MikaStars39/nano-eval huggingface dataset:
Constant pressure filtration of a certain suspension (medium resistance can be ignored, filter cake is incompressible) was tested, and it was found that 0.1 m³/m² of filtrate was obtained in 10 minutes. Now, if 2 m³ of filtrate is required in 40 minutes, what is the required filter area in m²?

Options:
A. 18
B. 24
C. 26
D. 14
E. 28
F. 10
G. 12
H. 16
I. 20
J. 22
Answer: F
If the ratio of the washing rate to the final filtration rate $\mathrm{d}V/\mathrm{d}\tau$ for a plate-and-frame filter press is 1/4, what is the ratio of the washing rate to the final filtration rate for a leaf filter?

Options:
A. 4
B. 1
C. 0.5
D. 3
E. 2.5
F. 2
G. 5
H. 6
I. 0.75
J. 1.5
Answer: B
In a certain dust settling chamber, each layer has a bottom area of $10\,\mathrm{m}^{2}$, with 5 layers of baffle plates evenly arranged inside. This dust settling chamber is currently used to purify dust-laden air with a mass flow rate of 6000 kg/h, where $\rho_{\mathrm{p}}=2500\,\mathrm{kg}/\mathrm{m}^{3}$. The temperature of the air entering the dust settling chamber is 150°C. It is known that at 150°C, the density of air is $0.836\,\mathrm{kg}/\mathrm{m}^{3}$ and the viscosity is $\mu=2.41\times 10^{-5}\,\mathrm{Pa}\cdot\mathrm{s}$. What is the minimum particle diameter completely removed?

Options:
A. $$
3 1. 5 \mu\mathrm{m}
$$
B. $$
2 4. 2 \mu\mathrm{m}
$$
C. $$
2 2. 9 \mu\mathrm{m}
$$
D. $$
1 5. 8 \mu\mathrm{m}
$$
E. $$
3 0. 1 \mu\mathrm{m}
$$
F. $$
2 1. 3 \mu\mathrm{m}
$$
G. $$
2 8. 6 \mu\mathrm{m}
$$
H. $$
1 8. 7 \mu\mathrm{m}
$$
I. $$
1 9. 2 \mu\mathrm{m}
$$
J. $$
2 6. 4 \mu\mathrm{m}
$$
Answer: B
In a packed tower with a diameter of 0.8 meters, $1200 \, \mathrm{kg/h}$ of clean water is used to absorb $\mathrm{SO}_{2}$ from a mixture of air and $\mathrm{SO}_{2}$. The mixture flow rate is $1000 \, \mathrm{m}^{3}/\mathrm{h}$, with an $\mathrm{SO}_{2}$ concentration of 1.3% (by volume). The required recovery rate is 99.5%. The operating conditions are 20°C and 101.3 kPa, with the equilibrium relationship expressed as $y = 0.75 x$. The overall volumetric mass transfer coefficient is $K_{y} a = 0.055 \, \mathrm{kmol}/(\mathrm{m^{3} \cdot s})$. What is the height of the packing layer?

Options:
A. 3.5m
B. 3.7m
C. 2.3m
D. 5.7m
E. 2.0m
F. 4.2m
G. 6.9m
H. 4.9m
I. 5.1m
J. 1.8m
Answer: F
In a certain packed absorption tower, methanol is absorbed from a mixed gas using pure water in a countercurrent flow. The gas inlet flow rate is 20 kmol/($\mathrm{m^{2}} \cdot \mathrm{h}$), with a gas inlet concentration of 0.06, achieving a recovery rate of 99%. The water flow rate is 50 kmol/($\mathrm{m^{2}} \cdot \mathrm{h}$). The packed bed height is 4 meters, and the operating pressure is 101.3 kPa, with the equilibrium relationship given by $y=0.9x$. If technological innovations in the entire process result in the operating pressure of this tower doubling, how high must the packed bed be to achieve the original absorption rate?

Options:
A. 3.55m
B. 0.85m
C. 2.25m
D. 2.75m
E. 0.45m
F. 1.25m
G. 4.95m
H. 5.35m
I. 2.05m
J. 1.65m
Answer: J
In a certain packed absorption tower, water is used in countercurrent flow to absorb acetone from an air mixture. Under the original operating conditions, the gas concentration entering the tower is 0.015 (mole fraction, the same below), and the operating liquid-to-gas ratio is 1.5 times the minimum liquid-to-gas ratio. The acetone recovery rate can reach 0.99. Currently, the gas concentration entering the tower has decreased to 0.010, and the gas volume entering the tower has increased by 20%, while the amount of absorbent, inlet concentration, temperature, and other operating conditions remain unchanged. It is known that under the operating conditions, the equilibrium relationship satisfies Henry's Law, and the overall mass transfer coefficient $K_{y} a \propto G^{0.8}$. Calculate the acetone recovery rate under the new operating conditions is ().

Options:
A. 0.85
B. 0.88
C. 0.94
D. 0.92
E. 0.89
F. 0.91
G. 0.97
H. 0.90
I. 0.83
J. 0.95
Answer: G
A 32-year-old woman was admitted to the emergency department in a state of shock, with profuse active vaginal bleeding and tissue resembling necrotic material visible. Gynecological examination revealed the uterus to be the size of a 6-week pregnancy, with no masses detected in the adnexal regions. Which sign is most significant for further management?

Options:
A. Condition of Pelvic Floor Muscles
B. Presence of Fetal Heartbeat
C. Presence of Adnexal Masses
D. Degree of Cervical Dilation
E. Location of Hematoma Formation
F. Necrotic Tissue Consistency
G. Uterine Wall Thickness
H. Length of Vaginal Canal
I. Presence of Abdominal Tenderness
J. Volume of Vaginal Bleeding
Answer: D
A 30-year-old woman presents with a history of pregnancy: miscarriage? Termination... followed by secondary infertility for 3 years. In the past six months, her menstrual cycle has been irregular. After 3 months of amenorrhea, she experienced irregular vaginal bleeding for 20 days before seeking medical care. Examination reveals enlarged, pigmented breasts, and pigmented cervix and vagina. On the left vaginal wall, there is a purple-blue nodule measuring 3cm x 2cm x 1cm. The uterus is slightly enlarged and soft, and both sides have palpable cystic masses measuring 4cm x 3cm x 2cm. These masses are mobile and non-tender. The pregnancy test is strongly positive. Which of the following diseases is most likely?

Options:
A. Choriocarcinoma
B. Epithelial ovarian tumor
C. Ectopic pregnancy
D. Uterine fibroids
E. Pelvic inflammatory disease
F. Molar pregnancy
G. Ovarian cysts torsion
H. Endometrial hyperplasia
I. Tubo-ovarian abscess
J. Polycystic ovary syndrome
Answer: A
110 kg of water is heated by an electric heater from an ambient temperature of 15°C to 50°C and then naturally cooled back to 15°C. Assuming the electric heater maintains a constant temperature of 370 K, calculate the loss associated with each process.

Options:
A. $$
2 \ 8 0 5. 3 9 \ \mathrm{k J}
$$
$$
9 9 9. 6 0 \ \mathrm{k J}
$$
B. $$
3 \ 7 0 1. 0 2 \ \mathrm{k J}
$$
$$
1 0 2 0. 4 6 \ \mathrm{k J}
$$
C. $$
2 \ 5 9 8. 7 1 \ \mathrm{k J}
$$
$$
8 7 6. 9 4 \ \mathrm{k J}
$$
D. $$
2 \ 6 1 7. 2 2 \ \mathrm{k J}
$$
$$
8 8 8. 2 8 \ \mathrm{k J}
$$
E. $$
2 \ 4 5 6. 3 9 \ \mathrm{k J}
$$
$$
9 0 1. 4 7 \ \mathrm{k J}
$$
F. $$
2 \ 7 4 0. 4 4 \ \mathrm{k J}
$$
$$
9 5 0. 8 0 \ \mathrm{k J}
$$
G. $$
2 \ 6 8 9. 9 3 \ \mathrm{k J}
$$
$$
9 5 9. 5 2 \ \mathrm{k J}
$$
H. $$
2 \ 6 5 9. 0 8 \ \mathrm{k J}
$$
$$
9 1 3. 5 5 \ \mathrm{k J}
$$
I. $$
2 \ 9 4 7. 6 0 \ \mathrm{k J}
$$
$$
9 8 7. 3 1 \ \mathrm{k J}
$$
J. $$
2 \ 3 2 0. 8 5 \ \mathrm{k J}
$$
$$
7 5 3. 7 4 \ \mathrm{k J}
$$
Answer: H
What is the feed ratio of hexamethylenediamine to adipic acid required to obtain nylon-66 with a number-average molecular weight of 10,000 when the reaction extent is at 99.5%?

