
where T is the temperature and Q = 100. kJ/mol is the activation energy. How long t will it take for a rod of this polymer to extend from 10. mm to 15 mm at 100. °C?
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- Creep compliance J(t) An amorphous polymer has Tg = 100 °C. A creep modulus of 1/J = 1 GPa was measured after t₁ = 1 h at T₁ = 90 °C. Suppose that log 10 a (T) = 17.5(T-Tg) 52+(T-Tg) 1 for this material. What is the shift factor a at T = T₁ relative to the reference Tg? What is the time t₂ required to reach a modulus of 1 GPa at T2 = 80 °C? TR = T = 100 °C |J(t) = 1 GPa-1 + log a(T₁) T₁ = 75 °C T₂ = 50 °C log tr log t₁ log t log t₂ = ?arrow_forwardA 0.45 mol/kg aqueous solution of 3-(methylamino)propylamine and 1-methylpiperazine (1:1 molar) flows at 0.5 g/s through a 2.5 m horizontal stainless steel coil (inner diameter 1.2 mm), entering at 358.15 K and 22 MPa and exiting at 20 MPa. A constant wall heat flux of 28 W is applied. Local density and isobaric heat capacity are obtained through from the Benedict–Webb–Rubin equation of state, with a 3% increase in heat capacity to account for wall sorption. Dynamic viscosity is obtained using the Green-Kubo relation with a given integral value of 2.1 × 10⁻¹⁰ Pa².s, and thermal conductivity is assumed constant. The local Nusselt number is corrected for thermal development using Nu(x) = 3.66 + (0.065 · Gz(x)^0.7) / (1 + 0.04 · Gz(x)^0.7), where Gz(x) = D · Re(x) · Pr(x) / x. Through a spatially resolved numerical integration of the 1D steady-state energy equation and determine the outlet temperature (K).arrow_forwardA pilot process is being planned to produce antibiotic P. Antibiotic P is a compound secreted by microorganism A during the stationary phase. To produce P, substrate S is required. The growth of microorganism A follows the Monod equation, with a maximum specific growth rate $\mu_m = 1 h^{-1}$ and a half-saturation constant $K_s = 700\ mg/L$.The pilot process uses a chemostat with a working volume of $1000\ L$. In this chemostat, the outflow is processed to separate microorganisms, which are then concentrated tenfold and recycled. A sterile medium containing $15\ g/L$ of substrate is supplied at a flow rate of $100\ L/h$, while the recycled flow (concentrated) contains $5\ g/L$ and is also fed into the chemostat.Microorganism A yields $0.5\ g$ of biomass per $1\ g$ of substrate consumed $(Y^M_{X/S} = 0.5\ g\ A/g\ S)$, and its death rate $(k_d)$ is negligible. Additionally, $1\ g$ of microorganism A produces $0.05\ g$ of antibiotic P per hour $(q_P = 0.05 g\ P/h\cdot g\ A)$, and $1\ g$…arrow_forward
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- صورة من s94850121arrow_forward11:01 ☑ canvas.ucsd.edu 口 : ... Page 1 > of 2 Q - ZOOM + 4. Consider the two separate sets of measured data for a silt-loam soil measured by Mualem (1976): (1) suction versus water content, and (2) suction versus relative permeability of unsaturated soil, k/ks. Assume that 0s 0.396, 0res = 0.131, and Ks=5.74×10-7 m/s. a. Using the method of least squares in Excel, compute the best-fit values for αNG (kPa¹) and nvg for the van Genuchten (1980) relationship for data set # 1 (assume m = 1-1/nvG). See the example spreadsheet in the homework folder under the files section of Canvas for help in performing this calculation. b. Repeat part (a) and estimate the λ and ac parameters for the Brooks and Corey (1964) SWRC for data set #1. Note that you may need to include an "if" statement at the air entry suction. c. Plot the data for the SWRC versus the fitted van Genuchten (1980) and Brooks and Corey (1964) curves. Which relationship matches the capillary pressure data better (BC or VG)? Explain…arrow_forwardSolve h.w 6arrow_forward
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