MikaStars39/nano-eval huggingface dataset:
Under the action of a catalyst, ethylene gas passes through a water column to form an aqueous ethanol solution, with the reaction as follows: $\mathrm{C_{2} H_{4} \left( \ g \right)}+\mathrm{H_{2} O} \longrightarrow\mathrm{C_{2} H_{5} OH \left( \ aq \right)}$. It is known that at 298 K, the saturated vapor pressure of pure ethanol is $7.6 \times 10^{3} \mathrm{~Pa}$, and its equilibrium vapor pressure at standard state $c_{\mathrm{C_{2} H_{5} OH}}^{\Theta}=1 \, \mathrm{mol \cdot dm}^{-3}$ is $5.33 \times 10^{2} \mathrm{~Pa}$. The available $\Delta_{\mathrm{f}} G_{\mathrm{m}}^{\mathrm{\Theta}}$ data are as follows: for $\mathrm{C_{2} H_{5} OH}$ (pure), $\Delta_{\mathrm{f}} G_{\mathrm{m}}^{\mathrm{\Theta}}$ is -174.77 kJ·mol$^{-1}$; for $\mathrm{H}_{2} \mathrm{O}$ (pure), $\Delta_{\mathrm{f}} G_{\mathrm{m}}^{\mathrm{\Theta}}$ is -237.19 kJ·mol$^{-1}$; for $\mathrm{C_{2} H_{4} \left( \ g \right)}$, $\Delta_{\mathrm{f}} G_{\mathrm{m}}^{\mathrm{\Theta}}$ is 68.18 kJ·mol$^{-1}$. Find the equilibrium constant for the reaction.

Options:
A. 98.7
B. 72.1
C. 204.5
D. 145.6
E. 126.4
F. 185.3
G. 110.6
H. 158.9
I. 194.8
J. 133.2
Answer: D
Attempts have been made to use methane and benzene as raw materials to produce toluene $\mathrm{C H_{4} ~ (g) ~+~ C_{6} H_{6} ~ (g) ~ \longrightarrow~}$ $\mathrm{C_{6} H_{5} C H_{3} (g) \ +H_{2} (g)}$, using different catalysts and selecting various temperatures, but all have ended in failure. In the petrochemical industry, the reverse reaction is used, where toluene is hydrogenated to obtain benzene. Try to theoretically calculate the equilibrium conversion rate under the following conditions:
Under conditions of 500 K and 100 kPa, using an appropriate catalyst, if the molar ratio of methane to benzene is 1:1, estimate the potential mole fraction of toluene obtained using thermodynamic data.

Options:
A. 0.0015
B. 0.0027
C. 0.0048
D. 0.0035
E. 0.0037
F. 0.0021
G. 0.0050
H. 0.0042
I. 0.0031
J. 0.0019
Answer: B
At 298 K and 100 kPa, determine the standard molar entropy of $1 \mathrm{mol \ NO} ( \mathrm{g} )$ (assuming it is an ideal gas). It is known that the rotational characteristic temperature of $\mathrm{NO (g)}$ is 2.42 K, the vibrational characteristic temperature is 2690 K, and the degeneracy of the electronic ground state and the first excited state is both 2. The energy difference between the two levels is $\Delta\varepsilon = 2.473 \times 10^{-21} \ \mathrm{J}$.

Options:
A. $$
2 8 0. 4 1 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
B. $$
1 8 9. 4 8 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
C. $$
2 1 0. 7 5 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
D. $$
2 1 5. 6 0 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
E. $$
1 9 5. 6 3 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
F. $$
2 4 4. 1 5 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
G. $$
2 5 8. 0 9 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
H. $$
2 0 8. 3 3 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
I. $$
2 0 2. 9 7 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
J. $$
2 3 5. 8 2 \mathrm{~ J \cdot\ m o l^{-1} \cdot~ K^{-1} ~}
$$
Answer: C
At 298K, using Pb(s) as the electrode, electrolysis is performed on a Pb(NO₃)₂ solution, with a concentration of 16.64 g of Pb(NO₃)₂ per 1,000 g of water. The current is stopped once 0.1658 g of silver is deposited in a silver coulometer in series with the electrolytic cell. It is known that the mass of the solution at the anode is 62.50 g, and analysis shows it contains 1.151 g of Pb(NO₃)₂. Calculate the transference number of Pb²⁺ ions.

Options:
A. 0.72
B. 0.17
C. 0.49
D. 0.88
E. 0.04
F. 0.36
G. 0.58
H. 0.63
I. 0.81
J. 0.28
Answer: C
Under isothermal and isobaric conditions, solvent A and solute $\mathrm{B}$ form a dilute solution of a certain concentration. If expressed in terms of different concentrations, then _____.

Options:
A. The entropy change values of $\mathrm{A}$ and $\mathrm{B}$ in the solution increase rapidly.
B. The solubility factor values of $\mathrm{A}$ and $\mathrm{B}$ in the solution are unpredictable.
C. The partial pressure values of $\mathrm{A}$ and $\mathrm{B}$ in the solution shift occasionally.
D. The osmotic pressure values of $\mathrm{A}$ and $\mathrm{B}$ in the solution decrease uniformly.
E. The molar concentration values of $\mathrm{A}$ and $\mathrm{B}$ in the solution vary significantly.
F. The temperature and pressure values of $\mathrm{A}$ and $\mathrm{B}$ in the solution remain constant.
G. The density profile values of $\mathrm{A}$ and $\mathrm{B}$ in the solution become indistinct.
H. The chemical potential values of $\mathrm{A}$ and $\mathrm{B}$ in the solution remain unchanged.
I. The equilibrium constant values of $\mathrm{A}$ and $\mathrm{B}$ in the solution are altered consistently.
J. The volumetric ratio values of $\mathrm{A}$ and $\mathrm{B}$ in the solution experience adjustments.
Answer: H
The effective mass of electrons for $InSb$ is $m_{\mathrm{e}} = 0.015m$, the dielectric constant is $\varepsilon = 18$, and the lattice constant is $a = 6.479 \overset{\circ}{\mathrm{A}}$. Try to calculate the orbital radius of the ground state, which is ().

Options:
A. $$
6 5 7 \stackrel{\circ} {\mathrm{A}}
$$
B. $$
9 6 2 \stackrel{\circ} {\mathrm{A}}
$$
C. $$
5 2 8 \stackrel{\circ} {\mathrm{A}}
$$
D. $$
6 3 6 \stackrel{\circ} {\mathrm{A}}
$$
E. $$
4 5 1 \stackrel{\circ} {\mathrm{A}}
$$
F. $$
8 1 7 \stackrel{\circ} {\mathrm{A}}
$$
G. $$
7 9 4 \stackrel{\circ} {\mathrm{A}}
$$
H. $$
1 8 9 \stackrel{\circ} {\mathrm{A}}
$$
I. $$
3 0 4 \stackrel{\circ} {\mathrm{A}}
$$
J. $$
2 3 3 \stackrel{\circ} {\mathrm{A}}
$$
Answer: D
It is known that after cold rolling, the time required for 50% recrystallization of pure iron is 10*s when heated at $527^{\circ} \ \mathrm{C}$, and the time required for 50% recrystallization when heated at $727^{\circ} \ \mathrm{C}$ is only $0.1s$. What is the minimum temperature of 50% recrystallization in $10 ^{5}$s?