Options:
A. $$
1 : 1 . 1 0 9
$$
B. $$
1 : 1 . 0 1 2
$$
C. $$
1 : 0 . 9 7 4
$$
D. $$
1 : 1 . 0 5 6
$$
E. $$
1 : 1 . 0 0 5
$$
F. $$
1 : 0. 9 8 7
$$
G. $$
1 : 0 . 9 2 5
$$
H. $$
1 : 0 . 9 5 3
$$
I. $$
1 : 1 . 0 8 0
$$
J. $$
1 : 0 . 9 6 8
$$
Answer: F
The ____ of the bromine atom is weaker than that of the chlorine atom, thus the ____ of the former is also weaker.

Options:
A. Molecular vibration frequency, absorbance of light
B. Van der Waals radius, solubility of salts
C. Bond dissociation energy, stability of anions
D. Covalent bond strength, volatility of compounds
E. Atomic radius difference, reactivity of ions
F. Electron-withdrawing inductive effect, acidity of conjugate acids
G. Ionization potential, polarity of solutions
H. Valence shell electron repulsion, color of solutions
I. Electronegativity gradient, polarity of acids
Answer: F
The horizontal straight-line distance between points $A$ and $B$ is 300m. A motorcycle starts from rest at $A$ and stops at $B$. If the motorcycle's maximum acceleration is $a_1 = 0.7g$ and the maximum deceleration is $a_2 = 0.6g$, with both assumed to be constant. Find the minimum time $t$ required for the motorcycle to travel from $A$ to $B$ , and calculate its maximum speed $v$.

Options:
A. $$
1 6. 8 9 \mathrm{s}
$$
$$
1 4 8 \mathrm{k m / h}
$$
B. $$
1 3. 7 6 \mathrm{s}
$$
$$
1 5 7 \mathrm{k m / h}
$$
C. $$
1 3. 0 2 \mathrm{s}
$$
$$
1 5 4 \mathrm{k m / h}
$$
D. $$
1 4. 2 1 \mathrm{s}
$$
$$
1 5 0 \mathrm{k m / h}
$$
E. $$
1 7. 0 5 \mathrm{s}
$$
$$
1 3 2 \mathrm{k m / h}
$$
F. $$
1 5. 2 4 \mathrm{s}
$$
$$
1 3 8 \mathrm{k m / h}
$$
G. $$
1 1. 9 7 \mathrm{s}
$$
$$
1 6 4 \mathrm{k m / h}
$$
H. $$
1 4. 5 0 \mathrm{s}
$$
$$
1 4 0 \mathrm{k m / h}
$$
I. $$
1 5. 0 3 \mathrm{s}
$$
$$
1 6 0 \mathrm{k m / h}
$$
J. $$
1 2. 3 8 \mathrm{s}
$$
$$
1 6 2 \mathrm{k m / h}
$$
Answer: B
The crank $AB$, which has a sliding slot, is hinged at point $O$. A thin rope is connected to the slider $C$, with one end fixed at point $D$. It is known that the crank rotates around the $O$ axis at a constant angular velocity of $\dot{\theta}=4 \text{ rad/s}$, and when $\theta=0$, $r=0$. Assume the rope remains taut during motion, with distances $OB=OD=R-15 \text{ cm}$. Find the acceleration $a$ of the slider when $\theta=30°$.

Options:
A. $$
8 3 7 \mathrm{c m} / \mathrm{s}^{2}
$$
B. $$
4 0 9 \mathrm{c m} / \mathrm{s}^{2}
$$
C. $$
4 8 9 \mathrm{c m} / \mathrm{s}^{2}
$$
D. $$
7 4 1 \mathrm{c m} / \mathrm{s}^{2}
$$
E. $$
6 2 5 \mathrm{c m} / \mathrm{s}^{2}
$$
F. $$
9 7 2 \mathrm{c m} / \mathrm{s}^{2}
$$
G. $$
1 3 6 \mathrm{c m} / \mathrm{s}^{2}
$$
H. $$
3 5 0 \mathrm{c m} / \mathrm{s}^{2}
$$
I. $$
2 1 4 \mathrm{c m} / \mathrm{s}^{2}
$$
J. $$
5 8 6 \mathrm{c m} / \mathrm{s}^{2}
$$
Answer: C
Calculate the moment of inertia of a rectangular prism with a height of $6 in$, a width of $4 in$, and a length of $10 in$ about its longitudinal centroidal axis is(). The weight is given as $40 lb/ft³$.

Options:
A. $$
0. 0 3 9 \ \ \mathrm{s l u g-f t^{2}}
$$
B. $$
0. 0 6 8 \ \ \mathrm{s l u g-f t^{2}}
$$
C. $$
0. 0 8 7 \ \ \mathrm{s l u g-f t^{2}}
$$
D. $$
0. 1 1 2 \ \ \mathrm{s l u g-f t^{2}}
$$
E. $$
0. 0 2 1 \ \ \mathrm{s l u g-f t^{2}}
$$
F. $$
0. 0 9 9 \ \ \mathrm{s l u g-f t^{2}}
$$
G. $$
0. 0 1 3 \ \ \mathrm{s l u g-f t^{2}}
$$
H. $$
0. 0 7 4 \ \ \mathrm{s l u g-f t^{2}}
$$
I. $$
0. 1 0 3 \ \ \mathrm{s l u g-f t^{2}}
$$
J. $$
0. 0 0 5 \ \ \mathrm{s l u g-f t^{2}}
$$
Answer: J
A type of solid heat storage device uses solar energy to heat rocks for thermal storage, with the rock temperature reaching $400 \mathrm{K}$. There is currently a rock bed with a volume of $2 \ \mathrm{m}^{3}$, where the rock density is $\rho = 2750 \ \mathrm{kg/m}^{3}$ and the specific heat capacity is $c = 0.89 \ \mathrm{kJ/(kg \cdot K)}$. Determine the maximum amount of heat energy released when the rocks cool down to the ambient temperature of $290 \mathrm{K}$.

Options:
A. $$
73542.0 \mathrm{k J}
$$
B. $$
85120.0 \mathrm{k J}
$$
C. $$
81950.0 \mathrm{k J}
$$
D. $$
78432.0 \mathrm{k J}
$$
E. $$
90234.0 \mathrm{k J}
$$
F. $$
83015.0 \mathrm{k J}
$$
G. $$
81200.0 \mathrm{k J}
$$
H. $$
79325.0 \mathrm{k J}
$$
I. $$
84000.0 \mathrm{k J}
$$
J. $$
81946.0 \mathrm{k J}
$$
Answer: J
Concentrate a 2500 kg·h$^{-1}$ NaOH aqueous solution from 10% (mass fraction, the same below) to 30% in a single-effect evaporator. Given that the absolute pressure of the heating steam is 361.47 kPa, the pressure in the evaporation chamber is 101.33 kPa, the boiling point of the solution is 118°C, the specific heat at constant pressure is 3.6 kJ·$\text{kg}^{-1}*\text{C}^{-1}$, and the heat loss is 20 kW. What is the required unit steam consumption when the feed temperature is 20°C?

