Question 1 of 9: General Knowledge — True/False/Ambiguous

Question 1: General Knowledge — True/False/Ambiguous (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Each statement is judged against the governing law or correlation it invokes (Fick, Newton, kinetic theory, Fourier, Biot/Nusselt, reactor design, or radiative balance), with the deciding physics stated in one to two sentences.

(a) Fick's 1st Law of diffusion for one-dimensional mass flow can be written $N'_z = -D_{A/B}\dfrac{\partial C_A}{\partial x}$ — True. This is the standard statement of Fick’s first law for the diffusive flux in a dilute or equimolar-counterdiffusing binary system. It is written relative to the molar-average velocity of the mixture; when there is a net bulk (convective) flow superimposed — as in Stefan diffusion — a second, convective term $y_A(N_A+N_B)$ must be added to get the total flux $N_A$. As written (no bulk-flow term), the equation is Fick’s law in its classical diffusion-only form.

(b) Fick's law can also be written in another form to take into account molar convection of species for gaseous diffusion — True. The Stefan-diffusion form $N_A = -cD_{AB}\dfrac{dy_A}{dx} + y_A(N_A+N_B)$ adds the bulk molar-flow term to the pure-diffusion flux, and is the standard way gaseous mass transfer with net convection (e.g. evaporation into a stagnant film, or the CO/CO₂ halo of Q2) is treated.

(c) Newton's equation of viscosity, applies to gases and also to slags and liquid metals — True. Newton’s law of viscosity, $\tau_{yx} = -\mu\dfrac{dv_x}{dy}$, describes any Newtonian fluid: gases and fully molten (single-phase) liquid metals and slags all behave as Newtonian fluids well above their liquidus. The caveat is that partially crystallized or highly structured (e.g. very basic, near-solidus) slags carrying suspended solids can become shear-thinning/non-Newtonian — but for the homogeneous liquid state the statement is true.

(d) The viscosity of a gas increases with pressure and temperature — False. Kinetic theory gives $\mu \propto \sqrt{T}$ for a dilute gas — increasing with temperature only. Gas viscosity is essentially independent of pressure at moderate pressure: $\mu = \tfrac13\rho\bar c\lambda$, and since $\rho\propto P$ while the mean free path $\lambda\propto 1/P$, the two cancel. The statement is false on the pressure half.

(e) The thermal conductivity of a metal normally drops significantly on transforming from the solid to the liquid state — True. Solid-metal conduction is dominated by free-electron transport through a periodic lattice; melting destroys the long-range order and increases electron/phonon scattering, so $k$ typically falls by roughly 30–50% on melting (e.g. liquid iron’s $k$ is well below solid $\alpha$/$\gamma$-iron’s near the melting point).

(f) Contact angle $\phi=0^{\circ}$ — sketch the bubble shape entering a liquid through a small orifice — Sketch. A contact angle of $0^{\circ}$ means the liquid perfectly wets the container material. The gas therefore cannot maintain a stable, pinned neck at the orifice rim — the liquid climbs up and over the orifice lip, and the bubble detaches as a near-spherical cap sitting just above (not straddling) the orifice, with a thin, rapidly necking stem rather than the wide, flattened base a poorly-wetting ($\phi$ large) liquid would show.

(g) Kinetic theory: the thermal conductivity of a gas increases with the square root of absolute temperature, as does its viscosity — True. Simple kinetic theory gives both $\mu\propto\sqrt{T}$ and $k\propto\sqrt{T}$ (through the same mean-speed $\bar c\propto\sqrt{T}$ and mean-free-path $\lambda$ terms), so their ratio (related to the Eucken/Prandtl relation) is nearly temperature-independent — both correctly share the $\sqrt{T}$ scaling.

(h) Kinetic theory: the viscosity of a gas increases with absolute pressure — False. As in (d), $\mu=\tfrac13\rho\bar c\lambda$ is pressure-independent for a dilute gas because $\rho\lambda$ is constant (density rises with $P$, mean free path falls by the same factor).

(i) The solubility of oxygen in solid iron is zero — False. Oxygen solubility in solid iron is extremely small — on the order of a few hundred ppm at most in $\delta$/$\gamma$-iron near the melting point, dropping further at lower temperature — but it is not exactly zero. "Negligible" is a fair engineering approximation; "zero" is not literally true.

(j) A well-mixed reactor is less efficient than a plug-flow reactor for most, but not all, orders of reactions — True. For a fixed conversion, a CSTR needs a larger volume than a PFR for any positive reaction order (the CSTR operates entirely at the low, exit-condition rate rather than integrating up from the high inlet rate). The two are equal for zero-order kinetics, and for autocatalytic/negative-order kinetics the CSTR can actually outperform the PFR — consistent with "most, but not all."

(k) The Froude number represents gravitational/inertial forces; Reynolds represents inertial/viscous forces — False. Reynolds is correctly inertial/viscous ($Re=\rho VL/\mu$). The Froude number is defined as $Fr = V^2/(gL)$, i.e. inertial over gravitational force — the statement has the Froude ratio inverted.

(l) Fourier's 2nd Law of heat conduction contains the thermal conductivity of a substance in the thermal diffusivity term — True. Fourier’s second law is $\dfrac{\partial T}{\partial t}=\alpha\nabla^2T$ with $\alpha=k/(\rho C_p)$ — $k$ enters exactly through the diffusivity $\alpha$.

(m) The difference between the Biot number and the Nusselt number relates to the thermal conductivity of the phases — True. $Bi=hL/k_{solid}$ uses the conductivity of the conducting body, while $Nu=hL/k_{fluid}$ uses the conductivity of the fluid film. Mathematically identical ratios, they differ only in which phase’s $k$ is used — exactly what distinguishes "is conduction inside the solid limiting?" (Biot) from "how good is convection at the surface, non-dimensionalised?" (Nusselt).

(n) Liquid metals have relatively thick thermal boundary layers as compared to gases and ionic liquids — True. Liquid metals have very low Prandtl number ($Pr\ll1$, high thermal diffusivity relative to momentum diffusivity), so the thermal boundary layer grows much faster than, and extends well beyond, the momentum boundary layer ($\delta_t/\delta\sim Pr^{-1/2}$). Gases ($Pr\approx0.7$) have $\delta_t\approx\delta$, and ionic liquids/molten salts ($Pr$ of order several) have $\delta_t<\delta$ — liquid metals sit at the thick-thermal-layer extreme of this family, exactly as Q4’s own plug-flow derivation exploits.

(o) Radiation can be transmitted, reflected, and/or absorbed — True. The basic radiative energy balance on an irradiated surface is $\alpha+\rho+\tau=1$ (absorptivity + reflectivity + transmissivity), so incident radiation is always partitioned among exactly these three fates.