Options:
A. $496.23(^{\circ} \ \mathrm{C})$
B. $512.34(^{\circ} \ \mathrm{C})$
C. $450.89(^{\circ} \ \mathrm{C})$
D. $530.56(^{\circ} \ \mathrm{C})$
E. $480.68(^{\circ} \ \mathrm{C})$
F. $475.79(^{\circ} \ \mathrm{C})$
G. $515.02(^{\circ} \ \mathrm{C})$
H. $465.37(^{\circ} \ \mathrm{C})$
I. $500.95(^{\circ} \ \mathrm{C})$
J. $490.11(^{\circ} \ \mathrm{C})$
Answer: A
A cylindrical container is divided into two parts by an adiabatic, impermeable piston, with each part containing $1 mol$ of monoatomic ideal gas. The initial volumes are \( $V_{i}^{\prime}=10 \, \text{L}$ \) and \( $V_{i}^{1}=1 \, \text{L}$ \) respectively. The container walls are heat conductive, and the entire container is placed in a "thermal bath" at a temperature of \( $0^{\circ} \, \text{C}$ \). The piston moves reversibly, and the final volumes are \( $V^{\prime} = 6 \, \text{L}$ \) and \( $V^{\prime \prime} = 5 \, \text{L}$ \). What is the work done by the system on the surroundings ?

Options:
A. $$
3. 4 \times1 0^{3} ( \mathrm{J} )
$$
B. $$
1. 4 \times1 0^{3} ( \mathrm{J} )
$$
C. $$
3. 2 \times1 0^{3} ( \mathrm{J} )
$$
D. $$
5. 2 \times1 0^{3} ( \mathrm{J} )
$$
E. $$
2. 6 \times1 0^{3} ( \mathrm{J} )
$$
F. $$
2. 4 \times1 0^{3} ( \mathrm{J} )
$$
G. $$
3. 6 \times1 0^{3} ( \mathrm{J} )
$$
H. $$
4. 0 \times1 0^{3} ( \mathrm{J} )
$$
I. $$
2. 2 \times1 0^{3} ( \mathrm{J} )
$$
J. $$
1. 8 \times1 0^{3} ( \mathrm{J} )
$$
Answer: E
A solid consists of $N$ magnetic dipoles each with a spin of $1/2$. At high temperatures, the spins are randomly oriented; at low temperatures, all spins align uniformly. If the heat capacity as a function of temperature is approximately given by the following expression
$$
C \left( T \right)=\left\{\begin{array} {l l} {c_{1} \left[ \frac{2 T} {T_{1}}-1 \right],} & {\text{when } \frac{1}{2} T_{1} < T < T_{1} \,} \\ {0,} & {\text{otherwise.}} \\ \end{array} \right.
$$
where $T_1$ is a constant. What is $c_{1}$ ?. (Hint: consider using entropy).

Options:
A. $$
c_{1}={\frac{N k \ln3} {1-\ln3}}
$$
B. $$
c_{1}={\frac{3 N k \ln2} {1-\ln5}}
$$
C. $$
c_{1}={\frac{4 N k \ln2} {2-\ln3}}
$$
D. $$
c_{1}={\frac{N k \ln3} {2-\ln2}}
$$
E. $$
c_{1}={\frac{5 N k \ln1} {1-\ln2}}
$$
F. $$
c_{1}={\frac{2 N k \ln2} {1-\ln4}}
$$
G. $$
c_{1}={\frac{N k \ln4} {1-\ln1}}
$$
H. $$
c_{1}={\frac{N k \ln2} {2-\ln2}}
$$
I. $$
c_{1}={\frac{N k \ln2} {1-\ln2}}
$$
J. $$
c_{1}={\frac{N k \ln5} {1-\ln3}}
$$
Answer: I
At a specific moment, an ascending airplane reaches a speed of 180 m/s, forming a 40° angle with the horizontal line. At this instant, the airplane decelerates at a rate of 4 m/s². The airplane is also moving along a concave upward circular path with a radius of 2600 m. Under these conditions, what is the slope of the free surface of the liquid in the airplane's fuel tank ? (keep three significant digits)

Options:
A. $$
0.432
$$
B. $$
0.660
$$
C. $$
4 2. 3^{\circ}
$$
D. $$
4 8. 8^{\circ}
$$
E. $$
2 6. 5^{\circ}
$$
F. $$
4 7. 9^{\circ}
$$
G. $$
0.533
$$
H. $$
2 9. 0^{\circ}
$$
I. $$
2 7. 2^{\circ}
$$
J. $$
3 6. 1^{\circ}
$$
Answer: B
A submerged body moves horizontally in oil $( \gamma=521 \, \mathrm{bf/ft^3}, \, \mu=0.0006 \, \mathrm{lbf \cdot sec/ft^2} )$ at a speed of 45 ft/sec. To study the characteristics of this motion, an enlarged model of this object is tested in water at $60^\circ \mathrm{F}$. The scale ratio of the model is 8:1. If the resistance acting on the model is 0.80 lbf, what is the resistance acting on the prototype ?

Options:
A. $$
6 0 4 \mathrm{l b f}
$$
B. $$
9 1 2 \mathrm{l b f}
$$
C. $$
3 7 8 \mathrm{l b f}
$$
D. $$
5 8 2 \mathrm{l b f}
$$
E. $$
8 5 6 \mathrm{l b f}
$$
F. $$
5 3 9 \mathrm{l b f}
$$
G. $$
7 3 4 \mathrm{l b f}
$$
H. $$
6 2 1 \mathrm{l b f}
$$
I. $$
4 9 7 \mathrm{l b f}
$$
J. $$
7 6 5 \mathrm{l b f}
$$
Answer: H
Rectangle Clark $\mathbf{Y}$ airfoil has a wingspan of 36 ft and a chord length of 6 ft. What horsepower is required by the engine when the airfoil is flying at an altitude of 10,000 ft with a speed of 300 ft/s at an angle of attack of $5.4^{\circ}$?

Options:
A. $$
4 6 0 \mathrm{h p}
$$
B. $$
4 1 0 \mathrm{h p}
$$
C. $$
3 9 0 \mathrm{h p}
$$
D. $$
5 2 0 \mathrm{h p}
$$
E. $$
3 8 5 \mathrm{h p}
$$
F. $$
4 0 0 \mathrm{h p}
$$
G. $$
4 2 5 \mathrm{h p}
$$
H. $$
4 4 5 \mathrm{h p}
$$
I. $$
4 0 5 \mathrm{h p}
$$
J. $$
4 3 8 \mathrm{h p}
$$
Answer: J
A culvert under a circular road is 30 meters long, with a slope of 0.003 and a flow rate of 4.3 cubic meters per second. If the maximum allowable water depth above the culvert is 3.6 meters, what size corrugated pipe should be selected? (Given: $n=0.025$, ignoring entrance velocity. Assume a square entrance with $k_e=0.5$, and $C_{\delta}=0.65$, with an outlet for free outflow.)

Options:
A. $$
3.5 \mathrm{m}
$$
B. $$
2.5 \mathrm{m}
$$
C. $$
2.2 \mathrm{m}
$$
D. $$
1. 1 \mathrm{m}
$$
E. $$
1. 5 \mathrm{m}
$$
F. $$
1. 4 \mathrm{m}
$$
G. $$
1.8 \mathrm{m}
$$
H. $$
1. 3 \mathrm{m}
$$
I. $$
1. 2 \mathrm{m}
$$
J. $$
2.8 \mathrm{m}
$$
Answer: I
Water flows in a steel pipe with a length of 400 feet, an inner diameter of 8 inches, and a wall thickness of 0.25 inches at a speed of 10 feet per second. If the valve at the end is suddenly partially closed, the speed at this time reduces to 6 feet per second. At this time, what is the maximum pressure generated ?