Options:
A. 1.32
B. 1.28
C. 1.36
D. 1.45
E. 1.50
F. 1.38
G. 1.25
H. 1.22
I. 1.40
J. 1.60
Answer: A
At a temperature of 25°C and a total pressure of 101.3 kPa, the Henry's law constant for $mathrm{CO}_2$ is found to be $E = 14.39 \times 10^4$kPa. What is the value of the solubility coefficient $H$ ?(for the symmetric aqueous solution $\rho = 998 \mathrm{kg/m}^3$)

Options:
A. $1.38×10^3$
B. $1.42×10^3$
C. $1.50×10^3$
D. $1.32×10^3$
E. $1.44×10^3$
F. $1.52×10^3$
G. $1.39×10^3$
H. $1.48×10^3$
I. $1.46×10^3$
J. $1.40×10^3$
Answer: B
Given that a certain distillation column operates with binary feed, the operating lines for the enriching and stripping sections are as follows: Enriching section \( y = 0.714x + 0.271 \); Stripping section \( y = 1.25x - 0.01 \). What is the mole fraction of the more volatile component in the bottom product and in the feed?

Options:
A. 0.783
B. 0.741
C. 0.563
D. 0.482
E. 0.529
F. 0.655
G. 0.637
H. 0.708
I. 0.716
J. 0.694
Answer: G
The acceleration at a point on the edge of the flywheel forms a $60^{\circ}$ angle with the radius at that point. At this instant, the tangential acceleration of the point is $w_{r}=10 \sqrt{3} \ \mathrm{m / s^{2}}$. What is the normal acceleration of a point that is $r=0.5$ m away from the axis of rotation ? ( The radius of the flywheel $R=1 \mathrm{~m}$ is given. )

Options:
A. $$3 \ \mathrm{m / s^{2}}$$
B. $$9 \ \mathrm{m / s^{2}}$$
C. $$7 \ \mathrm{m / s^{2}}$$
D. $$2 \ \mathrm{m / s^{2}}$$
E. $$11 \ \mathrm{m / s^{2}}$$
F. $$4 \ \mathrm{m / s^{2}}$$
G. $$6 \ \mathrm{m / s^{2}}$$
H. $$8 \ \mathrm{m / s^{2}}$$
I. $$5 \ \mathrm{m / s^{2}}$$
J. $$10 \ \mathrm{m / s^{2}}$$
Answer: I
At a distance of 500 m from the station, the train driver closes the throttle and begins braking. The station is located on a slope that is 2 m high, and the train's speed is 12 m/s. Assuming the train's mass is 1000 t and the frictional resistance is equal to 20 kN. How much should the braking resistance be (assuming it is a constant) to bring the train to a stop at the station?

Options:
A. $$92.5 kN$$
B. $$101.3 kN$$
C. $$79.8 kN$$
D. $$82.1 kN$$
E. $$76.5 kN$$
F. $$67.4 kN$$
G. $$88.2 kN$$
H. $$90.7 kN$$
I. $$84.8 kN$$
J. $$95.6 kN$$
Answer: I
In a homogeneous disk with a radius of $R=1$ m, a circular hole with a radius of $r$ is drilled at a distance $l$ from the center. Both $l$ and $r$ can take on various values. They are considered as independent random variables following a Gaussian distribution, and it is assumed that their expected values are $m_{l}=0.1$ m and $m_{r}=0.05$ m, with mean square errors of $\sigma_{l}=0.01$ m and $\sigma_{r}=0.005$ m, respectively. How much must the center of mass of the disk deviate from the center of the disk for the probability of deviation exceeding 0.001? ( In the calculation of the value of the center of mass deviation, the product terms of deviations of $I$ and $r$ from their expected values are neglected. )

Options:
A. $$4. 2 \times1 0^{-4} \, \mathrm{m}$$
B. $$7. 4 \times1 0^{-4} \, \mathrm{m}$$
C. $$2. 9 \times1 0^{-4} \, \mathrm{m}$$
D. $$3. 5 \times1 0^{-4} \, \mathrm{m}$$
E. $$1. 8 \times1 0^{-4} \, \mathrm{m}$$
F. $$0. 5 \times1 0^{-4} \, \mathrm{m}$$
G. $$9. 6 \times1 0^{-4} \, \mathrm{m}$$
H. $$8. 3 \times1 0^{-4} \, \mathrm{m}$$
I. $$6. 1 \times1 0^{-4} \, \mathrm{m}$$
J. $$5. 0 \times1 0^{-4} \, \mathrm{m}$$
Answer: A
Flow through a Laval nozzle. The inlet pressure is known at $p_{0}=400 \, \text{kN/m}^2$, and the back pressure is $p_{a}=100 \, \text{kN/m}^2$. The inlet Mach number $M$ is less than 1, while the exit Mach number $M$ is greater than 1. The ratio of the exit cross-sectional area to the throat area is $\frac{A_{\bullet}}{A_{T}}=2$. Given that there is an oblique shock wave at the exit, the shock wave angle is ().

Options:
A. 70°
B. 75°
C. 45°
D. 50°
E. 30°
F. 60°
G. 55°
H. 65°
I. 40°
J. 35°
Answer: C
The buoy on the sea moves up and down 15 times per minute. Assuming the wave is a plane wave, the wavelength and the propagation speed of the wave is ().

Options:
A. 9.02m/s
B. 10.64m/s
C. 8.16m/s
D. 5.13m/s
E. 2.98m/s
F. 4.89m/s
G. 7.47m/s
H. 1.29m/s
I. 3.75m/s
J. 6.25m/s
Answer: J
The reading of the mercury barometer inside the submarine is $h_{1}$ = 800 mm, the reading of the U-tube mercury manometer is $h_{2}$ = 500 mm, the reading of the mercury barometer at sea level is 760 mm, and the density of seawater is 1025 $kg/{m}^{3}$. The depth $H$ of the submarine below the sea surface is ().

Options:
A. 16.0m
B. 10.3m
C. 15.4m
D. 19.8m
E. 11.7m
F. 14.2m
G. 13.8m
H. 12.6m
I. 17.5m
J. 18.9m
Answer: G
Two conductive spheres 1 and 2 of the same radius are hung from the same point using two equally long insulating thin strings. When spheres 1 and 2 carry equal and like charges $q$, they are 5 cm apart. If an initially uncharged sphere 3 with an insulating handle (which is identical to spheres 1 and 2) is brought into contact with sphere 1 and sphere 2 sequentially, and then removed, how far apart are spheres 1 and 2 when they reach a new equilibrium position?

Options:
A. $$
9. 4 {\mathrm{~ c m}}
$$
B. $$
5. 8 {\mathrm{~ c m}}
$$
C. $$
8. 1 {\mathrm{~ c m}}
$$
D. $$
4. 9 {\mathrm{~ c m}}
$$
E. $$
7. 2 {\mathrm{~ c m}}
$$
F. $$
1. 5 {\mathrm{~ c m}}
$$
G. $$
2. 5 {\mathrm{~ c m}}
$$
H. $$
3. 6 {\mathrm{~ c m}}
$$
I. $$
6. 7 {\mathrm{~ c m}}
$$
J. $$
4. 3 {\mathrm{~ c m}}
$$
Answer: H
There are $n$ points in space, labeled as points $1, 2, \cdots, n$. Each pair of points is connected by a wire with resistance $R$. Points 1 and $n$ are then connected to a power source with electromotive force $E$ and internal resistance $r$. What is the current flowing through the resistor connecting points 1 and $n$?

Options:
A. $$
I_{n-1}=\frac{U} {R}=\frac{3 E} {r + 2 R}
$$
B. $$
I_{n-1}=\frac{U} {R}=\frac{2 E} {n R + r}
$$
C. $$
I_{n-1}=\frac{U} {R}=\frac{E} {2 n R + r}
$$
D. $$
I_{n-1}=\frac{U} {R}=\frac{2 E} {2 r + n R}
$$
E. $$
I_{n-1}=\frac{U} {R}=\frac{E} {n R + r}
$$
F. $$
I_{n-1}=\frac{U} {R}=\frac{3 E} {n r + 3 R}
$$
G. $$
I_{n-1}=\frac{U} {R}=\frac{E} {n r + R}
$$
H. $$
I_{n-1}=\frac{U} {R}=\frac{2 E} {R + n r}
$$
I. $$
I_{n-1}=\frac{U} {R}=\frac{2 E} {n r+2 R}
$$
J. $$
I_{n-1}=\frac{U} {R}=\frac{E} {R + n r}
$$
Answer: I
The conductor has a radius of $a$, and the inner and outer radii of the cylindrical tube are $b$ and $c$, respectively. The current $I$ flows through the tube and returns via the conductor; $I$ is uniformly distributed across their cross-sections. When $a = 1.0 \, \text{mm}$, $b = 4.0 \, \text{mm}$, $c = 5.0 \, \text{mm}$, and $I = 10 \, \text{A}$, what is the value of the magnetic field energy inside the tube itself?

