MikaStars39/nano-eval huggingface dataset:
The car is traveling on a level road at a speed of 72 km/h, and the raindrops falling vertically leave traces on the car's side windows at an angle of $40^{\circ}$ to the vertical line. What is the absolute speed of the raindrops falling? ( Ignore the friction between the raindrops and the glass. )

Options:
A. $$2 3. 8 \ \mathrm{m / s}.$$
B. $$1 9. 5 \ \mathrm{m / s}.$$
C. $$2 8. 4 \ \mathrm{m / s}.$$
D. $$2 2. 1 \ \mathrm{m / s}.$$
E. $$2 4. 6 \ \mathrm{m / s}.$$
F. $$2 5. 7 \ \mathrm{m / s}.$$
G. $$2 6. 3 \ \mathrm{m / s}.$$
H. $$2 7. 2 \ \mathrm{m / s}.$$
I. $$2 1. 3 \ \mathrm{m / s}.$$
J. $$2 0. 9 \ \mathrm{m / s}.$$
Answer: A
A beam of engineering length $l=4$ m is placed on two identical spring supports, each with a stiffness coefficient of $c=1.5$ kN/cm. A weight of $Q=2$ kN is positioned at the midpoint of the beam. The moment of inertia of the I-beam's cross-section is $J = 180 \, \mathrm{~cm^4}$. Disregarding the weight of the beam, what is the period of free vibration of the system ? ( The elastic modulus of the beam material is $E=2 \times 10^4 \, \mathrm{~kN/cm^2}$. )

Options:
A. $$0. 2 2 6s$$
B. $$0. 3 4 2s$$
C. $$0. 2 7 9s$$
D. $$0. 2 6 5s$$
E. $$0. 3 1 1s$$
F. $$0. 2 8 9s$$
G. $$0. 2 1 7s$$
H. $$0. 2 5 0s$$
I. $$0. 2 3 8s$$
J. $$0. 2 4 5s$$
Answer: I
In an incompressible, initially stationary fluid with an unbounded domain, a sphere moves according to $R_b=a\sin\omega t$, where $\alpha$ and $\omega$ are constants. It is known that the pressure at infinity is $P_{∞}$, and body forces are neglected.The acceleration distribution in the flow field as well as the fluid acceleration and pressure distribution on the surface of the object is ().

Options:
A. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\mathrm{sin}^{2}\omega t+\frac{3}{2}\mathrm{cos}^{2}\omega t\biggr)$$
B. $$p\mid_{R\to R_{b}}=p_{∞}-a^{2}\omega^{2}\rho\biggl(\mathrm{sin}^{2}\omega t+\frac{3}{2}\mathrm{cos}^{2}\omega t\biggr)$$
C. $$p\mid_{R\to R_{b}}=p_{∞}-a^{2}\omega^{2}\rho\biggl(\mathrm{cos}^{2}\omega t-\frac{3}{2}\mathrm{sin}^{2}\omega t\biggr)$$
D. $$p\mid_{R\to R_{b}}=p_{∞}-a^{2}\omega^{2}\rho\biggl(\frac{3}{2}\mathrm{cos}^{2}\omega t+\mathrm{sin}^{2}\omega t\biggr)$$
E. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\frac{1}{2}\mathrm{sin}^{2}\omega t-\mathrm{cos}^{2}\omega t\biggr)$$
F. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\frac{3}{2}\mathrm{cos}^{2}\omega t+\mathrm{sin}^{2}\omega t\biggr)$$
G. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\frac{3}{2}\mathrm{sin}^{2}\omega t+\mathrm{cos}^{2}\omega t\biggr)$$
H. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\mathrm{cos}^{2}\omega t-\frac{3}{2}\mathrm{sin}^{2}\omega t\biggr)$$
I. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\frac{3}{2}\mathrm{cos}^{2}\omega t-\mathrm{sin}^{2}\omega t\biggr)$$
J. $$p\mid_{R\to R_{b}}=p_{∞}+a^{2}\omega^{2}\rho\biggl(\frac{3}{2}\mathrm{sin}^{2}\omega t-\mathrm{cos}^{2}\omega t\biggr)$$
Answer: I
The cylindrical chimney has a height of $l=20\mathbf{m}$ and a diameter of $d=0.6 \mathrm{m}$, with a horizontal wind speed of $V_{\mathrm{\infty}}=18\mathrm{m/s}$. The air has a density $\rho=1.293$ and a kinematic viscosity $\nu=13 \mathrm{mm/s}$. The horizontal thrust $T$ acting on the chimney is ().

Options:
A. 782N
B. 795N
C. 820N
D. 807N
E. 790N
F. 812N
G. 799N
H. 815N
I. 775N
J. 804N
Answer: J
1 kilogram of hydrogen gas, at a temperature of $-40{°C}$, is enclosed in a 0.1 cubic meter container. What is the pressure in $\mathrm{K N / m^{2}}$?

Options:
A. 10200
B. 10560
C. 11350
D. 8900
E. 8500
F. 9700
G. 9400
H. 9250
I. 9600
J. 9100
Answer: I
Three small balls, each with a mass of $m=2.0 \times 10^{-4} \ \mathrm{kg}$, are suspended from the same point by three insulating strings, each with a length of $l=1.0$ m. After the balls are charged with the same amount of charge, they separate so that the angle between each pair of strings is $60^\circ$. What is the charge on each small ball?

Options:
A. $$
3. 2 5 \times1 0^{-7} \mathrm{C}
$$
B. $$
2. 9 8 \times1 0^{-7} \mathrm{C}
$$
C. $$
2. 9 9 \times1 0^{-7} \mathrm{C}
$$
D. $$
4. 0 5 \times1 0^{-7} \mathrm{C}
$$
E. $$
3. 7 8 \times1 0^{-7} \mathrm{C}
$$
F. $$
3. 4 2 \times1 0^{-7} \mathrm{C}
$$
G. $$
3. 0 2 \times1 0^{-7} \mathrm{C}
$$
H. $$
3. 5 0 \times1 0^{-7} \mathrm{C}
$$
I. $$
3. 1 1 \times1 0^{-7} \mathrm{C}
$$
J. $$
4. 0 9 \times1 0^{-7} \mathrm{C}
$$
Answer: G
A large metal sphere with a radius of $R=1~\mathrm{m}$ is charged to an electric potential of $U$. Then, $n=10$ small, initially uncharged metal spheres with a radius of $r=\frac{1}{9}~\mathrm{m}$ are sequentially brought into contact with the large sphere and then removed. These 10 charged small spheres are then placed apart from each other along the circumference of a circle with a radius of $R_{0}=10~\mathrm{m}$, with the large metal sphere removed. What is the electric potential at the center of the circle? (Assuming there is no leakage of the total charge in the system throughout this process)

Options:
A. $$
0. 1 0 4 U
$$
B. $$
0. 0 8 3 U
$$
C. $$
0. 0 4 9 U
$$
D. $$
0. 0 5 6 U
$$
E. $$
0. 0 7 2 U
$$
F. $$
0. 1 1 0 U
$$
G. $$
0. 0 6 5 U
$$
H. $$
0. 0 6 1 U
$$
I. $$
0. 0 9 9 U
$$
J. $$
0. 0 5 8 U
$$
Answer: G
In an $RL$ series circuit, apply a mains voltage of $U=220 \mathrm{V}, \nu=50 \mathrm{Hz}$, with known values of $R=6.0 \Omega$ and inductive reactance $X_{L}=8.0 \Omega$. To increase the power factor to 0.95, what capacitance should be added in series to this circuit?

Options:
A. $$
6. 0 \times1 0^{2}~\mu\mathrm{F}
$$
B. $$
2. 0 \times1 0^{2}~\mu\mathrm{F}
$$
C. $$
0. 9 \times1 0^{2}~\mu\mathrm{F}
$$
D. $$
9. 6 \times1 0^{2}~\mu\mathrm{F}
$$
E. $$
4. 1 \times1 0^{2}~\mu\mathrm{F}
$$
F. $$
3. 2 \times1 0^{2}~\mu\mathrm{F}
$$
G. $$
7. 4 \times1 0^{2}~\mu\mathrm{F}
$$
H. $$
5. 0 \times1 0^{2}~\mu\mathrm{F}
$$
I. $$
2. 5 \times1 0^{2}~\mu\mathrm{F}
$$
J. $$
1. 8 \times1 0^{2}~\mu\mathrm{F}
$$
Answer: F
An infinitely long straight cylindrical surface with a radius of $a$ is uniformly charged, with a charge density of $\sigma$ per unit area. When this cylindrical surface rotates around its geometric axis with a constant angular velocity of $\omega$, what is the magnetic field energy per unit length inside the cylinder?