Options:
A. $$
3 5 0 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
B. $$
3 2 5 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
C. $$
4 0 3 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
D. $$
4 8 0 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
E. $$
2 9 5 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
F. $$
4 1 7 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
G. $$
2 6 1 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
H. $$
4 5 2 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
I. $$
3 1 8 0 0 \mathrm{l b f} / \mathrm{f t}^{2}
$$
J. $$
3 9 0 0 0 \mathrm{l b t} / \mathrm{f t}^{2}
$$
Answer: I
The water temperature is $50 \mathrm{^\circ~F}$, and the water pump transfers water between reservoirs A and B. The water surface elevations are 5910 ft and $6060 \mathrm{~ft}$, respectively. The pump operates with a flow rate of $20 \mathrm{ft}^{3} / \mathrm{sec}$, through a pipeline with a diameter of 24 in and a length of 2000 ft. Assume $f=0.03$. What height at least over reservoir A should be the pump installed at to prevent cavitation?

Options:
A. $$
10. 0 {\mathrm{f t}}
$$
B. $$
9. 6 {\mathrm{f t}}
$$
C. $$
7. 2 {\mathrm{f t}}
$$
D. $$
8. 7 {\mathrm{f t}}
$$
E. $$
9. 9 {\mathrm{f t}}
$$
F. $$
1 0. 5 {\mathrm{f t}}
$$
G. $$
7. 8 {\mathrm{f t}}
$$
H. $$
7. 1 {\mathrm{f t}}
$$
I. $$
8. 3 {\mathrm{f t}}
$$
J. $$
8. 4 {\mathrm{f t}}
$$
Answer: F
The bandgap of $\mathrm{InSb}$ is known to be $E_{g} = 0.15 \, \text{eV}$, the effective mass of the electron is $m_{\mathrm{e}} = 0.014 \, m_{0}$, and the effective mass of the hole is $m_{\mathrm{h}} = 0.18 \, m_{0}$ (where $m_{0}$ is the inertial mass of an electron). If only electrons are the effective charge carriers, try to calculate the Hall coefficient of pure $\mathrm{InSb}$ at 300 K. If a current of 100 mA flows through an $\mathrm{InSb}$ sample with a width $b$ of 5 mm and a thickness $d$ of 1 mm, and a magnetic field of 0.1 T is applied in the perpendicular direction, what is the magnitude of the Hall voltage generated?

Options:
A. $11.4\mathrm{mV}$
B. $4.7\mathrm{mV}$
C. $6.0\mathrm{mV}$
D. $3.5\mathrm{mV}$
E. $6.5\mathrm{mV}$
F. $9.3\mathrm{mV}$
G. $8.0\mathrm{mV}$
H. $7.2\mathrm{mV}$
I. $5.1\mathrm{mV}$
J. $10.2\mathrm{mV}$
Answer: H
The thermal conductivity of germanium is $60 \mathrm{W / m} \cdot \mathrm{K}$, and the resistivity is $0.01\Omega ·m$ for an $\mathbf{n}$-type germanium single crystal. What percentage of the thermal conductivity at 300K is contributed by the charge carriers (assuming long-wavelength acoustic phonon scattering)?

Options:
A. $$
1. 7 \times1 0^{-4} \%
$$
B. $$
7. 3 \times1 0^{-4} \%
$$
C. $$
8. 9 \times1 0^{-2} \%
$$
D. $$
2. 5 \times1 0^{-5} \%
$$
E. $$
9. 1 \times1 0^{-2} \%
$$
F. $$
4. 8 \times1 0^{-6} \%
$$
G. $$
7. 4 \times1 0^{-4} \%
$$
H. $$
5. 6 \times1 0^{-5} \%
$$
I. $$
3. 2 \times1 0^{-3} \%
$$
J. $$
6. 0 \times1 0^{-3} \%
$$
Answer: G
Light converged by a cylindrical lens illuminates on a stripe-shaped semiconductor pn junction. It is known that at room temperature, the resistivity of the n-region is $40 \ \Omega \cdot \text{cm}$, the resistivity of the p-region is $0.1 \ \Omega \cdot \text{cm}$, the reverse saturation current is 1 µA, the electron mobility is $3600 \ \text{cm}^2/(\text{V} \cdot \text{s})$, the hole mobility is $1800 \ \text{cm}^2/(\text{V} \cdot \text{s})$, and the electron concentration in the n-region is $3 \times 10^{13} \ \text{cm}^{-3}$. It is known that the semiconductor in the n-region generates $10^{13}/\text{cm}^3$ electron-hole pairs under 100 lux illumination, and the number of generated electron-hole pairs is proportional to the illumination intensity. When light is irradiated on point A, (Point O, A and B are located at the n-region, and O is at the edge of the n-region, $O A = \frac{1}{2} O B$),the resistivity of the illuminated part drops to $20 \ \Omega \cdot \text{cm}$. How many lux (lx) of illumination is needed?

Options:
A. $$
8 0. 2 ( \mathrm{l x} )
$$
B. $$
1 8. 6 ( \mathrm{l x} )
$$
C. $$
7 0. 3 ( \mathrm{l x} )
$$
D. $$
1 5. 7 ( \mathrm{l x} )
$$
E. $$
2 3. 1 ( \mathrm{l x} )
$$
F. $$
4 0. 5 ( \mathrm{l x} )
$$
G. $$
2 2. 5 ( \mathrm{l x} )
$$
H. $$
1 0. 0 ( \mathrm{l x} )
$$
I. $$
5 0. 0 ( \mathrm{l x} )
$$
J. $$
6 4. 9 ( \mathrm{l x} )
$$
Answer: E
A MOS structure capacitor consisting of Metal-SiO₂-Si (p-type) has a hole concentration $N_{A} = 1.5 \times 10^{15} \ \text{cm}^{-3}$. The SiO₂ layer thickness is $d_{0} = 0.2 \ \mu\text{m}$ with a relative permittivity $\varepsilon_{\tau_{0}} = 3.9$. The silicon's relative permittivity is $\varepsilon_{\mathrm{m}} = 12$, and $\varepsilon_{0} = 8.85 \times 10^{-14} \ \text{F/cm}$. At room temperature, the intrinsic carrier concentration $n_{i} = 1.5 \times 10^{10} \ \text{cm}^{-3}$. Assuming an ideal MOS structure, what is the threshold voltage $V_{\mathrm{T}}$?

Options:
A. $$
5. 5 5 ( \mathrm{V} )
$$
B. $$
2. 8 4 ( \mathrm{V} )
$$
C. $$
6. 1 2 ( \mathrm{V} )
$$
D. $$
2. 3 3 ( \mathrm{V} )
$$
E. $$
4. 2 2 ( \mathrm{V} )
$$
F. $$
4. 8 8 ( \mathrm{V} )
$$
G. $$
6. 7 0 ( \mathrm{V} )
$$
H. $$
3. 5 6 ( \mathrm{V} )
$$
I. $$
5. 1 9 ( \mathrm{V} )
$$
J. $$
3. 9 1 ( \mathrm{V} )
$$
Answer: E
At room temperature, the effective density of states in the valence band $N_{\tau}=1.04 \times 10^{19} / \mathrm{cm}^{3}$. A $\mathbf{p}$-type semiconductor has an acceptor density $N_{A}=1.04 \times 10^{16} / \mathrm{cm}^{3}$, the bandgap energy of the semiconductor $E_{\mathrm{g}} = 1.12 \mathrm{eV}$, electron affinity $X=3.4 \mathrm{eV}$. At room temperature, the work function measured is $W=3.9 \mathrm{eV}$. What is the surface potential $V_{\mathrm{s}}$ of this semiconductor?