Options:
A. $$
3. 0 \times1 0^{-7}~\mathrm{J / m}
$$
B. $$
6. 1 \times1 0^{-7}~\mathrm{J / m}
$$
C. $$
2. 5 \times1 0^{-7}~\mathrm{J / m}
$$
D. $$
9. 5 \times1 0^{-7}~\mathrm{J / m}
$$
E. $$
4. 9 \times1 0^{-7}~\mathrm{J / m}
$$
F. $$
7. 1 \times1 0^{-7}~\mathrm{J / m}
$$
G. $$
5. 3 \times1 0^{-7}~\mathrm{J / m}
$$
H. $$
8. 3 \times1 0^{-7}~\mathrm{J / m}
$$
I. $$
1. 2 \times1 0^{-7}~\mathrm{J / m}
$$
J. $$
6. 8 \times1 0^{-7}~\mathrm{J / m}
$$
Answer: H
The diameter of the central line of an iron ring is $D = 40 \, \text{cm}$. A single layer of surface-insulated wire is wound uniformly around the ring, carrying a steady current. If a 1.0 mm wide air gap is cut in the iron ring, the magnetic flux through the cross-section of the ring is $3.0 \times 10^{-4} \, \text{Wb}$. If the width of the air gap is 2.0 mm, the magnetic flux through the cross-section of the ring is $2.5 \times 10^{-4} \, \text{Wb}$. Neglecting magnetic leakage, what is the magnetic permeability of the iron ring?

Options:
A. $$
2. 6 \times1 0^{2}
$$
B. $$
2. 9 \times1 0^{2}
$$
C. $$
3. 2 \times1 0^{2}
$$
D. $$
3. 5 \times1 0^{2}
$$
E. $$
3. 1 \times1 0^{2}
$$
F. $$
3. 0 \times1 0^{2}
$$
G. $$
3. 4 \times1 0^{2}
$$
H. $$
2. 7 \times1 0^{2}
$$
I. $$
2. 8 \times1 0^{2}
$$
J. $$
3. 3 \times1 0^{2}
$$
Answer: C
The mass of an $\alpha$ particle is known to be $m = 6.7 \times 10^{-27} \, \mathrm{kg}$, and its charge is $e = 3.2 \times 10^{-19} \, \mathrm{C}$. It moves in a uniform magnetic field of $B = 1.2 \, \mathrm{T}$ along a circular path with a radius of 45 cm. If it was initially at rest, through how much voltage must it be accelerated to reach this velocity?

Options:
A. $$
4. 8~\mathrm{M V}
$$
B. $$
7. 1~\mathrm{M V}
$$
C. $$
8. 5~\mathrm{M V}
$$
D. $$
7. 9~\mathrm{M V}
$$
E. $$
6. 9~\mathrm{M V}
$$
F. $$
8. 0~\mathrm{M V}
$$
G. $$
5. 3~\mathrm{M V}
$$
H. $$
6. 5~\mathrm{M V}
$$
I. $$
5. 7~\mathrm{M V}
$$
J. $$
9. 2~\mathrm{M V}
$$
Answer: B
The parallel plate capacitor's plates each have an area of $S$ and are separated by a distance $d$. The plates are placed vertically and disconnected from the power supply after being charged to a voltage $U$. Then, the lower half is immersed in a non-conductive liquid with a dielectric constant of $\varepsilon$. How much does the electrostatic energy of this capacitor decrease (ignoring capillary effects and gravity, and neglecting edge effects)?

Options:
A. $$
\frac{( \varepsilon-\varepsilon_{0} ) S U} {2 (\varepsilon+\varepsilon_{0}) d}
$$
B. $$
\frac{( \varepsilon-\varepsilon_{0} ) S^{2} U^{2}} {2 (\varepsilon+\varepsilon_{0}) d^{2}}
$$
C. $$
\frac{( \varepsilon-\varepsilon_{0} ) SU } {2 \varepsilon d}
$$
D. $$
\frac{(\varepsilon-\varepsilon_{0}) S U^{3}} {2 d (\varepsilon+\varepsilon_{0})}
$$
E. $$
\frac{( \varepsilon-\varepsilon_{0} )_{\varepsilon_{0}} S U^{2}} {2 ( \varepsilon+\varepsilon_{0} ) d}
$$
F. $$
\frac{\varepsilon_{0} (\varepsilon-\varepsilon_{0}) U^{2}} {2 (\varepsilon+\varepsilon_{0}) S d}
$$
G. $$
\frac{\varepsilon_{0} S U^{2}} {2 \varepsilon d (\varepsilon+\varepsilon_{0})}
$$
H. $$
\frac{2 \varepsilon_{0} S U^{2}} {\varepsilon d ( \varepsilon+\varepsilon_{0} )}
$$
I. $$
\frac{\varepsilon_{0} S U^{2}} {d ( \varepsilon+\varepsilon_{0} )^{2}}
$$
J. $$
\frac{(\varepsilon+\varepsilon_{0}) S U^{2}} {2 \varepsilon_{0} d (\varepsilon-\varepsilon_{0})}
$$
Answer: E
Near the surface of the ceramic with $\varepsilon_{\mathrm{r}}=6.0$, the magnitude of the electric field $E$ in the air is $6.0 \times 10^{4} \mathrm{V/m}$, with the direction of $E$ making a 45° angle with the outward normal of the ceramic surface. What is the surface charge density of the polarized charge, $\sigma^{\prime}$, on the ceramic surface at that location?

Options:
A. $$
4. 2 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
B. $$
4. 9 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
C. $$
2. 0 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
D. $$
5. 8 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
E. $$
3. 0 \times1 0^{-8}~\mathrm{C} / \mathrm{m}^{2}
$$
F. $$
2. 9 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
G. $$
3. 1 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
H. $$
1. 5 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
I. $$
6. 3 \times1 0^{-7}~\mathrm{C} / \mathrm{m}^{2}
$$
J. $$
7. 2 \times1 0^{-8}~\mathrm{C} / \mathrm{m}^{2}
$$
Answer: G
A factory needs to concentrate a certain aqueous solution with an initial concentration of 0.10 to 0.35 at a rate of 850 kg/h. The solution is at its boiling point. A rising film evaporator with a heat transfer area of $10 \, \text{m}^2$ is available for use. The vacuum degree of the condenser is 80 kPa, and the boiling point elevation of the solution under operating conditions is 18°C. The heating tube length is 6 m, and the heat transfer coefficient of the evaporator can be taken as $1000 \, \text{W/m}^2 \cdot \text{°C}$. Heat loss can be neglected. Determine the pressure of the heating steam (local atmospheric pressure is 100 kPa) is ().

Options:
A. 140.00 kPa
B. 165.40 kPa
C. 110.50 kPa
D. 143.35 kPa
E. 132.20 kPa
F. 150.90 kPa
G. 152.15 kPa
H. 127.80 kPa
I. 125.65 kPa
J. 160.75 kPa
Answer: D
In a single-effect cycle evaporator, a NaCl aqueous solution with a concentration of 0.05 is concentrated to 0.20, with an operating pressure of 50 kPa. Try to determine the boiling point of the solution.

Options:
A. 88.90°C
B. 70.85°C
C. 80.00°C
D. 87.10°C
E. 82.60°C
F. 84.75°C
G. 75.30°C
H. 78.45°C
I. 85.16°C
J. 90.25°C
Answer: I
Determine the heat transfer coefficient of a casing-type toluene cooler, with the experimental data obtained as follows: the heat transfer area of the cooler is $2.8{m}^{2}$, toluene flow rate is 2000 kg/h, cooling from 80°C to 40°C. The cooling water rises from 20°C to 30°C, with the two fluids flowing countercurrently. Try to find out what the measured heat transfer coefficient is ().