Options:
A. $$
\pi \sigma^{2} \omega a^{3}
$$
B. $$
\frac{1} {4} \pi\mu_{0} \sigma^{2} \omega^{2} a^{2}
$$
C. $$
\frac{1} {3} \pi\mu_{0} \sigma^{2} \omega a^{4}
$$
D. $$
\frac{1} {2} \pi\mu_{0} \sigma \omega a^{4}
$$
E. $$
\frac{1} {2} \mu_{0} \sigma \omega a^{3}
$$
F. $$
\mu_{0} \sigma^{2} \omega^{2} a^{5}
$$
G. $$
\frac{1} {2} \pi\mu_{0} \sigma^{2} \omega^{2} a^{4}
$$
H. $$
\pi\mu_{0} \sigma \omega^{2} a^{4}
$$
I. $$
\pi\mu_{0} \sigma^{2} \omega a^{2}
$$
J. $$
\frac{1} {2} \pi \sigma^{2} \omega^{2} a^{3}
$$
Answer: G
A cylindrical magnet made from type 5 alnico, with a diameter of 10 mm and a length of 100 mm, has a magnetization intensity of 1.2 Wb/m² after uniform magnetization. Given that the coercivity of the magnet is $H_C = 4.4 \times 10^4 \, \text{A/m}$, what is the ratio of the magnitude of the external magnetic field $H$ to $H_C$?

Options:
A. $$
4. 1 \%
$$
B. $$
7. 9 \%
$$
C. $$
5. 3 \%
$$
D. $$
9. 4 \%
$$
E. $$
8. 8 \%
$$
F. $$
3. 5 \%
$$
G. $$
1. 8 \%
$$
H. $$
0. 6 \%
$$
I. $$
6. 7 \%
$$
J. $$
2. 2 \%
$$
Answer: G
A very long conducting straight circular tube has a wall thickness of 5.0 mm and an outer diameter of 50.0 mm, carrying a current of 50 A. The current flows along the axis of the tube and is uniformly distributed across the cross-section of the tube. What is the magnitude of the magnetic field strength $H$ at the midpoint between the inner and outer walls?

Options:
A. $$
3. 9 \times1 0^{4} \mathrm{~A / m}
$$
B. $$
2. 3 \times1 0^{3} \mathrm{~A / m}
$$
C. $$
1. 7 \times1 0^{2} \mathrm{~A / m}
$$
D. $$
7. 1 \times1 0^{3} \mathrm{~A / m}
$$
E. $$
5. 2 \times1 0^{2} \mathrm{~A / m}
$$
F. $$
9. 0 \times1 0^{1} \mathrm{~A / m}
$$
G. $$
4. 8 \times1 0^{1} \mathrm{~A / m}
$$
H. $$
8. 5 \times1 0^{2} \mathrm{~A / m}
$$
I. $$
2. 0 \times1 0^{2} \mathrm{~A / m}
$$
J. $$
6. 4 \times1 0^{2} \mathrm{~A / m}
$$
Answer: C
What is the energy of the electric field of a charge distributed uniformly with charge density $Q$ within a spherical shell, with inner and outer radii $a$ and $b$ respectively?

Options:
A. $$
\frac{2 ( 3 a^{3}+5 a^{2} b+b a^{2}+3 b^{3} ) Q^{2}} {6 0 \pi\varepsilon_{0} ( a^{2}+b a+2 b^{2} )^{2}}
$$
B. $$
\frac{7 ( 2 a^{3}+6 a^{2} b+3 a b^{2}+b^{3} ) Q^{2}} {8 0 \pi\varepsilon_{0} ( a^{2}+a b+3 b^{2} )^{2}}
$$
C. $$
\frac{3 ( 3 a^{3}+5 a^{2} b+4 a b^{2}+3 b^{3} ) Q^{2}} {9 0 \pi\varepsilon_{0} ( a^{2}+a b+2 b^{2} )^{2}}
$$
D. $$
\frac{3 ( 3 a^{3}+6 a^{2} b+4 a b^{2}+2 b^{3} ) Q^{2}} {4 0 \pi\varepsilon_{0} ( a^{2}+a b+b^{2} )^{2}}
$$
E. $$
\frac{4 ( 2 a^{3}+5 a^{2} b+3 a b^{2}+b^{3} ) Q^{2}} {5 0 \pi\varepsilon_{0} ( a^{2}+2 a b+b^{2} )^{2}}
$$
F. $$
\frac{5 ( 2 a^{3}+3 a^{2} b+4 a b^{2}+2 b^{3} ) Q^{2}} {7 0 \pi\varepsilon_{0} ( a^{2}+2 b a+b^{2} )^{2}}
$$
G. $$
\frac{3 ( 5 a^{3}+4 a^{2} b+2 a b^{2}+b^{3} ) Q^{2}} {6 0 \pi\varepsilon_{0} ( a^{2}+b a+b^{2} )^{2}}
$$
H. $$
\frac{2 ( 4 a^{3}+7 a^{2} b+5 a b^{2}+b^{3} ) Q^{2}} {3 0 \pi\varepsilon_{0} ( a^{2}+3 a b+b^{2} )^{2}}
$$
I. $$
\frac{6 ( a^{3}+4 a^{2} b+3 a b^{2}+b^{3} ) Q^{2}} {4 0 \pi\varepsilon_{0} ( a^{2}+3 a b+b^{2} )^{2}}
$$
J. $$
\frac{8 ( 4 a^{3}+3 a^{2} b+2 a b^{2}+b^{3} ) Q^{2}} {5 0 \pi\varepsilon_{0} ( a^{2}+a b+b^{2} )^{2}}
$$
Answer: D
Using a vacuum cooling crystallizer to produce sodium nitrate (NaNO$_3$) crystal products. It is known that the raw material solution is a 57.6% sodium nitrate aqueous solution at 363K (mass fraction of solute, the same below), with a processing capacity of 5000 kg/h, and the mother liquor content is 51% at a temperature of 313K. If the amount of water evaporation during the crystallization process is set to 3% of the total water content, try to determine the product amount of this crystallizer is ().

Options:
A. 695.7kg/h
B. 812.4kg/h
C. 763.2kg/h
D. 689.4kg/h
E. 733.9kg/h
F. 655.0kg/h
G. 702.3kg/h
H. 780.1kg/h
I. 744.5kg/h
J. 720.8kg/h
Answer: I
In a single-effect standard evaporator, an aqueous solution of CaCl$_2$ is evaporated. The liquid layer height in the evaporator is 1 meter, with a concentration of 0.408 and a density of 1340 kg/m³. The operating pressure in the separation chamber is 101.3 kPa. Determine the boiling point of the solution inside the apparatus.

Options:
A. 118.22°C
B. 140.33°C
C. 126.44°C
D. 136.50°C
E. 129.65°C
F. 110.92°C
G. 132.11°C
H. 124.36°C
I. 115.87°C
J. 121.78°C
Answer: A
In a parallel flow heat exchanger, oil is cooled with water. The heat exchange tubes are 1.5 meters long. The inlet and outlet temperatures of the water are 15°C and 40°C, respectively; the inlet and outlet temperatures of the oil are 120°C and 90°C. If the flow rates and inlet temperatures of the oil and water remain unchanged, how many meters should the heat exchange tubes be extended to lower the oil's outlet temperature to 70°C? (Assuming no heat loss and no impact of temperature changes on material properties)

Options:
A. 2.33m
B. 3.92m
C. 4.15m
D. 2.79m
E. 3.25m
F. 3.47m
G. 1.89m
H. 2.56m
I. 3.61m
J. 2.05m
Answer: D
Atmospheric air flows through the shell side of a shell and tube heat exchanger equipped with standard segmental baffles. The tubes have a diameter of $\varPhi 25 \times 2mm$, are arranged in a square pattern, with a tube pitch of 51mm, a baffle spacing of 1.45m, and a shell diameter of 2.8m. The air flow rate is $4 \times 10^{4} \, \text{m}^{3} / \text{h}$, with an average temperature of 140°C. Determine the convective heat transfer coefficient of the air is ().