Options:
A. $$
1. 0 ( e V )
$$
B. $$
0. 2 ( e V )
$$
C. $$
0. 5 ( e V )
$$
D. $$
0. 6 ( e V )
$$
E. $$
0. 3 ( e V )
$$
F. $$
1. 1 ( e V )
$$
G. $$
0. 7 ( e V )
$$
H. $$
0. 8 ( e V )
$$
I. $$
0. 4 ( e V )
$$
J. $$
0. 9 ( e V )
$$
Answer: I
A Schottky diode is formed by a [100] oriented $\mathbf{n}$-type monocrystalline silicon wafer and a certain metal contact, with the parameters $W_{\mathrm{m}}=4.7 \, \mathrm{eV}$, $\chi_{\mathrm{s}}=4.0 \, \mathrm{eV}$, $N_{\mathrm{c}}=10^{19} \, \mathrm{cm}^{-3}$, $N_{\mathrm{D}}=10^{15} \, \mathrm{cm}^{-3}$. The relative dielectric constant of the semiconductor silicon is $\varepsilon_{\mathrm{r}}=12$, neglecting the influence of surface states. Given that $\frac{A^{*}}{A}=2.1$, $A=120 \, \mathrm{A/cm}^{2}$. What is the thermionic emission current at room temperature with a forward bias of 0.2V?

Options:
A. $$
4. 3 {\times} 1 0^{-3} ( {\mathrm{A / c m}}^{2} )
$$
B. $$
5. 9 {\times} 1 0^{-2} ( {\mathrm{A / c m}}^{2} )
$$
C. $$
1. 2 {\times} 1 0^{-1} ( {\mathrm{A / c m}}^{2} )
$$
D. $$
6. 3 {\times} 1 0^{-2} ( {\mathrm{A / c m}}^{2} )
$$
E. $$
7. 5 {\times} 1 0^{-2} ( {\mathrm{A / c m}}^{2} )
$$
F. $$
5. 8 {\times} 1 0^{-1} ( {\mathrm{A / c m}}^{2} )
$$
G. $$
9. 2 {\times} 1 0^{-3} ( {\mathrm{A / c m}}^{2} )
$$
H. $$
8. 4 {\times} 1 0^{-2} ( {\mathrm{A / c m}}^{2} )
$$
I. $$
8. 7 {\times} 1 0^{-2} ( {\mathrm{A / c m}}^{2} )
$$
J. $$
2. 4 {\times} 1 0^{-3} ( {\mathrm{A / c m}}^{2} )
$$
Answer: H
A silicon wafer with a donor concentration of $2 \times 10^{16} \, \text{cm}^{-3}$ is gold-doped to saturation concentration at 920°C. It is then subjected to oxidation and other treatments, resulting in a surface recombination center of $10^{10} \, \text{cm}^{-2}$ on the silicon wafer. If the wafer is irradiated and the sample uniformly absorbs light, with an electron-hole pair generation rate of $10^{11} \, \text{cm}^{-3} \cdot \text{s}^{-1}$, what is the hole flow density towards the surface?

Options:
A. $5. 5 0 \times1 0^{1 1} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
B. $9. 6 6 \times1 0^{1 1} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
C. $9. 6 6 \times1 0^{1 0} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
D. $7. 4 4 \times1 0^{1 1} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
E. $1. 9 5 \times1 0^{1 1} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
F. $4. 8 3 \times1 0^{1 2} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
G. $2. 6 8 \times1 0^{1 3} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
H. $8. 5 2 \times1 0^{1 2} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
I. $6. 3 1 \times1 0^{1 0} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
J. $3. 7 9 \times1 0^{1 1} [ 1 / ( \mathrm{c m}^{2} \cdot\mathrm{s} ) ]$
Answer: B
In the germanium semiconductor material, the donor impurity concentration is $N_{\mathrm{D}}=10^{14} \mathrm{cm}^{-3}$, and the acceptor impurity concentration is $N_{A}=7 \times 10^{13} \mathrm{cm}^{-3}$. Assume the resistivity of intrinsic germanium at room temperature is $\rho_{\mathrm{i}}=60 \Omega\cdot\mathrm{cm}$, and assume the electron and hole mobilities are $\mu_{\mathrm{n}} = 3800 \mathrm{cm}^{2}/(\mathrm{V}\cdot\mathrm{s})$ and $\mu_{\mathrm{p}} = 1800 \mathrm{cm}^{2}/(\mathrm{V}\cdot\mathrm{s})$, respectively. If the current density passing through the sample is 52.3 mA/cm², what is the applied electric field strength?

Options:
A. $$
5. 7 6 8 \mathrm{V / c m}$$
B. $$
10. 4 5 6 \mathrm{V / c m}$$
C. $$
6. 5 4 1 \mathrm{V / c m}$$
D. $$
1. 9 9 6 \mathrm{V / c m}$$
E. $$
2. 1 8 3 \mathrm{V / c m}$$
F. $$
8. 3 3 8 \mathrm{V / c m}$$
G. $$
9. 0 1 5 \mathrm{V / c m}$$
H. $$
4. 2 9 0 \mathrm{V / c m}$$
I. $$
3. 4 7 5 \mathrm{V / c m}$$
J. $$
7. 6 0 2 \mathrm{V / c m}$$
Answer: D
Zinc (Zn) has dual acceptor levels in silicon, meaning each Zn atom can accept one electron at the lower energy level $E_{A1}$ $( \Delta E_{A1}=E_{A1}-E_{\tau}=0.31 \, \mathrm{eV} )$, and two electrons at the higher energy level $E_{A2}$ $( \Delta E_{A2}=E_{A2}-E_{\tau}=0.55 \, \mathrm{eV} )$. What concentration of Zn atoms is needed to compensate $N_{\mathrm{D}}=10^{16} / \mathrm{cm}^{3}$ of n-type silicon?

Options:
A. $$
7. 8 \times1 0^{1 4} ( 1 / \mathrm{c m}^{3} )
$$
B. $$
8. 0 \times1 0^{1 4} ( 1 / \mathrm{c m}^{3} )
$$
C. $$
9. 7 \times1 0^{1 4} ( 1 / \mathrm{c m}^{3} )
$$
D. $$
6. 4 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
E. $$
6. 2 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
F. $$
2. 3 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
G. $$
5. 4 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
H. $$
1. 9 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
I. $$
4. 1 \times1 0^{1 6} ( 1 / \mathrm{c m}^{3} )
$$
J. $$
3. 5 \times1 0^{1 5} ( 1 / \mathrm{c m}^{3} )
$$
Answer: G
The dielectric constant of the semiconductor silicon single crystal is $\varepsilon_{\mathrm{r}}=11.8$, and the effective masses of electrons and holes are $m_{\mathrm{nl}}=0.97 m_{0}, m_{\mathrm{nt}}=0.19 m_{0}$, and $m_{\mathrm{pl}} = 0.16 m_{0}, m_{\mathrm{ph}} = 0.53 m_{0}$. Using a hydrogen-like model for estimation, what are the donor and acceptor concentrations when the electron orbitals of adjacent impurity atoms overlap significantly?

Options:
A. $$
1. 45 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.85 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
B. $$
1. 9 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.35 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
C. $$
1. 75 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.55 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
D. $$
1. 5 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.75 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
E. $$
1. 4 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.95 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
F. $$
1. 6 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.85 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
G. $$
1. 7 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.65 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
H. $$
1. 65 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.75 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
I. $$
1. 3 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 3.05 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
J. $$
1. 8 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} ),\ 2.45 \times1 0^{1 9} ( 1 / \mathrm{c m}^{3} )
$$
Answer: G
Known: Lubricating oil No. 14, with an average temperature of $40^{\circ} \mathrm{C}$, flows through a straight pipe with a wall temperature of $80^{\circ} \mathrm{C}$. The pipe is 1.5 meters long and has an inner diameter of 22.1 mm with a flow rate of 800 kg/h. Given that when the temperature is 80°C, the oil's $\eta = 28.4 \times 10^{-4} \, \text{kg} / \left( \text{m} \cdot \text{s} \right)$.
Find: The heat transfer rate between the oil and the pipe wall is().

