MikaStars39/nano-eval huggingface dataset:
Using a single-effect falling film vacuum evaporator, concentrate a 0.10 NaOH aqueous solution to 0.20. The feed flow rate is 10 t/h, with boiling point feed, and the operating pressure of the condenser is 40 kPa (absolute pressure). Heat loss can be ignored. The length of the evaporator tubes is 4 m, and the heat transfer coefficient of the evaporator is 2000 W/m²·°C. The pressure of the heating steam used is 300 kPa (absolute pressure). Determine the steam consumption and the heat transfer area of the evaporator is ().

Options:
A. 42.8 $m^{2}$
B. 49.3 $m^{2}$
C. 52.1 $m^{2}$
D. 45.6 $m^{2}$
E. 47.5 $m^{2}$
F. 40.5 $m^{2}$
G. 46.2 $m^{2}$
H. 44.3 $m^{2}$
I. 38.9 $m^{2}$
J. 50.7 $m^{2}$
Answer: H
Required to concentrate a 1500 kg/h calcium chloride (${CaCl}_{2}$) aqueous solution from a concentration of 0.10 to 0.25. The feed temperature is 25°C, and the boiling point of the solution under operating conditions is 110°C. The heating steam used is at 400 kPa, and heat loss accounts for 5% of the evaporator's heat load. Determine the consumption of heating steam is ().

Options:
A. 1265kg/h
B. 1195kg/h
C. 1150kg/h
D. 1300kg/h
E. 1325kg/h
F. 1255kg/h
G. 1184kg/h
H. 1230kg/h
I. 1200kg/h
J. 1290kg/h
Answer: G
In a certain shell-and-tube heat exchanger, the tubes are steel pipes with dimensions of $\Phi 25 \times 2.5mm$. The convective heat transfer coefficients for the fluid inside and outside the tubes are 200 ${W / m^{2} \cdot °C}$ and 2500 ${W / m^{2} \cdot °C}$ respectively. Ignoring the thermal resistance of fouling and the conductive thermal resistance of the tube walls, determine the heat transfer coefficient when $\alpha_o$ is doubled is ().(with other conditions remaining constant)

Options:
A. $500 {W / m^{2} \cdot °C}$
B. $195 {W / m^{2} \cdot °C}$
C. $290 {W / m^{2} \cdot °C}$
D. $125 {W / m^{2} \cdot °C}$
E. $250 {W / m^{2} \cdot °C}$
F. $155 {W / m^{2} \cdot °C}$
G. $175 {W / m^{2} \cdot °C}$
H. $310 {W / m^{2} \cdot °C}$
I. $220 {W / m^{2} \cdot °C}$
J. $100 {W / m^{2} \cdot °C}$
Answer: F
In a single-pass shell and tube heat exchanger, a high-temperature ${SO}_{3}$ mixed gas is used to preheat the raw gas. Known data includes: the heat exchanger's heat transfer area is $90 \, \text{m}^2$; the inlet temperature of the raw gas is 300°C, and the outlet temperature is 430°C; the inlet temperature of the ${SO}_{3}$ mixed gas is 560°C; the flow rates of both fluids are 10000 kg/h each, and the heat loss is 6% of the heat gained by the raw gas. Assume the specific heat capacities of both gases can be considered as $1.05 \, \text{kJ} / \text{kg} \cdot °\text{C}$. Calculate the heat transfer coefficient is ().

Options:
A. $47.58 {W / m^{2} \! \cdot\! °C}$
B. $36.90 {W / m^{2} \! \cdot\! °C}$
C. $42.67 {W / m^{2} \! \cdot\! °C}$
D. $31.21 {W / m^{2} \! \cdot\! °C}$
E. $33.11 {W / m^{2} \! \cdot\! °C}$
F. $28.75 {W / m^{2} \! \cdot\! °C}$
G. $35.43 {W / m^{2} \! \cdot\! °C}$
H. $30.56 {W / m^{2} \! \cdot\! °C}$
I. $39.89 {W / m^{2} \! \cdot\! °C}$
J. $45.02 {W / m^{2} \! \cdot\! °C}$
Answer: G
In a heat exchanger, ethylene gas at a flow rate of 2000 kg/h needs to be cooled from 100°C to 50°C. The inlet temperature of the cooling water is 30°C, and the temperature difference between the inlet and outlet should be controlled within 8°C. Determine the consumption of cooling water in this process.