Options:
A. $24.6 1 \mathrm{W / m^{2} \! \cdot\! °C}$
B. $16.5 1 \mathrm{W / m^{2} \! \cdot\! °C}$
C. $30.4 1 \mathrm{W / m^{2} \! \cdot\! °C}$
D. $21.0 1 \mathrm{W / m^{2} \! \cdot\! °C}$
E. $22.3 1 \mathrm{W / m^{2} \! \cdot\! °C}$
F. $18.9 1 \mathrm{W / m^{2} \! \cdot\! °C}$
G. $28.2 1 \mathrm{W / m^{2} \! \cdot\! °C}$
H. $27.1 1 \mathrm{W / m^{2} \! \cdot\! °C}$
I. $19.3 1 \mathrm{W / m^{2} \! \cdot\! °C}$
J. $25.7 1 \mathrm{W / m^{2} \! \cdot\! °C}$
Answer: E
Use a shell-and-tube heat exchanger with one shell pass and four tube passes to heat a certain solution from 30°C to 50°C, while the heating medium cools from 120°C to 45°C. Try to calculate the mean temperature difference of the heat exchanger is ().

Options:
A. 25.672°C
B. 35.123°C
C. 33.210°C
D. 29.601°C
E. 22.980°C
F. 27.834°C
G. 30.345°C
H. 32.789°C
I. 31.456°C
J. 28.910°C
Answer: G
What is the amount of heat transferred when 1500 kg/h of nitrobenzene is cooled from 80°C to 20°C?

Options:
A. 42.5 $kW$
B. 41.7 $kW$
C. 44.9 $kW$
D. 47.3 $kW$
E. 46.5 $kW$
F. 43.2 $kW$
G. 39.4 $kW$
H. 45.1 $kW$
I. 38.9 $kW$
J. 40.2 $kW$
Answer: A
Using a small plate and frame filter press with a filtration area of $0.093 \, \text{m}^2$, a constant pressure filtration is performed on a water suspension containing calcium carbonate particles. When the filtration reaches 50 seconds, a total of $2.27 \times 10^{-3} \, \text{m}^3$ of filtrate is obtained; when the filtration reaches 100 seconds, a total of $3.35 \times 10^{-3} \, \text{m}^3$ of filtrate is obtained. How much filtrate can be obtained when the filtration time is 200 seconds?

Options:
A. $5. 8 4 \times1 0^{-3} {m}^{3}$
B. $4. 5 6 \times1 0^{-3} {m}^{3}$
C. $7. 2 9 \times1 0^{-3} {m}^{3}$
D. $9. 7 8 \times1 0^{-3} {m}^{3}$
E. $8. 3 4 \times1 0^{-3} {m}^{3}$
F. $1. 0 1 \times1 0^{-2} {m}^{3}$
G. $6. 5 5 \times1 0^{-3} {m}^{3}$
H. $3. 3 8 \times1 0^{-3} {m}^{3}$
I. $7. 9 0 \times1 0^{-3} {m}^{3}$
J. $1. 1 5 \times1 0^{-2} {m}^{3}$
Answer: D
Introduce flue gas at a temperature of 200°C and a flow rate of 1.6 $m^3/s$ into a settling chamber for separation with dimensions of 10 (length) $\times$ 2 (width) $\times$ 2 (height) $({m}^{3})$. Given a dust density of 4880 $kg/{m}^{3}$, find the minimum particle size of dust that can be completely separated is ().

Options:
A. $10 5. 5 9 \mu\mathrm{m}$
B. $5 0. 7 8 \mu\mathrm{m}$
C. $6 1. 2 1 \mu\mathrm{m}$
D. $9 6. 7 3 \mu\mathrm{m}$
E. $11 3. 3 4 \mu\mathrm{m}$
F. $8 4. 9 0 \mu\mathrm{m}$
G. $2 7. 9 7 \mu\mathrm{m}$
H. $3 5. 3 4 \mu\mathrm{m}$
I. $7 2. 8 4 \mu\mathrm{m}$
J. $4 1. 5 9 \mu\mathrm{m}$
Answer: G
A solution with a density of $1600 \mathrm{kg/m^{3}}$ and a viscosity of 2 cP flows through a steel pipe with $\phi80 \times 2.5 \mathrm{mm}$. To measure the flow rate, a standard orifice plate flow meter is installed in the pipeline. A U-tube mercury differential manometer, using flange taps, measures the pressure difference across the orifice plate. If the minimum flow rate of the solution is 300 L/min, determine the specifications of the orifice plate is ().

Options:
A. $$48.7mm$$
B. $$37.5mm$$
C. $$50.3mm$$
D. $$45.0mm$$
E. $$33.1mm$$
F. $$40.2mm$$
G. $$29.6mm$$
H. $$25.8mm$$
I. $$60.5mm$$
J. $$22.9mm$$
Answer: B
A smooth flat plate with a width of 6 inches (150 mm) and a length of 18 inches (500 mm) is placed in a stream of crude oil with a steady flow rate of 2 feet per second (fps) and a temperature of 60°F $(s=0.925)$. Calculate the frictional resistance on one side of the plate.

Options:
A. $$
0. 0 7 2 1 \mathrm{lb f}
$$
B. $$
0. 1 2 0 9 \mathrm{lb f}
$$
C. $$
0. 0 3 8 2 \mathrm{lb f}
$$
D. $$
0. 1 5 4 3 \mathrm{lb f}
$$
E. $$
0. 0 8 0 5 \mathrm{lb f}
$$
F. $$
0. 0 9 7 6 \mathrm{lb f}
$$
G. $$
0. 0 6 6 8 \mathrm{lb f}
$$
H. $$
0. 0 4 3 2 \mathrm{lb f}
$$
I. $$
0. 0 5 9 4 \mathrm{lb f}
$$
J. $$
0. 1 8 7 0 \mathrm{lb f}
$$
Answer: G
A certain rotating shaft is subjected to regularly asymmetric cyclic stress: $\sigma_{1}=400 \mathrm{MPa}$, with a number of cycles $n_{1}=10^{4}$; $\sigma_{2}=500 \mathrm{MPa}$, with a number of cycles $n_{2}=10^{5}$. The material is tempered 45 steel with $\sigma_{-1}=307 \mathrm{MPa}$, material constant $m=9$, and cycle base number $N_{0}=5 \times 10^{6}$. Try to determine its reliability.

Options:
A. 0.8564
B. 0.9231
C. 0.9456
D. 0.8952
E. 0.7892
F. 0.9123
G. 0.9345
H. 0.9066
I. 0.8117
J. 0.8704
Answer: H
A steel shaft with a diameter of 30 mm is known to have an average force $P$ acting on it of $1500 \mathrm{N}$, with a standard deviation of 130 N. The average elastic modulus $E$ is $20 \times 10^{4} \, \mathrm{N/mm}^{2}$, with a standard deviation of $3 \times 10^{3} \, \mathrm{N/mm}^{2}$. Given that $a = 100 \, \mathrm{mm}$ and $l = 100 \, \mathrm{mm}$, determine the statistical measurement of the displacement at point $C$.

Options:
A. $$
9. \, 2 \times 10^{-3} \, ( \mathrm{m m} )
$$
B. $$
5. \, 6 \times 10^{-4} \, ( \mathrm{m m} )
$$
C. $$
1. \, 1 \times1 0^{-2} \, ( \mathrm{m m} )
$$
D. $$
4. \, 3 \times 10^{-1} \, ( \mathrm{m m} )
$$
E. $$
2. \, 5 \times 10^{-2} \, ( \mathrm{m m} )
$$
F. $$
10. \, 3 \times 10^{-2} \, ( \mathrm{m m} )
$$
G. $$
7. \, 4 \times 10^{-2} \, ( \mathrm{m m} )
$$
H. $$
6. \, 8 \times 10^{-5} \, ( \mathrm{m m} )
$$
I. $$
3. \, 7 \times 10^{-3} \, ( \mathrm{m m} )
$$
J. $$
8. \, 9 \times 10^{-1} \, ( \mathrm{m m} )
$$
Answer: C
Using anhydrous sodium carbonate and borax as two standard substances to determine the concentration of a certain hydrochloric acid solution, the results are as follows:
Using anhydrous sodium carbonate: 0.1005, 0.1007, 0.1003, 0.1009 (mol/L)
Using borax: 0.1008, 0.1007, 0.1010, 0.1013, 0.1017 (mol/L)
At a 95% confidence level, is there a significant difference in the precision of the HCl solution concentration determined by these two standard substances?