Options:
A. $$
7 8 2 W
$$
B. $$
5 9 9 W
$$
C. $$
6 7 1 W
$$
D. $$
9 8 7 W
$$
E. $$
1 0 4 5 W
$$
F. $$
9 0 3 W
$$
G. $$
8 9 5 W
$$
H. $$
3 4 8 W
$$
I. $$
4 8 3 W
$$
J. $$
2 0 6 W
$$
Answer: G
If a general-purpose computer requires an average of $100 \mu s$ per complex multiplication and $20 \mu s$ per complex addition, then when $N=1024$, estimate the highest frequency at which real-time processing of signals can be achieved using FFT for fast convolution is ().

Options:
A. $$
f_{\mathrm{m a x}} < {\frac{f_{s} + 100} {3}}={\frac{4 4 4. 4 4} {2}} \mathrm{H z}=2 2 2. 2 \mathrm{H z}
$$
B. $$
f_{\mathrm{m a x}} < {\frac{f_{s}} {4}}={\frac{8 8 8. 8 8} {2}} \mathrm{H z}=4 4 4. 4 \mathrm{H z}
$$
C. $$
f_{\mathrm{m a x}} < {\frac{3f_{s}} {2}}={\frac{9 9 9. 9 9} {2}} \mathrm{H z}=4 9 9. 9 \mathrm{H z}
$$
D. $$
f_{\mathrm{m a x}} < {\frac{f_{s} \cdot 2} {3}}={\frac{1 1 1 1. 1 1} {2}} \mathrm{H z}=5 5 5. 5 \mathrm{H z}
$$
E. $$
f_{\mathrm{m a x}} < {\frac{f_{s} - 100} {2}}={\frac{5 5 5. 5 5} {2}} \mathrm{H z}=2 7 7. 7 \mathrm{H z}
$$
F. $$
f_{\mathrm{m a x}} < {\frac{f_{s}} {2}}={\frac{6 6 6. 6 7} {2}} \mathrm{H z}=3 3 3. 3 \mathrm{H z}
$$
G. $$
f_{\mathrm{m a x}} < {\frac{f_{s}} {5}}={\frac{4 4 4. 4 4} {2}} \mathrm{H z}=2 2 2. 2 \mathrm{H z}
$$
H. $$
f_{\mathrm{m a x}} < {\frac{f_{s}} {8}}={\frac{5 5 5. 5 5} {2}} \mathrm{H z}=2 2 2. 2 \mathrm{H z}
$$
I. $$
f_{\mathrm{m a x}} < {\frac{f_{s}} {6}}={\frac{3 3 3. 3 3} {2}} \mathrm{H z}=1 6 6. 6 \mathrm{H z}
$$
J. $$
f_{\mathrm{m a x}} < {\frac{2f_{s}} {3}}={\frac{7 7 7. 7 7} {2}} \mathrm{H z}=3 8 8. 8 \mathrm{H z}
$$
Answer: F
A uniformly charged sphere has a radius of α and a charge density of $\rho$, where the dielectric constant inside and outside the sphere is $\varepsilon_{0}$. Potential distribution inside and outside the sphere is (). (The potential reference point is at infinity)

Options:
A. $$\frac{\rho a^2}{3 \varepsilon_0}-\frac{\rho R^2}{3 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {6 \varepsilon_{0} R}$$, when $$R>a$$
B. $$\frac{\rho a^3}{2 \varepsilon_0}-\frac{\rho R^2}{3 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{2}} {3 \varepsilon_{0} R}$$, when $$R>a$$
C. $$\frac{\rho a^3}{6 \varepsilon_0}-\frac{\rho R^2}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {2 \varepsilon_{0} R}$$, when $$R>a$$
D. $$\frac{\rho a^2}{2 \varepsilon_0}-\frac{\rho R^2}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{2}} {2 \varepsilon_{0} R}$$, when $$R>a$$
E. $$\frac{\rho a^2}{2 \varepsilon_0}-\frac{\rho R^3}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {2 \varepsilon_{0} R}$$, when $$R>a$$
F. $$\frac{\rho a^2}{6 \varepsilon_0}-\frac{\rho R^2}{2 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {2 \varepsilon_{0} R}$$, when $$R>a$$
G. $$\frac{\rho a^2}{2 \varepsilon_0}-\frac{\rho R^2}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {3 \varepsilon_{0} R}$$, when $$R>a$$
H. $$\frac{\rho a^3}{3 \varepsilon_0}-\frac{\rho R^2}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{3}} {6 \varepsilon_{0} R}$$, when $$R>a$$
I. $$\frac{\rho a^2}{2 \varepsilon_0}-\frac{\rho R^2}{2 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{2}} {3 \varepsilon_{0} R}$$, when $$R>a$$
J. $$\frac{\rho a^2}{6 \varepsilon_0}-\frac{\rho R^3}{6 \varepsilon_0}$$, when $$R \leqslant a$$
$$\frac{\rho a^{2}} {3 \varepsilon_{0} R}$$, when $$R>a$$
Answer: G
A tank filled with water has a diameter of 1 meter and a height of 3 meters. Water is being discharged through a small hole at the bottom of the tank. The diameter of the hole is 4 centimeters. The measured relationship between the flow velocity \( u_0 \) of the water through the hole and the water surface height \( z \) inside the tank is given by
$$
u_0 = 0.62 \, (2gz)^{0.5}
$$
Find the time required to discharge 1 cubic meter of water is ().

Options:
A. $$
1 8 9. 8 s
$$
B. $$
1 7 5. 2 s
$$
C. $$
2 3 0. 5 s
$$
D. $$
1 6 8. 4 s
$$
E. $$
2 4 9. 1 s
$$
F. $$
2 0 3. 4 s
$$
G. $$
1 9 7. 3 s
$$
H. $$
2 7 1. 6 s
$$
I. $$
2 5 7. 8 s
$$
J. $$
1 5 6. 9 s
$$
Answer: A
A rotor flowmeter, with the rotor material being aluminum. At the time of factory calibration, using air at 20°C with a pressure of 0.1MPa, the flow rate at a rotor height of 100mm is 10 m³/h. Now, if this flowmeter is used to measure chlorine gas at 50°C with a pressure of 0.15MPa, what will the flow rate be at the same height?

Options:
A. $$
4. 8 9 m^{3} / s
$$
B. $$
2. 3 1 m^{3} / s
$$
C. $$
3. 5 9 m^{3} / s
$$
D. $$
7. 2 8 m^{3} / s
$$
E. $$
1. 1 2 m^{3} / s
$$
F. $$
6. 0 3 m^{3} / s
$$
G. $$
9. 0 6 m^{3} / s
$$
H. $$
8. 9 0 m^{3} / s
$$
I. $$
6. 7 5 m^{3} / s
$$
J. $$
5. 4 7 m^{3} / s
$$
Answer: J
A shallow dish contains clear water with a depth of 5mm. Water molecules gradually evaporate into the atmosphere through molecular diffusion. Calculate the time required for the water in the dish to completely evaporate is ().
Assume that during diffusion, water molecules pass through a stationary air layer 4mm thick at a temperature of 30°C, and the partial pressure of water vapor in the air outside this layer is zero. The molecular diffusion coefficient is $0.11 \mathrm{m}^2/\mathrm{h}$. The temperature of the water can be considered the same as the air, and the local atmospheric pressure is 101kPa.