Options:
A. 4530.9 kg/h
B. 4810.3 kg/h
C. 4395.2 kg/h
D. 5190.7 kg/h
E. 4222.9 kg/h
F. 4750.1 kg/h
G. 4561.7 kg/h
H. 3920.5 kg/h
I. 4105.6 kg/h
J. 4688.8 kg/h
Answer: G
Using a ${B M S 5 0} / 8 1 0-2 5$ model plate and frame filter press, a suspension is filtered under constant pressure. The known dimensions of the filter frames are $810 \times 810 \times 25$ mm, with a total of 36 frames. Under operating conditions, the filtration constant $K$ is $2.72 \times 10^{-5} \, \text{m}^{2}/\text{s}$, and the filter cake yield is 0.148. The resistance of the filtering medium can be neglected. If the filter cake is washed with 0.8 $m^{2}$ of clean water at the end of filtration, what is the washing time?

Options:
A. 284s
B. 421s
C. 657s
D. 312s
E. 234s
F. 598s
G. 376s
H. 532s
I. 487s
J. 439s
Answer: B
Use a standard cyclone separator with a cylinder diameter of 650mm to remove dust from the airflow. Given: the dust density is 2630 $kg/m^{3}$, and the gas viscosity is $2.6 \times 10^{-5} \, Pa \cdot s$. Find the critical diameter of the particles when the air flow rate is $1 \, m^{3}/s$ is ().

Options:
A. $$
9. 3 2 \mu\mathrm{m}
$$
B. $$
2. 1 9 \mu\mathrm{m}
$$
C. $$
8. 0 5 \mu\mathrm{m}
$$
D. $$
4. 8 1 \mu\mathrm{m}
$$
E. $$
3. 6 4 \mu\mathrm{m}
$$
F. $$
7. 2 6 \mu\mathrm{m}
$$
G. $$
6. 9 7 \mu\mathrm{m}
$$
H. $$
8. 5 9 \mu\mathrm{m}
$$
I. $$
5. 4 3 \mu\mathrm{m}
$$
J. $$
4. 2 8 \mu\mathrm{m}
$$
Answer: G
A steel pipe with an inner diameter of 106mm is used to transport a certain solution with properties similar to water at a temperature of 20°C from a pool to a high-level tank. The required flow rate is $45 \mathrm{m}^{3} / \mathrm{h}$, and the friction factor can be considered as 0.03. The total calculated length of the pipeline is 240m, and the vertical distance between the two liquid surfaces is 8m. What is the energy loss caused by adjusting the operating point through a valve during the use of the pump?

Options:
A. $$5.3J/N$$
B. $$6.7J/N$$
C. $$7.0J/N$$
D. $$8.4J/N$$
E. $$2.9J/N$$
F. $$4.7J/N$$
G. $$6.1J/N$$
H. $$5.9J/N$$
I. $$9.5J/N$$
J. $$3.8J/N$$
Answer: A
If oxygen is compressed isentropically at 100°F and 15 psia to 40% of its original volume, what are its temperature and pressure at that time?