Options:
A. No significant difference
B. Significant deviation present
C. Meaningful discrepancy exists
D. Observable inconsistency found
E. Consistent disparity noted
F. Precision gap noticeable
G. Apparent contradiction observed
H. Clear divergence observed
I. Evidence of variance detected
Answer: A
Among the following polyprotic acids or mixed acids, which shows two jumps when titrated with $NaOH$?

Options:
A. $$
\mathrm{H_{3} P O_{4} ~ ( K_{s_{1}}=6. 9 \times1 0^{-3}, K_{s_{2}}=6. 2 \times1 0^{-8}, K_{s_{3}}=4. 8 \times1 0^{-1 3} )}
$$
B. $$
\mathrm{H_{2} C O_{3} ~ ( K_{s_{1}}=4. 3 \times1 0^{-7}, K_{s_{2}}=4. 7 \times1 0^{-1 4}, K_{s_{3}}=2. 8 \times1 0^{-1 9} )}
$$
C. $$
\mathrm{H_{4} S i O_{4} ~ ( K_{s_{1}}=2. 5 \times1 0^{-5}, K_{s_{2}}=6. 9 \times1 0^{-1 0}, K_{s_{3}}=3. 4 \times1 0^{-1 5} )}
$$
D. $$
\mathrm{H_{2} N O_{3} ~ ( K_{s_{1}}=5. 9 \times1 0^{-4}, K_{s_{2}}=6. 8 \times1 0^{-1 0}, K_{s_{3}}=8. 1 \times1 0^{-1 4} )}
$$
E. $$
\mathrm{H_{3} B O_{3} ~ ( K_{s_{1}}=4. 5 \times1 0^{-9}, K_{s_{2}}=5. 4 \times1 0^{-1 4}, K_{s_{3}}=3. 5 \times1 0^{-1 9} )}
$$
F. $$
\mathrm{H_{2} S O_{3} ~ ( K_{s_{1}}=1. 4 \times1 0^{-2}, K_{s_{2}}=1. 0 \times1 0^{-7}, K_{s_{3}}=1. 8 \times1 0^{-1 2} )}
$$
G. $$
\mathrm{H_{2} S O_{3} ~ ( K_{s_{1}}=5. 6 \times1 0^{-3}, K_{s_{2}}=2. 9 \times1 0^{-7}, K_{s_{3}}=4. 1 \times1 0^{-1 1} )}
$$
Answer: A
In a solution with a pH of 6.0, containing EDTA, $\mathbf{Ca}^{2+}$, and $\mathrm{Zn}^{2+}$ all at a concentration of 0.010 mol/L. What is the $\alpha_{\mathrm{Y}}$ value?

Options:
A. $$ \approx10^{9.41} $$
B. $$
\approx1 0^{8. 6 9}
$$
C. $$ \approx10^{5.74} $$
D. $$ \approx10^{9.18} $$
E. $$ \approx10^{8.25} $$
F. $$ \approx10^{7.92} $$
G. $$ \approx10^{5.89} $$
H. $$ \approx10^{7.36} $$
I. $$ \approx10^{6.57} $$
J. $$ \approx10^{8.02} $$
Answer: B
Titrate $\mathrm{Pb}^{2+}$ at the same concentration with $2 \times 10^{-4} mol/L$ EDTA at pH 5.0, using xylenol orange as an indicator. Control acidity with an HAc-NaAc buffer solution where $[\text{HAc}] = 0.2 \text{ mol/L}$ and $[\text{Ac}^-] = 0.4 \text{ mol/L}$. Calculate the endpoint error.

Options:
A. $$
- 0. 1 \%
$$
B. $$
0. 7 \%
$$
C. $$
- 0. 4 \%
$$
D. $$
0. 2 \%
$$
E. $$
0. 4 \%
$$
F. $$
0. 1 \%
$$
G. $$
0. 5 \%
$$
H. $$
0. 3 \%
$$
I. $$
- 0. 5 \%
$$
J. $$
- 0. 3 \%
$$
Answer: A
Weigh a phenol sample of $0.7380 \mathrm{g}$ and place it in a 500 ml volumetric flask. Add an appropriate amount of water to dissolve and dilute to the mark. Transfer 25.00 ml of the solution to an iodine flask, add 30.00 ml of bromine solution $\left( \mathrm{KBrO}_{3} + \mathrm{KBr} \right)$ along with an appropriate amount of hydrochloric acid and potassium iodide test solution. After the reaction is complete, titrate with $\mathrm{Na_{2}S_{2}O_{3}}$ titrant (0.1123 mol/L) until the endpoint is reached, using 19.02 ml. Separately, perform a blank test using 30.00 ml of bromine solution, consuming 39.80 ml of the aforementioned $\mathrm{Na_{2}S_{2}O_{3}}$ titrant. Calculate the phenol content in the sample is().($M_{\mathrm{C_{6}H_{6}O}} 94.11$)

Options:
A. $$ 1 0 1. 7 5 \% $$
B. $$ 8 9. 3 7 \% $$
C. $$ 9 8. 0 6 \% $$
D. $$ 9 5. 1 6 \% $$
E. $$ 1 0 2. 8 4 \% $$
F. $$ 9 6. 3 2 \% $$
G. $$
9 9. 1 9 \%
$$
H. $$ 1 0 4. 3 9 \% $$
I. $$ 9 2. 4 8 \% $$
J. $$ 8 7. 4 5 \% $$
Answer: G
In a 100ml solution containing 0.1000g of $\mathrm{Ba^{2+}}$, 50ml of 0.010mol/L $\mathrm{H_{2}SO_{4}}$ solution is added. If the precipitate is washed with 100ml of 0.010mol/L $\mathrm{H_{2}SO_{4}}$, assuming dissolution equilibrium is reached during washing, how many milligrams of $\mathrm{BaSO_{4}}$ are lost?

Options:
A. $$
6. 2 \times1 0^{-4} \mathrm{m g}
$$
B. $$
7. 3 \times1 0^{-5} \mathrm{m g}
$$
C. $$
8. 9 \times1 0^{-5} \mathrm{m g}
$$
D. $$
9. 0 \times1 0^{-5} \mathrm{m g}
$$
E. $$
7. 6 \times1 0^{-4} \mathrm{m g}
$$
F. $$
4. 7 \times1 0^{-5} \mathrm{m g}
$$
G. $$
1. 4 \times1 0^{-5} \mathrm{m g}
$$
H. $$
3. 5 \times1 0^{-4} \mathrm{m g}
$$
I. $$
5. 1 \times1 0^{-4} \mathrm{m g}
$$
Answer: A
The purpose of using the "Two Measurements Method" to determine the $\mathrm{p H}$ value of a solution is ().

Options:
A. Neutralize the acidic ions in the solution and improve measurement reliability.
B. Calculate the molarity of the solution and enhance the precision of the reading.
C. Adjust the calibration curve and balance the pH of standard solutions.
D. Eliminate the constants in the formula and remove the asymmetric potential of the glass electrode.
E. Maximize the conductivity of the solution and calibrate the glass electrode.
F. Enhance the response time of the sensor and maintain buffer capacity.
G. Correct the slope of the calibration curve and adjust the pH meter settings.
H. Determine the temperature coefficient and stabilize the pH reading over time.
I. Minimize errors in calculation and balance the ionic strength of the solution.
J. Increase the sensitivity of the sensor and reduce the drift over time.
Answer: D
The electromotive force of the following battery is 0.460V. What is the stability constant $K_{\mathrm{M Y}_{4}^{2-}}$ for the complex $\mathbf{M Y}_{4}^{2-}$ formed by the reaction $\mathbf{M}^{2+}+4 \mathbf{Y}^{-} \rightleftharpoons\mathbf{M} \mathbf{Y}_{4}^{2-}$ ?(given $\varphi_{{\bf M}^{2+} / {\bf M}}^{\Theta}=+0.0221 {\bf V}$).