Options:
A. $$
3 1 4. 7 \mathrm{W / m^{2} \cdot °C}
$$
B. $$
5 8 7. 6 \mathrm{W / m^{2} \cdot °C}
$$
C. $$
4 0 2. 1 \mathrm{W / m^{2} \cdot °C}
$$
D. $$
6 4 3. 8 \mathrm{W / m^{2} \cdot °C}
$$
E. $$
5 2 1. 9 \mathrm{W / m^{2} \cdot °C}
$$
F. $$
4 5 6. 8 \mathrm{W / m^{2} \cdot °C}
$$
G. $$
5 7 1. 5 \mathrm{W / m^{2} \cdot °C}
$$
H. $$
6 1 9. 2 \mathrm{W / m^{2} \cdot °C}
$$
I. $$
4 3 6. 3 \mathrm{W / m^{2} \cdot °C}
$$
J. $$
3 8 9. 4 \mathrm{W / m^{2} \cdot °C}
$$
Answer: I
When water is in forced turbulent flow within a circular straight pipe, if both the flow rate and physical properties remain unchanged and the pipe diameter is halved, how many times is the convective heat transfer coefficient inside the pipe compared to the original?

Options:
A. 3.212
B. 4.867
C. 3.482
D. 1.975
E. 5.634
F. 6.542
G. 2.756
H. 4.159
I. 1.423
J. 2.998
Answer: C
In a tube heat exchanger, a certain solution is heated with hot water at a flow rate of 600 kg/h. The average specific heat of the solution is known to be 3.05 kJ/(kg·°C), with inlet and outlet temperatures of 35°C and 60°C respectively. The inlet and outlet temperatures of the hot water are 90°C and 70°C, respectively. If the heat loss is 5% of the heat released by the thermal fluid, try to determine the heat load of the heat exchanger is ().

Options:
A. 12.71kW
B. 14.32kW
C. 15.28kW
D. 18.65kW
E. 16.47kW
F. 11.25kW
G. 10.93kW
H. 13.78kW
I. 11.89kW
J. 17.56kW
Answer: A
A drum vacuum filter with a diameter of 1.75 m and a length of $0.9 \, \text{m}$ has an immersion angle of 126° and a rotation speed of 1 r/min. The filtration constant under operational conditions is $K = 5.15 \times 10^{-5} \, \text{m}^2/\text{s}$, and the medium resistance can be neglected. Try to determine its production capacity is ().

Options:
A. $6. 3 2 8 \mathrm{m}^{3} / \mathrm{h}$
B. $3. 8 4 9 \mathrm{m}^{3} / \mathrm{h}$
C. $1. 6 2 3 \mathrm{m}^{3} / \mathrm{h}$
D. $4. 7 6 5 \mathrm{m}^{3} / \mathrm{h}$
E. $2. 9 1 5 \mathrm{m}^{3} / \mathrm{h}$
F. $0. 8 4 7 \mathrm{m}^{3} / \mathrm{h}$
G. $5. 9 8 1 \mathrm{m}^{3} / \mathrm{h}$
H. $8. 6 3 2 \mathrm{m}^{3} / \mathrm{h}$
I. $7. 5 4 9 \mathrm{m}^{3} / \mathrm{h}$
J. $9. 7 5 8 \mathrm{m}^{3} / \mathrm{h}$
Answer: J
In a gas with a viscosity of $2.53 \times 10^{-5} \text{Pa} \cdot \text{s}$ and a density of $0.779 \text{kg/m}^3$, there is dust with a density of $2750 \text{kg/m}^3$. A standard cyclone separator with a cylinder diameter of 500 mm is used for dust removal. If it is required to remove dust particles with a diameter larger than $6 \mu\text{m}$, what is the corresponding pressure differential for its production capacity?

Options:
A. 1150Pa
B. 965Pa
C. 1075Pa
D. 1230Pa
E. 1045Pa
F. 985Pa
G. 890Pa
H. 1020Pa
I. 1120Pa
J. 995Pa
Answer: E
The diameter of the plunger of a certain double-acting reciprocating pump is 180mm, the diameter of the plunger rod is 60mm, the radius of the crank is 145mm, and the plunger reciprocates 55 times per minute. To determine the performance of this pump, the discharged water is injected into a storage tank with a diameter of $3{m}$. During an experiment lasting 26.6 minutes, the water level in the tank rises by 2.6m. Calculate the volumetric efficiency of the pump is ().

Options:
A. $$78.32%$$
B. $$80.56%$$
C. $$67.24%$$
D. $$74.50%$$
E. $$91.20%$$
F. $$77.68%$$
G. $$88.96%$$
H. $$82.11%$$
I. $$85.39%$$
J. $$90.07%$$
Answer: G
Petroleum with a specific gravity of 0.86 and a viscosity of 3 cP flows through a seamless steel pipe with specifications $159 \times 4.5 \mathrm{mm}$. When the oil flow rate is 15.5 t/h, calculate the flow resistance loss for a straight pipe with a total length of 1000 m is ().

Options:
A. 4.901J/kg
B. 5.291J/kg
C. 5.488J/kg
D. 6.789J/kg
E. 4.322J/kg
F. 5.825J/kg
G. 9.332J/kg
H. 7.552J/kg
I. 3.678J/kg
J. 8.127J/kg
Answer: C
The rectangular Clark $\mathbf{Y}$ airfoil has a wingspan of 36 ft and a chord length of 6 ft. What is the friction correction coefficient $\eta$ when the angle of attack is $5.4°$ and the airfoil is flying at an altitude of 10,000 ft with a speed of 300 ft/s?

Options:
A. 0.829
B. 0.583
C. 0.758
D. 0.945
E. 0.991
F. 0.896
G. 0.777
H. 0.952
I. 0.812
J. 0.673
Answer: F
A beam under load is given with a known bending moment $M$, with a mean $\mu_{M} \!=\! 1 8 7 5 0 \mathrm{N \cdot m}$, and standard deviation $\sigma_{M}=2 8 1 2.5 \mathrm{N \cdot m}$; the beam's ultimate stress is $F$, with a mean $\mu_{F}=7 0 0 \mathrm{N/m}^{2}$ and standard deviation $\sigma_{F}=1 4 0 \mathrm{N/m}^{2}$; the reciprocal of the beam's section modulus is $A$, with a mean $\mu_{A}=0.024 \, \mathrm{m}^{-3}$ and standard deviation $\sigma_{A}=1.44 \times 10^{-3} \, \mathrm{m}^{-3}$. $M$, $F$, and $A$ are all independent random variables. Determine the reliability coefficient $\beta$ of this beam.

Options:
A. 0.86781
B. 0.82314
C. 0.48753
D. 0.03264
E. 0.25108
F. 0.11532
G. 0.68947
H. 0.75319
I. 0.39675
J. 0.94296
Answer: J
Given that the diameter $d$ at the inlet cross-section of a certain power plant's spiral casing is 6200mm, the static pressure head at the center of this cross-section is measured to be $60 \mathrm{m}$, the flow rate $Q$ through the turbine is 123m$^3/\mathrm{s}$, and the outlet area $A_{5}$ of the draft tube is $(5 \operatorname{m}) \times (8 \operatorname{m}) = 40 \operatorname{m}$, with a height difference of ±2m between the center of the spiral casing cross-section and the downstream water level. What is the operational head of the hydropower station's turbine?

Options:
A. 66.00m
B. 63.50m
C. 65.20m
D. 64.80m
E. 61.00m
F. 62.36m
G. 59.75m
H. 58.92m
I. 60.15m
J. 67.10m
Answer: F
Weigh 0.2002g of the aluminum-containing sample, dissolve it and adjust the pH to 9. Add 8-hydroxyquinoline ($\mathrm{HOC}_{9}\mathrm{H}_{6}\mathrm{N}$) to precipitate $\mathrm{Al}^{3+}$ as $\mathrm{Al}(\mathrm{OC}_{9}\mathrm{H}_{6}\mathrm{N})_{3}$. After filtering and washing the precipitate, dissolve it in HCl, and add 35.00 ml of 0.04000 mol/L KBr (containing an excess of KBr). After the reaction is complete, add an excess of KI to precipitate $\mathrm{I}_{2}$, which consumes 20.05 ml of 0.1000 mol/L Na2S2O3 standard solution. What is the aluminum content in the sample?