Options:
A. $$
5 1. 3 \mathrm{p s i a}
$$
$$
3 3 5 \, \mathrm{{\mathrm{~ °F}}}
$$
B. $$
5 0. 0 \mathrm{p s i a}
$$
$$
3 4 4 \, \mathrm{{\mathrm{~ °F}}}
$$
C. $$
5 4. 8 \mathrm{p s i a}
$$
$$
3 4 3 \, \mathrm{{\mathrm{~ °F}}}
$$
D. $$
5 4. 1 \mathrm{p s i a}
$$
$$
3 4 8 \, \mathrm{{\mathrm{~ °F}}}
$$
E. $$
5 2. 9 \mathrm{p s i a}
$$
$$
3 4 0 \, \mathrm{{\mathrm{~ °F}}}
$$
F. $$
5 3. 0 \mathrm{p s i a}
$$
$$
3 3 8 \, \mathrm{{\mathrm{~ °F}}}
$$
G. $$
5 0. 5 \mathrm{p s i a}
$$
$$
3 5 0 \, \mathrm{{\mathrm{~ °F}}}
$$
H. $$
5 5. 5 \mathrm{p s i a}
$$
$$
3 4 2 \, \mathrm{{\mathrm{~ °F}}}
$$
I. $$
5 6. 0 \mathrm{p s i a}
$$
$$
3 4 6 \, \mathrm{{\mathrm{~ °F}}}
$$
J. $$
5 3. 7 \mathrm{p s i a}
$$
$$
3 4 5 \, \mathrm{{\mathrm{~ °F}}}
$$
Answer: D
A uniform flow with a depth of 1mm passes over the glass roof. If the temperature is 15°, and the roof slope is 0.08, what is the flow rate per meter of the roof?

Options:
A. $$
q \,=\, 0. 0 0 0 1 2 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
B. $$
q \,=\, 0. 0 0 0 2 3 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
C. $$
q \,=\, 0. 0 0 1 2 0 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
D. $$
q \,=\, 0. 0 0 0 7 1 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
E. $$
q \,=\, 0. 0 0 0 4 7 5 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
F. $$
q \,=\, 0. 0 0 0 0 9 5 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
G. $$
q \,=\, 0. 0 0 0 8 6 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
H. $$
q \,=\, 0. 0 0 0 5 0 5 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
I. $$
q \,=\, 0. 0 0 0 3 4 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
J. $$
q \,=\, 0. 0 0 0 6 9 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
Answer: B
The shaft of a single-stage, single-suction cantilever pump is given. Upon analysis, the bending moment at the critical cross-section is $T = 3 \times 10^{4} \mathrm{~N \cdot mm}$, and the torque is $M = 2 \times 10^{5} \mathrm{N \cdot mm}$. The shaft surface roughness is $Ra=3.2 μm$. Try to determine the diameter of the shaft.

Options:
A. $$
d \!=\! 3 2. \, 1 \, \mathrm{m m}
$$
B. $$
d \!=\! 3 4. \, 6 \, \mathrm{m m}
$$
C. $$
d \!=\! 3 7. \, 4 \, \mathrm{m m}
$$
D. $$
d \!=\! 3 1. \, 8 \, \mathrm{m m}
$$
E. $$
d \!=\! 4 0. \, 3 \, \mathrm{m m}
$$
F. $$
d \!=\! 3 8. \, 9 \, \mathrm{m m}
$$
G. $$
d \!=\! 3 6. \, 2 \, \mathrm{m m}
$$
H. $$
d \!=\! 3 0. \, 4 \, \mathrm{m m}
$$
I. $$
d \!=\! 3 3. \, 5 \, \mathrm{m m}
$$
J. $$
d \!=\! 3 9. \, 7 \, \mathrm{m m}
$$
Answer: B
The atmospheric pressure on the mountain is $660 \, \mathrm{mmHg}$. Hot water at 80°C is being transported using a pump. The pressure drop within the pump is 3.5 m, and the pressure loss in the suction pipe is 0.6 m. Calculate the allowable suction lift of the pump.