Options:
A. $$
2. 5 8 \times1 0^{1 6}
$$
B. $$
1. 9 7 \times1 0^{1 5}
$$
C. $$
4. 3 3 \times1 0^{1 7}
$$
D. $$
2. 4 1 \times1 0^{1 7}
$$
E. $$
3. 7 2 \times1 0^{1 6}
$$
F. $$
2. 9 9 \times1 0^{1 6}
$$
G. $$
5. 0 0 \times1 0^{1 4}
$$
H. $$
1. 5 4 \times1 0^{1 6}
$$
I. $$
3. 0 1 \times1 0^{1 8}
$$
J. $$
2. 6 5 \times1 0^{1 7}
$$
Answer: J
Using a chromatography column to separate components A and B, the theoretical plate number for this column is 4200. The retention times for A and B are measured as 15.05 minutes and 14.82 minutes, respectively. What is the resolution?

Options:
A. 3.15
B. 4.25
C. 0.50
D. 3.60
E. 0.25
F. 1.20
G. 14.50
H. 2.40
I. 0.10
J. 1.75
Answer: E
For a certain high-efficiency capillary electrophoresis system, the voltage is 25 kV, the column length $L_{\mathrm{d}}$ is 55 cm, and the diffusion coefficient of a certain ion is $2.0 \times 10^{-9} \, \mathrm{m}^2/\mathrm{s}$. The time it takes for the ion to pass through the column is 10 minutes. What is the theoretical plate number of this capillary column?

Options:
A. $$
4. 1 7 \times1 0^{5}
$$
B. $$
5. 7 6 \times1 0^{4}
$$
C. $$
1. 2 6 \times1 0^{5}
$$
D. $$
6. 8 9 \times1 0^{4}
$$
E. $$
0. 4 3 \times1 0^{6}
$$
F. $$
7. 4 2 \times1 0^{5}
$$
G. $$
3. 1 9 \times1 0^{5}
$$
H. $$
2. 5 8 \times1 0^{5}
$$
I. $$
8. 0 5 \times1 0^{5}
$$
J. $$
9. 3 4 \times1 0^{4}
$$
Answer: C
The total length of the radio antenna on the train is $3 \mathrm{m}$, composed of three sections, each with a length of 1m. Their diameters are $d_{1}=1.5 \mathrm{cm}, \; \; d_{2}=1.0 \mathrm{cm}, \; \; d_{3}=0.5 \mathrm{cm}$, respectively. The train's speed is 60 km/h, the air density $\rho = 1.293 \mathrm{kg/m^3}$, and the drag coefficient for a cylinder $C_{\mathrm{D}}=1.2$. What is the torque produced at the base of the antenna due to air resistance?

Options:
A. $$ 4. 5 1 6 8 \mathrm{N} \cdot\mathrm{m} $$
B. $$ 9. 0 5 8 6 \mathrm{N} \cdot\mathrm{m} $$
C. $$ 6. 8 3 5 9 \mathrm{N} \cdot\mathrm{m} $$
D. $$ 3. 2 9 4 7 \mathrm{N} \cdot\mathrm{m} $$
E. $$ 5. 7 2 4 3 \mathrm{N} \cdot\mathrm{m} $$
F. $$ 9. 3 4 8 7 \mathrm{N} \cdot\mathrm{m} $$
G. $$
7. 5 4 2 5 \mathrm{N} \cdot\mathrm{m}
$$
H. $$ 5. 9 2 8 3 \mathrm{N} \cdot\mathrm{m} $$
I. $$ 6. 4 3 7 2 \mathrm{N} \cdot\mathrm{m} $$
J. $$ 8. 6 2 5 1 \mathrm{N} \cdot\mathrm{m} $$
Answer: G
A data packet arriving at a certain computer follows a Poisson process with an arrival parameter, denoted as $\langle N(t), t \geq 0 \rangle$. Assume each packet contains data frames that are independently distributed and each follows a Poisson distribution with parameter $\beta$ and is independent of $\langle N(t), t \geq 0 \rangle$. Let $X(t)$ be the number of data frames arriving in the interval [0, t). Find $P \left\{X(t) = j \left| N(t) = n \right. \right\}$ and $E(X(t))$ is ().

Options:
A. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=\text{Norm} \big| \sum_{t=1}^{n} Y_{t}=t \Big| N ( t )=j\big|= \frac{( βt)^{j}} {s!} e^{-n t}}}} \\ {{{E ( X ( t ) )=E ( H ) ) E ( Y ) + \lambda t}}} \\ \end{array}
$$
B. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=P \big| \sum_{t=1}^{j} Y_{t}=n \Big| N ( t )=s\big|=\frac{( n β)^{j}} {t!} e^{-n s}}}} \\ {{{E ( X ( t ) )= \ln( N ( t ) ) \cdot E(Y)( t + λ)}}} \\ \end{array}
$$
C. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=B \big| \sum_{t=1}^{n} j_{t}=Y_{t} \big|=\frac{( t β)^{n}} {n!} e^{-j s}}}} \\ {{{E ( X ( t ) )=N ( t ) \times E ( H )+\gamma=λ t}}} \\ \end{array}
$$
D. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=P \big| \sum_{t=1}^{n} Y_{t}=0 \Big| n ( t )=j }} e^{t}} \\ {{{E ( X ( t ) )= N ( t ) E ( Y )+\gamma \lambda t-N ( t )}}} \\ \end{array}
$$
E. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=\text{Geom} \big| \sum_{t=1}^{s} Y_{t}=j \Big| X ( t )=n\big|= \frac{( βn)^{t}} {j!} e^{-s n}}}} \\ {{{E ( X ( t ) )=\lambda- E ( N ( t ) ) + E ( Y ) t}}} \\ \end{array}
$$
F. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=P \big| \sum_{t=1}^{s} Y_{t}=j \Big| N ( t )=n \big|=P \big| \sum_{t=1}^{s} Y_{t}=j \Big|=\frac{( n β)^{t}} {j!} e^{-s t}}}} \\ {{{E ( X ( t ) )=E ( N ( t ) ) E ( Y )=\lambda\partial t}}} \\ \end{array}
$$
G. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=\text{Binom} \big| \sum_{t=1}^{j} Y_{t}=n \Big| N ( t )=j\big|= \frac{( βn)^{s}} {n!} e^{-j s}}}} \\ {{{E ( X ( t ) )=E ( N ( t ) ) E ( H ) + \beta t}}} \\ \end{array}
$$
H. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=\text{Poisson} \big| \sum_{t=1}^{s} Y_{t}=n \Big| X ( t )=j\big|= \frac{( βj)^{n}} {t!} e^{-j t} }}} \\ {{{E ( X ( t ) )=E ( N ( t ) ) - E ( Y )\lambda + t}}} \\ \end{array}
$$
I. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=\text{Poiss} \big| \sum_{t=0}^{n} j_{t}=Y_{t} \big| \}}}} \\ {{{E ( X ( t ) )= N ( t ) ) E ( Y + ( \lambda t)}}} \\ \end{array}
$$
J. $$
\begin{array} {l} {{{P ( X ( t )=j \ \big| \ N ( t )=n )=P \big| Y_{t}=j \Big| N ( t )=1 )=\sum_{t=1}^{n} Y_{t}^2 j\psi }}} \\ {{{E ( X ( t ) )=\mathrm{ln}(E ( N ( t ) ) ) E ( N ( t )) \div Y}}} \\ \end{array}
$$
Answer: F
There is a multi-stage small-signal tuned amplifier with a single tuning circuit resonating at the same frequency. Its center frequency is $f_{0} = 30 \mathrm{MHz}$, and at the operating point, each transistor has the same $\mathbf{Y}$ parameters: $\mathbf{y}_{ie} = (1.62 + j4.07) \mathrm{mS}$, $\mathbf{y}_{re} = (-0.0308 - j0.176) \mathrm{mS}$,
$$\mathbf{y}_{fe} = (53.9 - j9.56) \mathrm{mS}, \ \ \mathbf{y}_{oe} = (0.0722 + j0.593) \mathrm{mS}$$If the $\frac{Q_{e}}{Q_{0}} = 0.5$ for each stage circuit, what should be the mismatch coefficient for each stage to ensure stable operation of the amplifier?