Options:
A. $$
2.1h
$$
B. $$
9.6h
$$
C. $$
8.3h
$$
D. $$
6.0h
$$
E. $$
4.5h
$$
F. $$
3.2h
$$
G. $$
3.8h
$$
H. $$
7.4h
$$
I. $$
5.8h
$$
J. $$
10.2h
$$
Answer: I
An oil droplet with a particle diameter of $76 \mu\mathrm{m}$ (non-volatile, considered to be rigid) freely settles in atmospheric air at 20°C. During the constant velocity phase, the measured settlement height is $2.7 \mathrm{m}$ within $20 \mathrm{s}$. It is known that at 20°C, the density of water is $998.2 \mathrm{kg/m}^{3}$ and the viscosity is $1.005 \times 10^{-3} \mathrm{Pa \cdot s}$; the density of air is $1.205 \mathrm{kg/m}^{3}$ and the viscosity is $1.81 \times 10^{-5} \mathrm{Pa \cdot s}$. Find: the distance traveled by the same oil droplet when injected into water at 20°C over 20 seconds is ().

Options:
A. $$
0. 0 6 1 4 \, m
$$
B. $$
0. 0 4 7 9 \, m
$$
C. $$
0. 0 1 9 2 \, m
$$
D. $$
0. 0 5 4 3 \, m
$$
E. $$
0. 0 1 3 8 \, m
$$
F. $$
0. 0 1 5 9 \, m
$$
G. $$
0. 0 2 1 1 \, m
$$
H. $$
0. 0 7 8 5 \, m
$$
I. $$
0. 0 2 5 6 \, m
$$
J. $$
0. 0 3 2 0 \, m
$$
Answer: E
Use an H-type strongly acidic cation exchange resin to remove a 5% concentration KCl solution. At exchange equilibrium, the mole fraction of H* exchanged from the column is 0.2. Try to calculate the removal rate of $\mathbf{K}^{+}$ is(). It is known that $K_{\mathrm{H^{+}}}^{\mathrm{K^{+}}}=2.5$, and the solution density is $1025 \mathrm{kg/m}^{3}$.

Options:
A. $$
0. 4 3
$$
B. $$
0. 2 9
$$
C. $$
0. 9 1
$$
D. $$
0. 7 5
$$
E. $$
1. 1 7
$$
F. $$
1. 3 5
$$
G. $$
0. 9 9
$$
H. $$
1. 0 2
$$
I. $$
0. 6 8
$$
J. $$
0. 5 7
$$
Answer: C
The filtration rate at the end of the plate-and-frame constant pressure filtration is known to be $0.04 \, \mathrm{m}^{3} / \mathrm{s}$. If the viscosity of the washing liquid is the same as that of the filtrate and the filter cake is washed under the same pressure, what is the washing rate in $m^{3}$/s?

Options:
A. 0.06
B. 0.10
C. 0.02
D. 0.05
E. 0.09
F. 0.03
G. 0.11
H. 0.07
I. 0.01
J. 0.08
Answer: I
A factory aims to obtain 5800 $\mathrm{m}^{3}$ of filtrate annually, operating 5000 hours per year, using a batch filter under constant pressure. Each operation cycle lasts 2.8 hours, with a filtration time of 1.5 hours. Under the same operating conditions, the filtration constant has been measured as $K=4\times10^{-6}\,\mathrm{m^{2}/s}$ and $q_{e}=2.5\times10^{-2}\,\mathrm{m}$. What is the required filtration area in $\mathrm{m}^{2}$?

Options:
A. $26.2m^{2}$
B. $21.5m^{2}$
C. $22.7m^{2}$
D. $28.1m^{2}$
E. $25.6m^{2}$
F. $30.4m^{2}$
G. $29.5m^{2}$
H. $27.9m^{2}$
I. $23.8m^{2}$
J. $24.3m^{2}$
Answer: A
A rotary vacuum filter rotates 3 times per minute, yielding a filtrate volume of 0.1 $\mathrm{m}^{3}$. If the resistance from the filter medium is negligible. In order to obtain $8\mathrm{m}^{3}$ of filtrate per hour, what is the thickness of the filter cake on the drum surface compared to the original? The vacuum level used during the operation remains constant.

Options:
A. 5.75 times
B. 7.00 times
C. 2.00 times
D. 3.50 times
E. 4.50 times
F. 6.25 times
G. 9.75 times
H. 0.75 times
I. 8.25 times
J. 1.50 times
Answer: H
Filter the titanium dioxide ($\mathrm{TiO}_{2}$) aqueous suspension using a plate and frame filter press under constant pressure difference. The frame dimensions are $700\,\mathrm{mm} \times 700\,\mathrm{mm} \times 42\,\mathrm{mm}$, with a total of 10 frames. It has been measured that: after filtering for 20 minutes, $0.98\,\mathrm{m}^{3}$ of filtrate is obtained, and after filtering for another 20 minutes, a total of $1.423\,\mathrm{m}^{3}$ of filtrate is collected. Given the ratio of the volume of the filter cake to the volume of the filtrate $\nu=0.1$, and a combined washing and auxiliary time of 30 minutes, calculate the production capacity of the device is (). (Measured by the volume of filter cake obtained per hour.)

Options:
A. $$
0. 1 1 2 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
B. $$
0. 1 0 5 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
C. $$
0. 1 5 0 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
D. $$
0. 1 2 5 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
E. $$
0. 1 2 0 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
F. $$
0. 0 9 8 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
G. $$
0. 1 6 2 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
H. $$
0. 1 4 8 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
I. $$
0. 1 7 5 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
J. $$
0. 1 3 5 {\mathrm{m}}^{3} / {\mathrm{h}}
$$
Answer: A
To purify dust-laden air using a dust settling chamber, it is required that the purified air contains no dust particles with a diameter greater than 0.01 mm. The air temperature should be 20°C, the flow rate is 1500 kg/h, and the dust particle density is 1800 kg/m³. Calculate the required settling area is ().

Options:
A. $65.4m^2$
B. $68.1m^2$
C. $70.8m^2$
D. $69.6m^2$
E. $74.5m^2$
F. $72.0m^2$
G. $73.8m^2$
H. $66.7m^2$
I. $71.2m^2$
J. $75.1m^2$
Answer: C
In a jacketed heating kettle equipped with a stirrer, there are 100 kg of oil. It takes 50 minutes to heat the oil from 25°C to 110°C using saturated steam at 120°C. How much time is needed to heat the oil to 115°C?

Options:
A. 65.5min
B. 59.8min
C. 67.1min
D. 62.4min
E. 53.7min
F. 64.3min
G. 72.3min
H. 66.0min
I. 70.9min
J. 58.2min
Answer: A
Desorption tower height is $6\mathrm{m}$, $L=200\mathrm{kmol}/\mathrm{h}$, $x_{\text{in}}=0.08$ (mole fraction, the same below), using an inert gas with $y_{\text{in}}=0$, $G=350\mathrm{kmol/h}$ for desorption, results in $y_{\text{out}}=0.036$. Given the equilibrium relation: $y=0.5x$, find the height of the gas-phase mass transfer unit $H_{\mathrm{OG}}$ for this tower is ().

Options:
A. 3.0m
B. 2.0m
C. 1.5m
D. 4.0m
E. 1.0m
F. 2.5m
G. 0.5m
H. 5.0m
I. 6.5m
J. 7.0m
Answer: E
At 15°C and 101.3 kPa, a large amount of sulfuric acid is used in counter-current to absorb water vapor from the air. The incoming air contains water vapor with a mole fraction of 0.0145 (same units apply hereafter). The concentration of sulfuric acid entering and exiting the tower is 80%, and the equilibrium concentration of water vapor above the sulfuric acid solution is $y_{e} = 1.05 \times 10^{-4}$. It is known that the volume mass transfer coefficient of the tower $K_{y} a \propto G^{0.8}$. After passing through the tower, the air is dried to a water vapor content of 0.000322. If the air flow rate is doubled, what will be the water content of the air exiting the tower?