Options:
A. 1.02m
B. 0.51m
C. 0.70m
D. 0.45m
E. 0.68m
F. 1.25m
G. 2.10m
H. 0.85m
I. 1.60m
J. 0.93m
Answer: E
A 15.00 ml NaOH standard solution with a concentration of 0.2000 mol/L can exactly neutralize a certain mass of $\mathrm{KHC}_2\mathrm{O}_4 \cdot \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \cdot 2\mathrm{H}_2\mathrm{O}$. How many milliliters of a $KMnO_4$ standard solution with a concentration of 0.04000 mol/L are needed to oxidize the same mass of $\mathrm{KHC}_2\mathrm{O}_4 \cdot \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \cdot 2\mathrm{H}_2\mathrm{O}$?

Options:
A. $$
2 0. 5 0 \mathrm{\ m l}
$$
B. $$
3 5. 0 0 \mathrm{\ m l}
$$
C. $$
5 0. 0 0 \mathrm{\ m l}
$$
D. $$
3 0. 0 0 \mathrm{\ m l}
$$
E. $$
2 5. 0 0 \mathrm{\ m l}
$$
F. $$
1 5. 0 0 \mathrm{\ m l}
$$
G. $$
2 0. 0 0 \mathrm{\ m l}
$$
H. $$
4 0. 0 0 \mathrm{\ m l}
$$
I. $$
1 0. 0 0 \mathrm{\ m l}
$$
J. $$
4 5. 0 0 \mathrm{\ m l}
$$
Answer: G
When calculating pH2, the acid effect coefficient of EDTA is().

Options:
A. 11.45
B. 10.52
C. 18.29
D. 12.65
E. 12.97
F. 15.23
G. 17.31
H. 13.51
I. 14.60
J. 16.88
Answer: H
Titrate $\mathrm{Cu}^{2+}$ ions of the same concentration with EDTA solution $(2.0 \times 10^{-2} \mathrm{mol/L})$. If the solution's pH is 10 and the free ammonia concentration is $0.20 \mathrm{mol/L}$, calculate the pCu' at the equivalence point.

Options:
A. 5.50
B. 9.35
C. 5.90
D. 3.75
E. 6.25
F. 8.10
G. 4.80
H. 7.45
I. 2.60
J. 6.95
Answer: A
A sample of chalcanthite ($\mathrm{CuSO}_{4} \cdot \mathrm{5H}_{2} \mathrm{O}$) weighing $0.5180 \ \mathrm{g}$ was analyzed using an iodometric titration method. At the endpoint of the titration, $18.58 \ \mathrm{mL}$ of $\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}$ standard solution was consumed. When the $\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}$ solution was standardized with $\mathbf{K}_{2} \mathbf{Cr}_{2} \mathbf{O}_{7}$, it was found that $41.22 \ \mathrm{mL}$ of $\mathbf{Na}_{2} \mathbf{S}_{2} \mathbf{O}_{3}$ solution corresponded to $0.2121 \ \mathrm{g}$ of $\mathbf{K}_{2} \mathbf{Cr}_{2} \mathbf{O}_{7}$. Calculate the content of $\mathrm{CuSO}_{4} \cdot \mathrm{5H}_{2} \mathrm{O}$ in the sample is().($M_{\mathrm{K_{2}Cr_{2}O_{7}}} = 294.2$, $M_{\mathrm{CuSO_{4} \cdot 5H_{2}O}} = 249.7$)

Options:
A. $$
1 0 0. 7 2 \%
$$
B. $$
9 8. 4 7 \%
$$
C. $$
8 2. 5 1 \%
$$
D. $$
8 8. 9 4 \%
$$
E. $$
8 5. 7 8 \%
$$
F. $$
9 4. 1 6 \%
$$
G. $$
1 0 2 . 3 0 \%
$$
H. $$
9 3. 9 5 \%
$$
I. $$
9 6. 8 9 \%
$$
J. $$
9 0. 6 3 \%
$$
Answer: H
Determine 0.1 mol/L $\mathrm{Cl}^{-}$ using the ferric ammonium alum indicator method. In the presence of $\mathrm{AgCl}$ precipitate, titrate back the excess 0.1 mol/L $\mathrm{AgNO_{3}}$ with a 0.1 mol/L $\mathrm{KSCN}$ standard solution. The final volume of the solution in titration is 70 ml, with $\left[ \mathrm{Fe^{3+}} \right] = 0.015 \mathrm{mol/L}$. When a distinct endpoint is observed, ($[\mathrm{FeSCN^{2+}}] = 6.0 \times 10^{-6} \mathrm{mol/L}$), what is the excess volume of $\mathrm{KSCN}$ standard solution consumed due to the conversion of the precipitate? ($K_{\mathrm{FeSCN}} = 200$)