Options:
A. $$
6. 2 5 4 \%
$$
B. $$
8. 1 1 5 \%
$$
C. $$
7. 5 0 0 \%
$$
D. $$
8. 3 9 8 \%
$$
E. $$
7. 1 8 2 \%
$$
F. $$
5. 8 8 8 \%
$$
G. $$
8. 0 5 1 \%
$$
H. $$
5. 6 7 3 \%
$$
I. $$
7. 2 0 0 \%
$$
J. $$
6. 9 9 9 \%
$$
Answer: E
To prepare 1000 ml of a perchloric acid-acetic acid solution (0.05000 mol/L), you need to use 70% HClO₄ and 2 ml of glacial acetic acid with a concentration of 99.8% and a relative density of 1.05. How many milliliters of acetic anhydride with a concentration of 98% and a relative density of 1.087 should be added to completely remove the water content?

Options:
A. $18.67ml$
B. $26.05ml$
C. $25.12ml$
D. $22.88ml$
E. $21.98ml$
F. $24.36ml$
G. $23.50ml$
H. $20.55ml$
I. $19.75ml$
Answer: D
In a $0.010 mol/L$ zinc-ammonia solution, if the concentration of free ammonia is $0.10 mol/L$.What is the total side reaction coefficient of zinc ions at $pH 10$?

Options:
A. $$
1 0^{4. 2 0}
$$
B. $$
1 0^{6. 5 2}
$$
C. $$
1 0^{7. 8 8}
$$
D. $$
1 0^{5. 0 1}
$$
E. $$
1 0^{2. 3 7}
$$
F. $$
1 0^{3. 5 8}
$$
G. $$
1 0^{3. 9 1}
$$
H. $$
1 0^{4. 8 5}
$$
I. $$
1 0^{5. 4 9}
$$
J. $$
1 0^{6. 9 4}
$$
Answer: I
Calculate the equilibrium constant of the reaction where the standard solution of $\mathbf{K}_{2} \mathbf{C r}_{2} \mathbf{O}_{7}$ titrates $\mathbf{F} \mathbf{e}^{2+}$ at 25°C. Given that at the stoichiometric point $c_{F e^{3+}} = 0.05000 \, \mathrm{mol/L}$, what is the required pH of the solution to ensure the reaction proceeds quantitatively? () ($c_{\mathrm{F e^{2+}}} \leqslant 10^{-6} \, \mathrm{mol/L}$)? $(\varphi_{F e^{3+} / F e^{2+}}^{\Theta} = 0.771 \, \mathbf{V}, \varphi_{Cr_{2}O_{7}^{2-} / Cr^{3+}}^{\Theta} = 1.33 \, \mathbf{V})$

Options:
A. 1.50
B. 3.05
C. 1.82
D. 0.75
E. 4.10
F. 2.78
G. 1.25
H. 3.55
I. 0.92
J. 2.15
Answer: C
At 25°C, calculate the conditional electrode potential for the $\mathrm{H}_{3}\mathrm{AsO}_{4} / \mathrm{HAsO}_{4}$ redox couple under the conditions of pH 8.0 and $\left[ \mathrm{H^+} \right]=1.0 \mathrm{mol/L}$. (Given: $\varphi_{\mathrm{H_{3}AsO_{4}/HAsO_{2}}}^{\Theta^{\prime}} = 0.56 \mathrm{V}$; the $K_{\mathrm{a}}$ of $\mathrm{HAsO}_{2}$ is $5.1 \times 10^{-10}$; the $K_{\mathrm{a}_{1}}, K_{\mathrm{a}_{2}}, K_{\mathrm{a}_{3}}$ of $\mathrm{H}_{3}\mathrm{AsO}_{4}$ are $5.5 \times 10^{-3}, 1.7 \times 10^{-7}, 5.1 \times 10^{-12}$, respectively.)

Options:
A. $$
\begin{array} {l} {{{{}=-0. 9 0 7 \mathrm{V}}}} \\ {{{{}=0. 3 4 \mathrm{V}}}} \\ \end{array}
$$
B. $$
\begin{array} {l} {{{{}=-0. 6 2 4 \mathrm{V}}}} \\ {{{{}=0. 1 2 \mathrm{V}}}} \\ \end{array}
$$
C. $$
\begin{array} {l} {{{{}=-0. 4 4 9 \mathrm{V}}}} \\ {{{{}=0. 7 7 \mathrm{V}}}} \\ \end{array}
$$
D. $$
\begin{array} {l} {{{{}=-0. 1 1 8 \mathrm{V}}}} \\ {{{{}=0. 5 6 \mathrm{V}}}} \\ \end{array}
$$
E. $$
\begin{array} {l} {{{{}=-0. 2 9 6 \mathrm{V}}}} \\ {{{{}=0. 6 3 \mathrm{V}}}} \\ \end{array}
$$
F. $$
\begin{array} {l} {{{{}=-0. 7 4 2 \mathrm{V}}}} \\ {{{{}=0. 1 8 \mathrm{V}}}} \\ \end{array}
$$
G. $$
\begin{array} {l} {{{{}=-0. 5 3 7 \mathrm{V}}}} \\ {{{{}=0. 4 5 \mathrm{V}}}} \\ \end{array}
$$
H. $$
\begin{array} {l} {{{{}=-0. 0 8 1 \mathrm{V}}}} \\ {{{{}=0. 9 5 \mathrm{V}}}} \\ \end{array}
$$
I. $$
\begin{array} {l} {{{{}=-0. 8 2 1 \mathrm{V}}}} \\ {{{{}=0. 2 9 \mathrm{V}}}} \\ \end{array}
$$
J. $$
\begin{array} {l} {{{{}=-0. 3 5 8 \mathrm{V}}}} \\ {{{{}=0. 8 9 \mathrm{V}}}} \\ \end{array}
$$
Answer: D
Weigh $0.4102 \, \mathrm{g} \, \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \cdot 18 \mathrm{H}_{2}\mathrm{O}$ to produce an $\mathrm{Al(OH)_{3}}$ precipitate. How many milliliters of ammonia solution containing 2.4% $\mathrm{NH_{3}}$ (relative density = 0.989) are needed?

Options:
A. $6.0ml$
B. $3.5ml$
C. $7.2ml$
D. $5.0ml$
E. $2.1ml$
F. $5.6ml$
G. $4.1ml$
H. $6.7ml$
I. $4.0ml$
J. $4.9ml$
Answer: J
When determining the $\mathbf{F}^{-}$ content in drinking water using a fluoride ion-selective electrode, 20.00 ml of water is taken and 20.00 ml of total ionic strength adjustment buffer is added, resulting in a measured electromotive force of 140.0 mV; then 1.00 ml of a fluoride standard solution with a concentration of 1.00× $10^{-2} \, \mathrm{mol/L}$ is added to this solution, and the measured electromotive force is 120.0 mV. Given that the response slope of the fluoride electrode is 58.5. What is the concentration of $\mathbf{F}^{-}$ in the drinking water?

Options:
A. $$
3. 9 9 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
B. $$
2. 3 3 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
C. $$
6. 7 8 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
D. $$
7. 4 5 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
E. $$
5. 2 0 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
F. $$
4. 5 0 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
G. $$
2. 6 7 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
H. $$
9. 6 1 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
I. $$
1. 1 5 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
J. $$
8. 0 4 \times1 0^{-4} ( \mathrm{m o l / L} )
$$
Answer: A
In the GC separation of components $\mathbf{A}$ and $\mathbf{B}$, their $t_{\mathrm{R}}$ are 5.5 min and 6.2 min, respectively. The retention time for components not entering the stationary phase is 1.0 min. What is the ratio of the migration rate of the mobile phase to that of $\mathbf{B}$?