Options:
A. $$
y^{\prime} _{out}=0.000234
$$
B. $$
y^{\prime} _{out}=0.000289
$$
C. $$
y^{\prime} _{out}=0.000415
$$
D. $$
y^{\prime} _{out}=0.000541
$$
E. $$
y^{\prime} _{out}=0.000438
$$
F. $$
y^{\prime} _{out}=0.000527
$$
G. $$
y^{\prime} _{out}=0.000600
$$
H. $$
y^{\prime} _{out}=0.000512
$$
I. $$
y^{\prime} _{out}=0.000478
$$
J. $$
y^{\prime} _{out}=0.000367
$$
Answer: I
To use a packed tower for countercurrent absorption of harmful component A from a mixed gas using water. It is known that the concentration of component A entering the tower is $y_{\mathrm{in}}=0.05$ (mole fraction, same below), and a recovery rate of 90% is required. The equilibrium relationship is given by $y=2x$, with $H_{\mathrm{OG}}=0.8 \mathrm{m}$. The liquid-to-gas ratio is 1.5 times the minimum liquid-to-gas ratio. If the concentration of component A entering the tower changes to $y_{\mathrm{in}}=0.1$, with other design conditions remaining unchanged, and a plate tower is used instead, how many theoretical plates are required?

Options:
A. 3
B. 5
C. 8
D. 4
E. 10
F. 9
G. 7
H. 12
I. 6
J. 15
Answer: B
A 25-year-old pregnant woman with severe pregnancy-induced hypertension, experiencing edema (+++), was treated with magnesium sulfate for convulsions and diuretics for one week. She delivered a full-term female infant weighing 3000g. During delivery, there was 200ml of bleeding. Ten minutes postpartum, she suddenly became pale with a blood pressure of 70/50mmHg and a pulse of 120/min. Which of the following is the most likely diagnosis?

Options:
A. Amniotic Fluid Embolism
B. Venous Air Embolism
C. Placenta Accreta
D. Deep Vein Thrombosis
E. Uterine Rupture
F. Cardiac Valve Malfunction
G. Postpartum Cystitis
H. Postpartum Exhaustion
I. Pulmonary Artery Spasm
J. Postpartum Pneumonia
Answer: H
Let the random variable $X$ follow a normal distribution $N(0,1)$. For a given $a \in (0,1)$, the number $u_{0}$ satisfies $P(X > u_{0}) = a$. If $P(|X| < x) = a$, then $x$ equals ().

Options:
A. $v\frac{1+a}{2}$
B. $v\frac{3a+1}{2}$
C. $u\frac{a}{2+1}$
D. $u\frac{1-a}{2}$
E. $v\frac{2a-1}{2}$
F. $v\frac{1-a}{3}$
G. $u\frac{1+a}{4}$
H. $u\frac{1-a}{3}$
I. $u\frac{a+1}{4}$
J. $u\frac{2-a}{3}$
Answer: D
Given that the $\Delta H^{-}$ of methyl methacrylate is $-56.5 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ and $\Delta S^{-}$ is $-117.2 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$, what is the equilibrium monomer concentration during the polymerization of methyl methacrylate at temperatures of $77^\circ \mathrm{C}$, $127^\circ \mathrm{C}$, $177^\circ \mathrm{C}$, and $227^\circ \mathrm{C}$?

Options:
A. $$
5.05 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0587 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.383 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.848 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
B. $$
5.07 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0631 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.408 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 2.061 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
C. $$
4.94 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0558 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.368 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.664 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
D. $$
4.82 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0569 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.361 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.683 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
E. $$
5.12 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0623 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.402 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 2.024 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
F. $$
5.01 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0616 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.396 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.825 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
G. $$
4.77 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0552 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.367 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.639 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
H. $$
5.14 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0604 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.399 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.907 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
I. $$
4.79 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0545 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.358 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.724 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
J. $$
4.88 \times10^{-3} {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.0574 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 0.375 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}\\ 1.745 {\mathrm{~ m o l ~}} \cdot{\mathrm{L}}^{-1}
$$
Answer: C
Consult the boiling points of the following compounds and arrange them in descending order of boiling points ().
(i) Ethyl chloride (ii) Acetyl bromide (iii) Acetic anhydride (iv) Ethyl acetate (v) Chloroethane (vi) Bromoethane (vii) Ethanol (viii) Acetic acid (ix) Diethyl ether

Options:
A. Acetic anhydride > Ethanol > Acetic acid > Ethyl acetate > Acetyl bromide > Acetyl chloride > Bromoethane > Chloroethane ≥ Ether
B. Acetic anhydride > Acetic acid > Ethanol > Acetyl bromide > Ethyl acetate > Acetyl chloride > Ether > Bromoethane ≥ Chloroethane
C. Acetic acid > Acetic anhydride > EthanAcetyl bromide > Ethanol > Ethyl acetate > Acetyl chloride > Bromoethane > Chloroethane ≥ Ether
D. Ethanol > Acetic acid > Acetic anhydride > Acetyl bromide > Ethyl acetate > Acetyl chloride > Bromoethane > Ether ≥ Chloroethane
E. Acetic acid > Acetic anhydride > Ethanol > Ethyl acetate > Acetyl bromide > Acetyl chloride > Ether > Chloroethane ≥ Bromoethane
F. Acetic acid > Ethanol > Acetic anhydride > Acetyl bromide > Acetyl chloride > Ethyl acetate > Chloroethane > Bromoethane ≥ Ether
G. Ethyl acetate > Acetic anhydride > Acetic acid > Ethanol > Acetyl bromide > Acetyl chloride > Bromoethane > Ether ≥ Chloroethane
H. Acetic anhydride > Ethanol > Acetic acid > Acetyl bromide > Acetyl chloride > Ethyl acetate > Ether > Chloroethane ≥ Bromoethane
I. Acetic anhydride > Acetic acid > Ethanol > Ethyl acetate > Acetyl bromide > Acetyl chloride > Bromoethane > Ether ≥ Chloroethane
J. Acetic anhydride > Acetic acid > Ethanol > Acetyl bromide > Ethyl acetate > Acetyl chloride > Chloroethane > Bromoethane ≥ Ether
Answer: I
Determine the configuration of the chiral center carbon atom in monophospho-L-glyceride.

Options:
A. $D$ configuration
B. $H$ configuration
C. $X$ configuration
D. $I$ configuration
E. $P$ configuration
F. $R$ configuration
G. $S$ configuration
H. $Q$ configuration
I. $T$ configuration
J. $L$ configuration
Answer: F
The guide rod with a vertical groove moves at a constant speed of $v=1$ m/s along the horizontal guide rail, driving pin $P$ to move along a parabolic-shaped groove in a fixed vertical plane. The equation of the parabola is given as $x=\frac{y^2}{3}$, with $x$ and $y$ measured in meters. Find the radius of curvature $\rho$ of the trajectory when $y=2$ m, and the tangential acceleration $a_\mathrm{\tau o}$ of the pin at that instant.