Options:
A. $0.35ml$
B. $0.15ml$
C. $0.23ml$
D. $0.33ml$
E. $0.25ml$
F. $0.29ml$
G. $0.27ml$
H. $0.19ml$
I. $0.21ml$
J. $0.31ml$
Answer: C
What is the amount of dissolution loss of $\mathbf{C a C}_{2} \mathbf{O}_{4}$ at pH 2.0 ?assuming the total volume of the solution is 500ml. ( $\mathbf{p} K_{\mathrm{s p ( C a C_{2} O_{4} )}} \ =$ ${\bf8.7 5}; {\bf H}_{2} {\bf C}_{2} {\bf O}_{4}$ has $\mathrm{p} K_{a_{1}} \;=\; 1.23 \; ; \mathrm{p} K_{a_{2}} \;=\; 4.19 \; ; M_{\mathrm{C a C_{2} O_{4}}} \;=\; 128.10$)

Options:
A. $44.6mg$
B. $45.2mg$
C. $28.7mg$
D. $47.1mg$
E. $50.3mg$
F. $41.5mg$
G. $36.9mg$
H. $25.3mg$
I. $33.2mg$
J. $39.8mg$
Answer: G
To determine the equilibrium constant of the proton transfer reaction between pyridine and water,
$$\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{N}+\mathrm{H_{2}O}\rightleftharpoons\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}+\mathrm{OH}^{-}$$
set up the following cell:
Pt, $H_2$ (0.200 atm) $\begin{vmatrix}\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N} (0.189 \text{ mol/L})&&\mathrm{Hg}_{2}\mathrm{Cl}_{2} (\text{saturated})\\\\\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}\mathrm{Cl}^{-} (0.0536 \text{ mol/L})&&\mathrm{KCl} (\text{saturated})\end{vmatrix}$ Hg
If the cell electromotive force at 25°C is 0.563V, what is the equilibrium constant $\kappa_\mathrm{b}$ for the above reaction?

Options:
A. $$
2 . 1 1 \times1 0^{-5}
$$
B. $$
9. 5 3 \times1 0^{-4}
$$
C. $$
8. 6 5 \times1 0^{-1}
$$
D. $$
7. 0 1 \times1 0^{-6}
$$
E. $$
1. 4 4 \times1 0^{-8}
$$
F. $$
5. 6 9 \times1 0^{-3}
$$
G. $$
3. 2 7 \times1 0^{-7}
$$
H. $$
1. 8 1 \times1 0^{-9}
$$
I. $$
6. 2 0 \times1 0^{-5}
$$
J. $$
4. 3 8 \times1 0^{-2}
$$
Answer: H
Using a chromatographic column to separate components $\mathbf{A}$ and $\mathbf{B}$, the retention times for peak A and peak B are 320s and 350s, respectively, with a dead time of 25s. If the peak widths are equal, what is the minimum length of the chromatographic column required for complete separation of the two peaks? (Assume a theoretical plate height of 0.11 mm)

Options:
A. $$
479(cm)
$$
B. $$
493(cm)
$$
C. $$
492(cm)
$$
D. $$
460(cm)
$$
E. $$
384(cm)
$$
F. $$
525(cm)
$$
G. $$
461(cm)
$$
H. $$
511(cm)
$$
I. $$
480(cm)
$$
J. $$
482(cm)
$$
Answer: A
Data measured on a high-performance thin-layer plate using thin-layer scanning method are as follows: the substance with $L_{0}=82 \text{mm}$ and $R_{f}=0$ has a half-peak width of $1.9 \text{mm}$, while the substance with $R_{f}=1$ has a half-peak width of $3.1 \text{mm}$. What is the separation number of the thin-layer plate?