Options:
A. 6.2
B. 6.7
C. 6.9
D. 4.9
E. 5.2
F. 7.5
G. 5.1
H. 5.8
I. 6.5
J. 7.0
Answer: A
Calculate the solvent strength factor for methanol-acetonitrile-water (60:10:30) in reversed-phase chromatography. If tetrahydrofuran-methanol-water is used instead, with the water content unchanged, what should the proportion of methanol be to maintain the same elution strength?

Options:
A. 0.712
B. 0.640
C. 0.911
D. 0.427
E. 0.687
F. 0.508
G. 0.275
H. 0.564
I. 0.843
J. 0.305
Answer: E
Given a working wavelength of 8 mm, a rectangular waveguide $(a \times b = 7.112 \times 3.556 \, \mathrm{mm}^2)$ is used for $\mathrm{TE}_{10}$ mode transmission. It is now necessary to convert to $\mathrm{TE}_{01}^{0}$ mode transmission in a circular waveguide, requiring equal phase velocities in both waveguides. What is the diameter $D$ of the circular waveguide? If converting to the $\mathrm{TE}_{11}^{0}$ mode transmission in a circular waveguide, with the same requirement for equal phase velocities in both waveguides, what would be the diameter $D$ of the circular waveguide?

Options:
A. $$
1 9. 4 0 ( \mathrm{m m} ),8.21mm
$$
B. $$
1 8. 1 1 ( \mathrm{m m} ),8.41mm
$$
C. $$
1 7. 8 3 ( \mathrm{m m} ),8.45mm
$$
D. $$
1 8. 4 2 ( \mathrm{m m} ),8.29mm
$$
E. $$
1 7. 2 9 ( \mathrm{m m} ),8.28mm
$$
F. $$
1 9. 0 7 ( \mathrm{m m} ),8.22mm
$$
G. $$
1 5. 9 6 ( \mathrm{m m} ),8.30mm
$$
H. $$
1 7. 3 5 ( \mathrm{m m} ),8.34mm
$$
I. $$
1 6. 8 5 ( \mathrm{m m} ),8.33mm
$$
J. $$
1 6. 5 9 ( \mathrm{m m} ),8.37mm
$$
Answer: H
Air flows from the gas tank through the nozzle into the atmosphere with a back pressure of $\phi_{\mathrm{b}} = 0.981 \times 10^{5} \mathrm{Pa}$. The pressure of the gas in the tank is $\boldsymbol{p}_{0} = 7 \times 10^{5} \mathrm{Pa}$, and the temperature is $T_{0} = 313 \mathrm{K}$. Given that the diameter of the throat of the nozzle is $d^{*} = 25 \mathrm{mm}$, what is the diameter $d_{2}$ at the exit cross-section of the nozzle?

Options:
A. $$
3 3. 5 4 \mathrm{m m}
$$
B. $$
4 0. 2 5 \mathrm{m m}
$$
C. $$
3 1. 6 9 \mathrm{m m}
$$
D. $$
3 5. 0 1 \mathrm{m m}
$$
E. $$
3 7. 7 2 \mathrm{m m}
$$
F. $$
2 9. 4 0 \mathrm{m m}
$$
G. $$
1 4. 5 7 \mathrm{m m}
$$
H. $$
1 8. 6 4 \mathrm{m m}
$$
I. $$
2 1. 8 3 \mathrm{m m}
$$
J. $$
2 6. 3 8 \mathrm{m m}
$$
Answer: C
During a tensile test, necking begins to appear when the tensile strength is reached, that is, when the slope of the engineering stress-strain curve becomes zero. Calculate the work done per unit volume when the specimen is stretched until necking occurs.

Options:
A. $$
{\frac{K n^{n}} {n+2}} ( \mathrm{J / m^{2}} )
$$
B. $$
{\frac{K n^{n+3}} {n+1}} ( \mathrm{J / m^{2}} )
$$
C. $$
{\frac{K n^{n+2}} {n+2}} ( \mathrm{J / m^{2}} )
$$
D. $$
{\frac{K n^{n+1}} {n}} ( \mathrm{J / m^{2}} )
$$
E. $$
{\frac{K n^{n+1}} {n+2}} ( \mathrm{J / m^{3}} )
$$
F. $$
{\frac{K n^{n}} {n+1}} ( \mathrm{J / m^{3}} )
$$
G. $$
{\frac{K n^{n+3}} {n+2}} ( \mathrm{J / m^{2}} )
$$
H. $$
{\frac{K n^{n}} {n}} ( \mathrm{J / m^{2}} )
$$
I. $$
{\frac{K n^{n+1}} {n+1}} ( \mathrm{J / m^{2}} )
$$
J. $$
{\frac{K n^{n+2}} {n+1}} ( \mathrm{J / m^{3}} )
$$
Answer: I
The radiation resistance of a certain antenna is 150Ω, fed with an effective current of 5A. Assuming that the power gain of the antenna in a given direction is 6dB compared to an isotropic radiator. Given that the effective aperture of the receiving antenna is 1.5 $m^{2}$, and assuming the antenna is matched with its receiver, what is the received power?

Options:
A. 0.3344μW
B. 2.3456μW
C. 4.5678μW
D. 1.7890μW
E. 0.8910μW
F. 1.2345μW
G. 3.4567μW
H. 0.4974μW
I. 0.1122μW
J. 0.6789μW
Answer: H
Given that a body is subjected to uniform stresses on mutually perpendicular sections, with $\sigma_{1}=50 kg/cm^{2}$ and $\sigma_{2}= -50 kg/cm^{2}$, find the stress on the section where the normal forms a 45° angle with $\sigma_{1}$.

Options:
A. $25kg/cm^{2}$
B. $-50kg/cm^{2}$
C. $-100kg/cm^{2}$
D. $100kg/cm^{2}$
E. $50kg/cm^{2}$
F. $35kg/cm^{2}$
G. $-75kg/cm^{2}$
H. $0kg/cm^{2}$
I. $-25kg/cm^{2}$
J. $75kg/cm^{2}$
Answer: E
A centrally compressed brick column has cross-sectional dimensions of $370 \mathrm{mm} \times 490 \mathrm{mm}$. It is constructed using MU10 grade clay bricks and $\mathbf{M} 2.5$ mixed mortar. The design value of axial pressure applied at the base section of the column (including self-weight) is 165.88 kN, and the calculated height of the column is $H_{0} = 3.60 \mathrm{m}$. Which of the following values is the closest to the load-bearing capacity of the brick column?

Options:
A. $$210.60kN$$
B. $$152.20kN$$
C. $$181.80kN$$
D. $$172.50kN$$
E. $$199.90kN$$
F. $$230.10kN$$
G. $$190.40kN$$
H. $$118.80kN$$
I. $$163.30kN$$
J. $$145.75kN$$
Answer: C
Steel Structure Heavy-Duty Work Platform, designed service life of 100 years. The platform's column grid is $5 \mathrm{m} \times 8 \mathrm{m}$, meaning the main beam spacing is $5 \mathrm{m}$ and the span is $8 \mathrm{m}$, with beams hinged to columns. The standard value for the dead load of the platform's dense ribbed decking and structure itself is $5 \mathrm{kN}/\mathrm{m}^{2}$, and the standard value for the load of stacked maintenance materials is $30 \mathrm{kN}/\mathrm{m}^{2}$. What should be the design value of the mid-span bending moment of the main beam?

Options:
A. 1650kN·m
B. 1530kN·m
C. 1325kN·m
D. 1566kN·m
E. 2013kN·m
F. 1234kN·m
G. 1425kN·m
H. 1789kN·m
I. 1760kN·m
J. 1901kN·m
Answer: D
When designing highway bridges and culverts, the vehicle load used consists of lane load and vehicle load, each used to calculate different bridge components. The following bridge component calculations are now required: ① overall calculation of the main beam; ② main beam deck slab calculation; ③ culvert calculation; ④ abutment calculation. Try to determine which of the following vehicle load models should be used for these four component calculations to meet the requirements of the "General Specifications for Design of Highway Bridges and Culverts"?