Options:
A. $\text{6.94m}$
$-0.169\mathrm{m/s}^{2}$
B. $\text{7.50m}$
$-0.210\mathrm{m/s}^{2}$
C. $\text{6.10m}$
$-0.130\mathrm{m/s}^{2}$
D. $\text{6.94m}$
$-0.190\mathrm{m/s}^{2}$
E. $\text{5.50m}$
$-0.200\mathrm{m/s}^{2}$
F. $\text{8.00m}$
$-0.120\mathrm{m/s}^{2}$
G. $\text{5.80m}$
$-0.240\mathrm{m/s}^{2}$
H. $\text{6.94m}$
$-0.180\mathrm{m/s}^{2}$
I. $\text{7.25m}$
$-0.150\mathrm{m/s}^{2}$
J. $\text{6.20m}$
$-0.170\mathrm{m/s}^{2}$
Answer: A
Ship $A$ is traveling northward at a constant speed of $v_A = 15$ km/h, while ship $B$ is moving at a constant speed of $v_B = 12$ km/h along a circular arc track. The angular velocity of its rotation is $10$ degrees per minute. At the position shown in the diagram, the distance between the two ships is $AB = 4$ km. Find the acceleration of ship $A$ relative to ship $B$, $\mathbf{a}_{A/B}$, and the acceleration of ship $B$ relative to ship $A$, $\mathbf{a}_{B/A}$.

Options:
A. $$
-130.1 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
320 \ i- 127.0 \ \mathbf{j km} / \mathbf{h}^{2}
$$
B. $$
-128.8 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
325 \ i- 123.7 \ \mathbf{j km} / \mathbf{h}^{2}
$$
C. $$
-123.5 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
300 \ i- 120.0 \ \mathbf{j km} / \mathbf{h}^{2}
$$
D. $$
-125.7 \, \mathbf{j k m} / \mathbf{h}^{2}
$$
$$
314 \ i- 125.3 \ \mathbf{j k m} / \mathbf{h}^{2}
$$
E. $$
-129.2 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
305 \ i- 122.6 \ \mathbf{j km} / \mathbf{h}^{2}
$$
F. $$
-125.5 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
318 \ i- 126.1 \ \mathbf{j km} / \mathbf{h}^{2}
$$
G. $$
-127.3 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
317 \ i- 128.4 \ \mathbf{j km} / \mathbf{h}^{2}
$$
H. $$
-124.9 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
315 \ i- 124.0 \ \mathbf{j km} / \mathbf{h}^{2}
$$
I. $$
-122.7 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
312 \ i- 121.9 \ \mathbf{j km} / \mathbf{h}^{2}
$$
J. $$
-126.0 \, \mathbf{j km} / \mathbf{h}^{2}
$$
$$
310 \ i- 126.5 \ \mathbf{j km} / \mathbf{h}^{2}
$$
Answer: D
The exhaust fan of a certain building can expel air with a pressure of 98 kPa and a temperature of 20°C at a rate of 2.5 kg/s through an exhaust port with a diameter of 0.4 m. After passing through the exhaust fan, the air pressure increases by 50 $mmH_2O$, but the temperature remains approximately unchanged. Determine the power of the exhaust fan and the exhaust velocity.

Options:
A. $$
0.415 ~ ~ \mathrm{kW}
$$
B. $$
0.458 ~ ~ \mathrm{kW}
$$
C. $$
0.389 ~ ~ \mathrm{kW}
$$
D. $$
0.254 ~ ~ \mathrm{kW}
$$
E. $$
0.276 ~ ~ \mathrm{kW}
$$
F. $$
0.365 ~ ~ \mathrm{kW}
$$
G. $$
0.341 ~ ~ \mathrm{kW}
$$
H. $$
0.298 ~ ~ \mathrm{kW}
$$
I. $$
0.432 ~ ~ \mathrm{kW}
$$
J. $$
0.512 ~ ~ \mathrm{kW}
$$
Answer: F
Using continuous distillation to separate a benzene-toluene binary mixture, the feed rate is known to be 4000 kg·h$^{-1}$, with a composition of 0.3 (mass fraction, same below). If the composition of the bottom liquid is required to be no more than 0.05, and the recovery rate $\eta$ of the distillate is 88%. What is the composition of the distillate in terms of mole fraction?

Options:
A. $10.75\mathrm{kmol}\bullet\mathrm{h}^{-1}$
B. $19.80\mathrm{kmol}\bullet\mathrm{h}^{-1}$
C. $13.66\mathrm{kmol}\bullet\mathrm{h}^{-1}$
D. $16.40\mathrm{kmol}\bullet\mathrm{h}^{-1}$
E. $17.50\mathrm{kmol}\bullet\mathrm{h}^{-1}$
F. $11.25\mathrm{kmol}\bullet\mathrm{h}^{-1}$
G. $14.20\mathrm{kmol}\bullet\mathrm{h}^{-1}$
H. $12.45\mathrm{kmol}\bullet\mathrm{h}^{-1}$
I. $18.35\mathrm{kmol}\bullet\mathrm{h}^{-1}$
J. $15.90\mathrm{kmol}\bullet\mathrm{h}^{-1}$
Answer: C
In order to absorb the aromatics in the coke oven gas, it is planned to use washing oil with an aromatic content of 0.006 (mole fraction, the same below) sprayed from the top of the absorption tower. The washing oil is used at a rate of 31.2 kmol·h$^{-1}$. When the temperature is 30°C and the operating pressure is 108.2 kPa, the flow rate of coke oven gas entering the absorption tower with an aromatic content of 0.022 is 4000 m$^3$·h$^{-1}$. If the requirement is that the aromatic content in the gas leaving the tower does not exceed 0.001 (assuming the coke oven gas is an ideal gas), What is the concentration of aromatic $x_1$ hydrocarbons in the washing oil flowing out from the bottom of the tower?

Options:
A. 0.1086
B. 0.2058
C. 0.1492
D. 0.1323
E. 0.0554
F. 0.0876
G. 0.0937
H. 0.0661
I. 0.1125
J. 0.1789
Answer: A
At 20°C and 101.3 kPa, a mixture of CO₂ and air slowly flows over a Na₂CO₃ solution. Air is insoluble in the Na₂CO₃ solution. CO₂ diffuses through a stationary air layer with a thickness of 1 mm into the Na₂CO₃ solution. The mole fraction of CO₂ in the gas is 0.2. At the surface of the Na₂CO₃ solution, CO₂ is rapidly absorbed, hence the concentration of CO₂ at the phase interface is negligible. At 20°C, the diffusion coefficient of CO₂ is D = 0.18 cm²·s⁻¹. What is the diffusion rate of CO₂?

Options:
A. $1.9\times10^{-3}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
B. $8.2\times10^{-5}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
C. $3.4\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
D. $2.3\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
E. $9.6\times10^{-6}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
F. $1.5\times10^{-5}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
G. $5.5\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
H. $1.7\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
I. $4.8\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
J. $2.0\times10^{-4}$kmol$\cdot\mathrm{m}^-2\cdot\mathrm{s}^{-1}$
Answer: H
On the inclined section of the road, the car maintains balance with the help of the brakes. When the brake pedal is moved by 2 cm, the brake pad on the disc brake moves 0.2 mm. The diameter of the working part of the disc is 220 mm, and the loading diameter of the wheel is 520 mm. The car weighs 14 kN. Given that the road gradient is 20°, what force must the driver exert to press the brake pedal? ( Ignore rolling friction. The coefficient of friction between the brake pad and disc is $f=0.5$. The working condition of each wheel's brake is the same. )

Options:
A. $$
0. 2 5 4 \mathrm{~ k N}
$$
B. $$
0. 1 0 7 \mathrm{~ k N}
$$
C. $$
0. 1 9 8 \mathrm{~ k N}
$$
D. $$
0. 1 2 3 \mathrm{~ k N}
$$
E. $$
0. 0 8 4 \mathrm{~ k N}
$$
F. $$
0. 3 4 5 \mathrm{~ k N}
$$
G. $$
0. 3 1 8 \mathrm{~ k N}
$$
H. $$
0. 2 9 9 \mathrm{~ k N}
$$
I. $$
0. 1 5 7 \mathrm{~ k N}
$$
J. $$
0. 2 2 6 \mathrm{~ k N}
$$
Answer: J