Options:
A. $$
K_{u 0}=1.5K_{u Y}
$$
B. $$
K_{u 0}=K_{u Y}-1
$$
C. $$
K_{u 0}=K_{u Y}
$$
D. $$
K_{u 0}=K_{u Y}+1
$$
E. $$
K_{u 0}=\sqrt{K_{u Y}}
$$
F. $$
K_{u 0}=0.5K_{u Y}
$$
G. $$
K_{u 0}=K_{u Y}^2
$$
H. $$
K_{u 0}=K_{u Y}/2
$$
I. $$
K_{u 0}=2K_{u Y}
$$
J. $$
K_{u 0}=K_{u Y}^3
$$
Answer: C
Near a certain town, there is a two-lane road without intersections, with a speed limit of 60 km/h. Each lane is 3.25 meters wide, with one shoulder width of 1.25 meters and the other shoulder width of 0.75 meters. Sections with insufficient visibility account for 20% of the road. There are a few buildings along the way, and the service level (according to Japanese standards) is level two. Try to determine the traffic capacity of this road.

Options:
A. $$
C_{D}=1440 \mathrm{~ p c u} / \mathrm{h}
$$
B. $$
C_{D}=1550 \mathrm{~ p c u} / \mathrm{h}
$$
C. $$
C_{D}=1625 \mathrm{~ p c u} / \mathrm{h}
$$
D. $$
C_{D}=1900 \mathrm{~ p c u} / \mathrm{h}
$$
E. $$
C_{D}=1694 \mathrm{~ p c u} / \mathrm{h}
$$
F. $$
C_{D}=1530 \mathrm{~ p c u} / \mathrm{h}
$$
G. $$
C_{D}=1800 \mathrm{~ p c u} / \mathrm{h}
$$
H. $$
C_{D}=1675 \mathrm{~ p c u} / \mathrm{h}
$$
I. $$
C_{D}=1750 \mathrm{~ p c u} / \mathrm{h}
$$
J. $$
C_{D}=2000 \mathrm{~ p c u} / \mathrm{h}
$$
Answer: E
A certain project is currently constructing an external longitudinal wall with a height of $9.5 \mathrm{m}$, a wall thickness of 240 mm, and a distance of 7.2 m between transverse walls. The masonry density is greater than $1600 \mathrm{kg}/\mathrm{m}^{3}$, and the wind load is $0.3 \mathrm{kN}/\mathrm{m}^{2}$. Inquire, when the roof has not yet been installed, what is the permissible free height for this wall?

Options:
A. $$2. 6m$$
B. $$2. 7m$$
C. $$3. 5m$$
D. $$2. 4m$$
E. $$2. 9m$$
F. $$2. 3m$$
G. $$3. 4m$$
H. $$3. 0m$$
I. $$1. 9m$$
J. $$3. 1m$$
Answer: A
A certain core-compressed reinforced brick column has a cross-sectional dimension of $490 \, \mathrm{mm} \times 490 \, \mathrm{mm}$, with an effective height of $H_{0} = 4900 \, \mathrm{mm}$. It is constructed using MU10-grade sintered ordinary bricks and M7.5-grade cement mortar, with the masonry construction quality control level being assessed as Grade $\mathbf{B}$. The reinforcement mesh uses HRB400-grade steel bars with a diameter of $4 \, \mathrm{mm}$, whose tensile strength design value is $f_{\mathrm{y}} = 360 \, \mathrm{MPa}$, with a cross-sectional area $A_{\mathrm{s}} = 12.6 \, \mathrm{mm}^{2}$. The vertical spacing of the reinforcement mesh is $s_{n} = 240 \, \mathrm{mm}$, and the horizontal spacing is @ $60 \times 60$.
The question is: which of the following values does the axial compression strength design value $f_{n} \, (\mathrm{MPa})$ of this reinforced brick column most closely approximate?

Options:
A. 2.92
B. 2.66
C. 3.08
D. 2.99
E. 2.55
F. 2.44
G. 2.37
H. 2.71
I. 2.81
J. 3.15
Answer: I
The main bridge of a certain highway bridge is a three-span variable cross-section prestressed concrete continuous box girder structure, with span arrangements of $85 \mathrm{m} + 120 \mathrm{m} + 85 \mathrm{m}$; each of the two approach bridges consists of 3 spans, with each span using a 50m prestressed concrete T-section girder; the abutment is an embedded ribbed slab structure, with a wing wall length of 3500mm and a front wall thickness of 400mm; the expansion joints at both ends have a width of 160mm each. Question: Which of the following values is the total length of the bridge (m) closest to?

Options:
A. 597.96
B. 593.60
C. 589.90
D. 620.15
E. 621.40
F. 608.85
G. 612.50
H. 605.75
I. 634.00
J. 602.20
Answer: A
In a heavily trafficked highway bridge near a certain city, the superstructure employs a prestressed concrete box-section beam. Assume that at the point of maximum bending moment in a certain span of the main beam of this bridge, the standard value of the bending moment caused by all permanent loads is $M_{\mathrm{G i k}}=4 3 0 0 0 \, \mathrm{kN} \cdot \mathrm{m}$, the standard value of the bending moment caused by vehicle loads is $M_{\mathrm{Q l k}}=1 4 7 0 0 \, \mathrm{kN} \cdot \mathrm{m}$ (with the impact factor $\mu=0.2$ already included), and the standard value of the bending moment caused by crowd loads is $M_{Q j \mathrm{k}}=1 3 0 0 \, \mathrm{kN} \cdot \mathrm{m}$. When designing this main beam as a fully prestressed concrete member, during the normal serviceability limit state design for checking the crack resistance of the main beam's normal section, which of the following values is the design value of the bending moment combination (in $\mathrm{kN} \cdot \mathrm{m}$) closest to, if the effects of prestressing are not considered?

Options:
A. 55500
B. 55000
C. 51450
D. 54000
E. 54500
F. 52000
G. 51000
H. 52800
I. 53500
J. 53050
Answer: H
At 293K, ethanol (A) is extracted from an ethanol-water (B) mixture using a certain organic solvent. Water is insoluble in the organic solvent, whereas ethanol is soluble. Assume that ethanol diffuses through a stagnant film 3mm thick in the aqueous phase. At one side of the film (point 1), the solution has a density of 972.8kg/m³ and an ethanol mass fraction of 0.168; at the other side (point 2), the solution's density is 988.1kg/m³ and the ethanol mass fraction is 0.068. The average diffusion coefficient of ethanol in water is $0.74×10^{-9}$m²/s. Find the diffusion flux of ethanol and the mole fraction of ethanol at half the film thickness.

Options:
A. $5.25\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0485$
B. $6.02\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0555$
C. $7.03\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0601$
D. $5.97\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0508$
E. $6.85\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0530$
F. $6.34\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0560$
G. $5.11\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0492$
H. $4.68\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0450$
I. $5.88\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0512$
J. $4.97\times10^{-7}\mathbf{kmol}/(\mathbf{m}^2·{s})$, $x_A=0.0479$
Answer: D
Air at a temperature of 318 K and normal pressure flows through a naphthalene pipe with an inner diameter of $20 \text{ mm}$ and a length of 0.6 m at a speed of 0.8 m/s, causing naphthalene to diffuse from the tube wall into the air. It is known that the diffusion coefficient of naphthalene in air at 318 K and 101.3 kPa is $6.87 \times 10^{-6} \, \text{m}^2/\text{s}$, and the saturation concentration of naphthalene is $2.80 \times 10^{-5} \, \text{kmol/m}^3$. Before entering the aforementioned naphthalene pipe, the air has already passed through a metal tube of the same diameter, which means that the velocity boundary layer is fully developed at the beginning of mass transfer. Calculate the concentration of naphthalene in the outlet gas and the total mass transfer rate of the entire naphthalene pipe.