Options:
A. ① Use vehicle load, ②, ③, ④ use lane load
B. ①, ②, ③ Use vehicle load, ④ use lane load
C. ① Use lane load, ②, ③, ④ use lane load
D. ①, ② Use lane load, ③, ④ use vehicle load
E. ① Use lane load, ②, ③, ④ use vehicle load
F. ①, ③ Use lane load, ②, ④ use vehicle load
G. ①, ②, ③ Use lane load, ④ use vehicle load
H. ①, ② Use vehicle load, ③, ④ use lane load
Answer: E
On a certain first-class highway, there is a simply supported prestressed concrete beam bridge with a calculated span of 20 meters. The concrete strength grade is C40. The simply supported beam is composed of T-shaped section beams, with a main beam height of 1.25 meters, a beam spacing of 2.25 meters, and a crossbeam spacing of 5.0 meters. The effective height of the main beam section is $h_{0}=1.15 \mathrm{m}$. When calculating according to the ultimate limit state of load-bearing capacity in the permanent condition, the designed shear force at the section of the interior beam support is 800 kN. If the section at the support point of the main beam satisfies the shear section requirements, which of the following numbers is closest to the minimum width of the web (in mm)?

Options:
A. 340
B. 300
C. 320
D. 280
E. 240
F. 180
G. 200
H. 220
I. 360
J. 260
Answer: H
A water film at 293K flows down a 0.6-meter-long vertical wall, absorbing CO gas from the gas phase. The known water film flow rate per unit width is $0.02 \mathbf{kg} / (\mathbf{m} \cdot \mathbf{s})$; the gas phase is pure CO with a pressure of 101.3 kPa and a temperature of 273K. The incoming water contains no CO. Calculate the total absorption rate per unit film width.
Known data: At 293K and 101.3 kPa, the solubility of CO in water is $c_{\mathrm{A i}}=0.00104 \mathrm{kmol} / m^{3}$, the diffusion coefficient of CO in water is $D=2.19 \times 10^{-10}$ m²/s, the density of water $\rho=998.2 \mathbf{kg} / \mathbf{m}^{3}$, and the viscosity $\mu=1.005 \times 10^{-3} \mathrm{~Pa \cdot s}$.

Options:
A. $$
6. 8 \times 1 0^{-9} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
B. $$
5. 3 \times 1 0^{-10} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
C. $$
2. 4 \times1 0^{-9} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
D. $$
9. 0 \times 1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
E. $$
8. 6 \times 1 0^{-9} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
F. $$
3. 6 \times 1 0^{-9} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
G. $$
4. 9 \times 1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
H. $$
7. 1 \times 1 0^{-8} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
I. $$
3. 7 \times 1 0^{-7} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
J. $$
1. 5 \times 1 0^{-8} \, \mathrm{k m o l} / ( \mathrm{m \cdot s} )
$$
Answer: C
Absorb sulfur dioxide from a mixed gas using an aqueous sulfur dioxide solution with a composition of $X_{2}=0.00113$. The flow rate of the absorbent $(H_{2}O)$ is 2100 kmol/h, and the flow rate of the mixed gas is 100 kmol/h, with a mole fraction of sulfur dioxide of 0.1. The required absorption rate of sulfur dioxide is 85%. Calculate the number of overall gas phase transfer units $N_\mathrm{OG}$.(under operating conditions, the equilibrium relationship is $Y_{\mathrm{e}}$=17.80X-0.008).

Options:
A. 8.452
B. 7.497
C. 9.367
D. 7.869
E. 6.821
F. 7.215
G. 5.324
H. 4.986
I. 6.134
J. 8.801
Answer: B
Separating a benzene-toluene mixture in a continuous distillation column. The feed flow rate is 12,000 kg/h, with a benzene mass fraction of 0.46. It is required that the benzene recovery rate in the distillate be 97.0% and the toluene recovery rate in the bottoms not be less than 98%. Determine the flow rate and composition of the distillate and bottoms, expressed in terms of molar flow rate and mole fraction.

Options:
A. 73.50kmol/h,0.08
B. 72.10kmol/h,0.02
C. 74.30kmol/h,0.01
D. 71.24kmol/h,0.06
E. 76.00kmol/h,0.00
F. 70.00kmol/h,0.05
G. 71.19kmol/h,0.03
H. 68.90kmol/h,0.09
I. 75.50kmol/h,0.04
J. 69.30kmol/h,0.07
Answer: G
Using a distillation column with two theoretical plates to extract volatile components from an aqueous solution, the processing capacity is $50 \mathrm{kmol} / \mathrm{h}$, with a composition of 0.2 (mole fraction of the volatile component). The thermal condition parameter of the feed $q=1.15$. The bottom of the column is directly heated with steam, with a steam input rate of $30 \mathrm{kmol} / \mathrm{h}$. There is no reflux at the top of the column. Within this composition range, the equilibrium relationship can be approximately expressed as $y=3x$. Determine the composition of the distillate and the recovery rate of the volatile component.

Options:
A. $x_D=0.3507. φ_A=74.2$%
B. $x_D=0.2983. φ_A=69.4$%
C. $x_D=0.2650. φ_A=78.7$%
D. $x_D=0.3769. φ_A=65.1$%
E. $x_D=0.4256. φ_A=62.3$%
F. $x_D=0.4100. φ_A=59.7$%
G. $x_D=0.2888. φ_A=80.5$%
H. $x_D=0.2314. φ_A=82.0$%
I. $x_D=0.4152. φ_A=58.6$%
J. $x_D=0.3195. φ_A=71.9$%
Answer: J
The dry bulb temperature is 20°C and the humidity of the moist air is $0.009 \mathbf{kg} / \mathbf{kg}$ (on an absolutely dry basis). This moist air is heated to 50°C through a preheater and then sent to an atmospheric dryer. When leaving the dryer, the relative humidity of the air is 80%. If the air undergoes an isothermal drying process in the dryer, calculate the amount of moisture obtained for 1m³ of the original moist air in the dryer.

Options:
A. $$
0. 0 1 2 0 \mathbf{k g} / \mathbf{m}^{3}
$$
B. $$
0. 0 1 1 5 \mathbf{k g} / \mathbf{m}^{3}
$$
C. $$
0. 0 1 0 7 \mathbf{k g} / \mathbf{m}^{3}
$$
D. $$
0. 0 1 3 5 \mathbf{k g} / \mathbf{m}^{3}
$$
E. $$
0. 0 0 7 3 \mathbf{k g} / \mathbf{m}^{3}
$$
F. $$
0. 0 9 2 0 \mathbf{k g} / \mathbf{m}^{3}
$$
G. $$
0. 0 0 9 8 \mathbf{k g} / \mathbf{m}^{3}
$$
H. $$
0. 0 8 4 0 \mathbf{k g} / \mathbf{m}^{3}
$$
I. $$
0. 0 0 8 9 \mathbf{k g} / \mathbf{m}^{3}
$$
J. $$
0. 0 7 1 0 \mathbf{k g} / \mathbf{m}^{3}
$$
Answer: C
Attempt to calculate the diffusion coefficient of ethanol (A) in dilute aqueous solution at 283K using the Wilke formula.

Options:
A. $$
1. 5 0 \times1 0^{-1 2}\ \mathrm{m}^{2} / \mathrm{s}
$$
B. $$
1. 2 5 \times1 0^{-9}\ \mathrm{m}^{2} / \mathrm{s}
$$
C. $$
2. 6 7 \times1 0^{-1 1} \ \mathrm{m}^{2} / \mathrm{s}
$$
D. $$
4. 3 9 \times1 0^{-9}\ \mathrm{m}^{2} / \mathrm{s}
$$
E. $$
9. 3 0 \times1 0^{-9}\ \mathrm{m}^{2} / \mathrm{s}
$$
F. $$
6. 5 8 \times1 0^{-9}\ \mathrm{m}^{2} / \mathrm{s}
$$
G. $$
5. 4 4 \times1 0^{-1 1} \ \mathrm{m}^{2} / \mathrm{s}
$$
H. $$
7. 9 6 \times1 0^{-1 1} \ \mathrm{m}^{2} / \mathrm{s}
$$
I. $$
9. 4 7 \times1 0^{-1 0} \ \mathrm{m}^{2} / \mathrm{s}
$$
J. $$
8. 1 3 \times1 0^{-1 0} \ \mathrm{m}^{2} / \mathrm{s}
$$
Answer: I