Options:
A. $$
c_{\mathrm{A 2}} \!=\! 8. \, 0 1 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 1 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
B. $$
c_{\mathrm{A 2}} \!=\! 8. \, 4 0 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 1 0 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
C. $$
c_{\mathrm{A 2}} \!=\! 7. \, 8 5 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 1. \, 9 5 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
D. $$
c_{\mathrm{A 2}} \!=\! 7. \, 9 9 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 1. \, 9 8 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
E. $$
c_{\mathrm{A 2}} \!=\! 8. \, 6 0 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 1 2 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
F. $$
c_{\mathrm{A 2}} \!=\! 8. \, 2 5 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 7 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
G. $$
c_{\mathrm{A 2}} \!=\! 8. \, 3 7 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 9 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
H. $$
c_{\mathrm{A 2}} \!=\! 8. \, 1 4 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 4 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
I. $$
c_{\mathrm{A 2}} \!=\! 8. \, 3 0 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 8 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
J. $$
c_{\mathrm{A 2}} \!=\! 8. \, 0 9 \times1 0^{-6} \, \mathrm{k m o l / m^{3}} \, ; \, \, \, G_{\mathrm{A}} \!=\! 2. \, 0 5 \times1 0^{-9} \, \mathrm{k m o l / s}
$$
Answer: H
Using a packed column to desorb the carbon dioxide from the propylene carbonate absorption liquid, the liquid phase compositions at the inlet and outlet of the column are $X_{2}=0.00849$ and $X_{1}=0.00283$, respectively. The carrier gas used for desorption is air at 35°C $(Y_{1}=0.0005)$, with operating conditions of 35°C and 101.3 kPa. At this time, the equilibrium relationship is given by $Y_{e}=106.03X$. If the operating gas-liquid ratio is 1.4 times the minimum gas-liquid ratio, determine the number of overall mass transfer units for the liquid phase.

Options:
A. $N_{OL}=1.823$
B. $N_{OL}=1.552$
C. $N_{OL}=3.689$
D. $N_{OL}=2.003$
E. $N_{OL}=2.547$
F. $N_{OL}=3.072$
G. $N_{OL}=1.945$
H. $N_{OL}=4.215$
I. $N_{OL}=2.161$
J. $N_{OL}=2.738$
Answer: I
Under normal pressure, a binary solution with a composition of 0.6 (mole fraction of the more volatile component) undergoes both simple distillation and equilibrium distillation. Assuming a vaporization rate of 1/3, and that within the operational range the vapor-liquid equilibrium can be expressed as $y = 0.46x + 0.549$, determine what is the yield of the more volatile component in the gas phase for both cases?

Options:
A. 46.55%,47.7%
B. 49.34%,44.8%
C. 47.89%,45.6%
D. 45.12%,41.0%
E. 40.23%,42.1%
F. 44.67%,43.5%
G. 48.16%,46.5%
H. 43.78%,40.2%
I. 41.99%,43.2%
J. 42.35%,44.9%
Answer: F
In a five-stage cross-current extraction apparatus, trichloroethane is used as the extracting agent to extract acetone from an acetone aqueous solution with an acetone mass fraction of 25%. It is known that the feed liquid is processed at a rate of 2400 kg/h, and it is required that the mass fraction of acetone in the final raffinate phase does not exceed 1%. It is assumed that under operating conditions, water (B) and trichloroethane (S) can be considered completely immiscible, and the partition coefficient of acetone is approximately constant, $K=1.71$. The amount of solvent used in each stage is equal, and the mass fraction of acetone in the extracting agent is 1%, with the rest being trichloroethane. Try to find the total amount of extracting agent used.

Options:
A. 8230kg/h
B. 8025kg/h
C. 7010kg/h
D. 7820kg/h
E. 7655kg/h
F. 6895kg/h
G. 7100kg/h
H. 7625kg/h
I. 7490kg/h
J. 7395kg/h
Answer: J
For $10 \,\text{kg}$ of a certain wet material, the intermittent drying is carried out under constant drying conditions. The material is spread out in a shallow pan measuring $0.8 \,\text{m} \times 1.0 \,\text{m}$, and air at normal pressure passes vertically through the material layer at a speed of $2\,\text{m/s}$. The air temperature is $t = 75\,\text{°C}$ and the humidity is $H = 0.018\,\text{kg/kg}$ of absolutely dry air. The initial moisture content of the dry material is $X_{1} = 0.25\,\text{kg/kg}$ of absolutely dry material. Under these drying conditions, the material's critical moisture content is $\mathbf{X}_{c} = 0.1\,\text{kg/kg}$ of absolutely dry material, and $X^{\circ} = 0$. Assume that the drying rate during the falling rate period is linearly related to the material's moisture content. If the air's $\boldsymbol{t}$ and $H$ remain unchanged but the flow velocity is doubled, and it takes 1.4 hours to dry the material from a moisture content of $0.25\,\text{kg/kg}$ to $0.02\,\text{kg/kg}$ (of absolutely dry material), find the critical moisture content $X_{c}$ under these drying conditions.

Options:
A. 0.087kg/kg
B. 0.095kg/kg
C. 0.145kg/kg
D. 0.121kg/kg
E. 0.135kg/kg
F. 0.140kg/kg
G. 0.109kg/kg
H. 0.132kg/kg
I. 0.120kg/kg
J. 0.114kg/kg
Answer: D
Under the conditions of 101.3 kPa and 52 K, the mole fraction of a certain gas mixture is as follows: $CO_2$ 0.080; $O_2$ 0.035; $H_2O$ 0.160; $N_2$ 0.725. The absolute velocities of each component in the $z$ direction are, respectively: 2.44 m/s; 3.66 m/s; 5.49 m/s; 3.96 m/s. Calculate the mass flux $j_{CO_2}$ of the component $\mathrm{CO_{2}}$.

Options:
A. $$
j_{\mathrm{C O_{2}}}=-1. 5 1 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
B. $$
j_{\mathrm{C O_{2}}}=-0. 5 5 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
C. $$
j_{\mathrm{C O_{2}}}=-2. 0 0 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
D. $$
j_{\mathrm{C O_{2}}}=-0. 8 9 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
E. $$
j_{\mathrm{C O_{2}}}=-1. 3 2 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
F. $$
j_{\mathrm{C O_{2}}}=-1. 1 8 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
G. $$
j_{\mathrm{C O_{2}}}=-1. 6 3 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
H. $$
j_{\mathrm{C O_{2}}}=-0. 7 6 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
I. $$
j_{\mathrm{C O_{2}}}=-1. 2 1 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
J. $$
j_{\mathrm{C O_{2}}}=-1. 4 0 \mathrm{k g} / ( \mathrm{m}^{2} \cdot\mathrm{s} )
$$
Answer: I
Use the Wilke equation to calculate the diffusion coefficient of acetic acid in a dilute aqueous solution at 283K.

Options:
A. $$
D \!=\! 2. \, 3 8 4 \! \times\! 1 0^{-8} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
B. $$
D \!=\! 3. \, 5 0 8 \! \times\! 1 0^{-9} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
C. $$
D \!=\! 8. \, 1 5 6 \! \times\! 1 0^{-1 1} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
D. $$
D \!=\! 1. \, 0 6 7 \! \times\! 1 0^{-6} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
E. $$
D \!=\! 1. \, 9 0 2 \! \times\! 1 0^{-7} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
F. $$
D \!=\! 1. \, 3 2 5 \! \times\! 1 0^{-9} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
G. $$
D \!=\! 9. \, 2 5 1 \! \times\! 1 0^{-1 0} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
H. $$
D \!=\! 1. \, 4 0 7 \! \times\! 1 0^{-9} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
I. $$
D \!=\! 1. \, 1 2 3 \! \times\! 1 0^{-8} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
J. $$
D \!=\! 2. \, 6 4 0 \! \times\! 1 0^{-9} \, {\mathrm{m}}^{2} / {\mathrm{s}}
$$
Answer: F
The results of the laboratory test for a certain undisturbed cohesive soil sample are as follows: the relative density of soil particles $d_{s} = 1.70$, and the weight of the soil sample when wet and after drying are 2.10 N and 1.25 N, respectively. Assuming the saturation of the wet soil sample $S_{r} = 0.75$, determine the total volume $V$, the void ratio $e$, and the porosity $n$ of the sample.

Options:
A. $$
1 7 0 \mathrm{c m}^{3}
$$
$$
2. 2 5
$$
$$
0.74
$$
B. $$
1 5 5 \mathrm{c m}^{3}
$$
$$
2. 6 0
$$
$$
0.69
$$
C. $$
1 5 0 \mathrm{c m}^{3}
$$
$$
2. 9 5
$$
$$
0.68
$$
D. $$
1 6 5 \mathrm{c m}^{3}
$$
$$
2. 5 0
$$
$$
0.70
$$
E. $$
1 6 8 \mathrm{c m}^{3}
$$
$$
2. 1 5
$$
$$
0.76
$$
F. $$
1 8 0 \mathrm{c m}^{3}
$$
$$
2. 3 5
$$
$$
0.72
$$
G. $$
1 4 5 \mathrm{c m}^{3}
$$
$$
2. 8 5
$$
$$
0.65
$$
H. $$
1 9 0 \mathrm{c m}^{3}
$$
$$
2. 4 0
$$
$$
0.73
$$
I. $$
1 6 0 \mathrm{c m}^{3}
$$
$$
2. 4 5
$$
$$
0.71
$$
J. $$
1 5 8 \mathrm{c m}^{3}
$$
$$
3. 0 0
$$
$$
0.67
$$
Answer: I
The foundation has a rectangular base, with an additional base pressure of 200 kPa. Below the base, there is a $2.5 \mathrm{m}$ thick layer of silty clay followed by a very thick layer of dense sand. It is known that the natural unit weight of the silty clay is $19 \mathrm{kN/m^{3}}$, the average void ratio is 0.750, the average coefficient of compressibility is $0.25 \mathrm{MPa}^{-1}$, and the additional stress coefficient at a depth of $2.5 \mathrm{m}$ below the center of the base is 0.48. If the deformation of the dense sand is disregarded, calculate the consolidation settlement of this foundation.(Note: For calculation, consider the foundation soil as a single layer.)

Options:
A. $$
4 8. 5 0 {\mathrm{m m}}
$$
B. $$
4 7. 9 7 {\mathrm{m m}}
$$
C. $$
5 2. 8 6 {\mathrm{m m}}
$$
D. $$
5 6. 9 2 {\mathrm{m m}}
$$
E. $$
4 9. 7 3 {\mathrm{m m}}
$$
F. $$
5 1. 3 2 {\mathrm{m m}}
$$
G. $$
5 0. 2 5 {\mathrm{m m}}
$$
H. $$
5 3. 6 8 {\mathrm{m m}}
$$
I. $$
5 5. 4 4 {\mathrm{m m}}
$$
J. $$
5 4. 1 0 {\mathrm{m m}}
$$
Answer: C
During a triaxial shear test, the first specimen experienced failure when the confining pressure was increased to 200 kPa and the vertical pressure was increased to 600 kPa. The second specimen experienced failure when the confining pressure was increased to 300 kPa and the vertical pressure was increased to 800 kPa. Determine the internal friction angle of the soil sample.

Options:
A. $$
1 7. 8^{\circ}
$$
B. $$
2 0. 1^{\circ}
$$
C. $$
1 5. 2^{\circ}
$$
D. $$
1 6. 7^{\circ}
$$
E. $$
2 5. 0^{\circ}
$$
F. $$
1 9. 5^{\circ}
$$
G. $$
2 2. 9^{\circ}
$$
H. $$
2 1. 5^{\circ}
$$
I. $$
1 8. 4^{\circ}
$$
J. $$
2 3. 3^{\circ}
$$
Answer: F
The soil layers below the surface of a certain building site are as follows: (1) medium sand, $2.0 \mathrm{m}$ thick, with the phreatic water level $1 \mathrm{m}$ below the surface, saturated unit weight $\gamma_{\mathrm{sat}}=20 \mathrm{kN/m}^{3}$; (2) clay intervening layer, $2.0 \mathrm{m}$ thick, unit weight $\gamma=19 \mathrm{kN/m}^{3}$; (3) coarse sand containing confined water, with the confined water level $2.0 \mathrm{m}$ above the surface (take $\gamma_{\mathrm{w}}=10 \mathrm{kN/m^{3}}$). If the foundation is buried at a depth of $d=1.5 \mathrm{m}$, during construction, apart from lowering the groundwater level in the medium sand layer to the bottom of the pit, by how many meters must the confined water level in the coarse sand layer also be lowered?

Options:
A. $$
2. 5 \mathbf{m}
$$
B. $$
1. 4 \mathbf{m}
$$
C. $$
0. 7 \mathbf{m}
$$
D. $$
0. 5 \mathbf{m}
$$
E. $$
0. 9 \mathbf{m}
$$
F. $$
2. 2 \mathbf{m}
$$
G. $$
1. 2 \mathbf{m}
$$
H. $$
1. 3 \mathbf{m}
$$
I. $$
3. 0 \mathbf{m}
$$
J. $$
1. 8 \mathbf{m}
$$
Answer: G
Given that the effective strength parameters of a certain saturated clay are $c^{\prime}=25 \mathrm{kPa}, \ \ \varphi^{\prime}=30^{\circ}$. An unconfined compression test was conducted on this soil, and the unconfined compressive strength was measured to be $q_{\mathrm{u}}=95 \mathrm{kPa}$. Try to find the pore pressure coefficient $A_{\mathrm{f}}$ when the soil sample fails.

Options:
A. $$
-0. 0 3 9 8
$$
B. $$
-0. 0 4 7 9
$$
C. $$
0. 1 7 8 6
$$
D. $$
-0. 0 5 6 7
$$
E. $$
0. 0 5 0 4
$$
F. $$
0. 1 2 3 4
$$
G. $$
0. 0 4 4 2
$$
H. $$
-0. 0 4 0 1
$$
I. $$
0. 2 1 0 5
$$
J. $$
-0. 0 4 4 2
$$
Answer: J
An astronaut piloted a spacecraft to a certain planet, bringing the spacecraft close for an orbit around the planet. The measured flight time for this orbit was $4.5 \times 10^{3} \, \text{s}$. What is the average density of this planet?

Options:
A. $$
9. 1 3 \times1 0^{3} k g / m^{3}
$$
B. $$
3. 5 2 \times1 0^{3} k g / m^{3}
$$
C. $$
7. 9 1 \times1 0^{3} k g / m^{3}
$$
D. $$
8. 2 1 \times1 0^{3} k g / m^{3}
$$
E. $$
5. 8 9 \times1 0^{3} k g / m^{3}
$$
F. $$
9. 8 5 \times1 0^{3} k g / m^{3}
$$
G. $$
7. 4 6 \times1 0^{3} k g / m^{3}
$$
H. $$
6. 9 8 \times1 0^{3} k g / m^{3}
$$
I. $$
6. 5 0 \times1 0^{3} k g / m^{3}
$$
J. $$
4. 7 7 \times1 0^{3} k g / m^{3}
$$
Answer: H
The store uses a crane BAC to lift a load $P = 20 \, \text{kN}$ with a chain passing over pulleys $A$ and $D$. Pulley $D$ is fixed to the wall, and $\angle CAD = 30^\circ$. The angles between the crane's arms are $\angle ABC = 60^\circ$ and $\angle ACB = 30^\circ$. What is the internal forces $Q_{1}$ in rod $AB$ and $Q_{2}$ in rod $AC$ ?

Options:
A. $$
Q_{1}=0, \ Q_{2}=7 5. 4 \ \mathrm{k N}.
$$
B. $$
Q_{1}=-5, \ Q_{2}=5. 0 \ \mathrm{k N}.
$$
C. $$
Q_{1}=15, \ Q_{2}=-3 0. 0 \ \mathrm{k N}.
$$
D. $$
Q_{1}=-3, \ Q_{2}=0. 0 \ \mathrm{k N}.
$$
E. $$
Q_{1}=8, \ Q_{2}=-7. 0 \ \mathrm{k N}.
$$
F. $$
Q_{1}=2, \ Q_{2}=-2 5. 0 \ \mathrm{k N}.
$$
G. $$
Q_{1}=5, \ Q_{2}=-2 0. 0 \ \mathrm{k N}.
$$
H. $$
Q_{1}=10, \ Q_{2}=-1 5. 0 \ \mathrm{k N}.
$$
I. $$
Q_{1}=3, \ Q_{2}=-1 8. 9 \ \mathrm{k N}.
$$
J. $$
Q_{1}=0, \ Q_{2}=-3 4. 6 \ \mathrm{k N}.
$$
Answer: J