Options:
A. 15
B. 17
C. 22
D. 25
E. 12
F. 10
G. 20
H. 30
I. 14
J. 18
Answer: A
What are the dimensions and relative bandwidth of the waveguide when the transmitter's operating wavelength range is 7.1 to 11.8 cm, and it is fed through a rectangular waveguide?

Options:
A. $$
a=6. 3 3 8 ( \mathrm{c m} ), \quad b \leqslant3. 1 7 5 ( \mathrm{c m} )
$$
$${73.4} \%$$
B. $$
a=6. 6 1 7 ( \mathrm{c m} ), \quad b \leqslant3. 3 0 7 ( \mathrm{c m} )
$$
$${71.4} \%$$
C. $$
a=6. 7 5 9 ( \mathrm{c m} ), \quad b \leqslant3. 2 9 7 ( \mathrm{c m} )
$$
$${71.8} \%$$
D. $$
a=6. 9 0 1 ( \mathrm{c m} ), \quad b \leqslant3. 4 3 8 ( \mathrm{c m} )
$$
$${69.1} \%$$
E. $$
a=6. 4 7 5 ( \mathrm{c m} ), \quad b \leqslant3. 3 0 5 ( \mathrm{c m} )
$$
$${72.0} \%$$
F. $$
a=6. 5 1 2 ( \mathrm{c m} ), \quad b \leqslant3. 2 8 0 ( \mathrm{c m} )
$$
$${71.1} \%$$
G. $$
a=6. 8 2 3 ( \mathrm{c m} ), \quad b \leqslant3. 4 1 2 ( \mathrm{c m} )
$$
$${69.9} \%$$
H. $$
a=6. 1 9 4 ( \mathrm{c m} ), \quad b \leqslant3. 1 5 8 ( \mathrm{c m} )
$$
$${74.2} \%$$
I. $$
a=7. 1 0 0 ( \mathrm{c m} ), \quad b \leqslant3. 5 2 0 ( \mathrm{c m} )
$$
$${70.6} \%$$
J. $$
a=7. 0 2 5 ( \mathrm{c m} ), \quad b \leqslant3. 5 5 0 ( \mathrm{c m} )
$$
$${68.5} \%$$
Answer: B
The characteristic function of the random variable $X$ is given by $\varphi(t) = \frac{1}{1 + t^{2}}$, $f_{x}(x)$ is ().

Options:
A. $$
f ( x ) \,=\, {\frac{2} {\pi}} \mathrm{e}^{-2 x^{2}} \,, \quad x \, \in\,{R}
$$
B. $$
f ( x ) \,=\, {\frac{1} {4}} \mathrm{e}^{-x^{2}} \,, \quad x \, \in\,{R}
$$
C. $$
f ( x ) \,=\, {\frac{1} {\pi}} \sin \pi x \,, \quad x \, \in\,{R}
$$
D. $$
f ( x ) \,=\, {\frac{1} {3}} \mathrm{e}^{-| x |^{3}} \,, \quad x \, \in\,{R}
$$
E. $$
f ( x ) \,=\, {\frac{1} {2}} \cos | x | \,, \quad x \, \in\,{R}
$$
F. $$
f ( x ) \,=\, {\frac{1} {\sqrt{2 \pi}}} \mathrm{e}^{- x^{2}/2} \,, \quad x \, \in\,{R}
$$
G. $$
f ( x ) \,=\, {\frac{1} {2}} | x | \mathrm{e}^{-| x |} \,, \quad x \, \in\,{R}
$$
H. $$
f ( x ) \,=\, x^{2} \mathrm{e}^{-x^{2}} \,, \quad x \, \in\,{R}
$$
I. $$
f ( x ) \,=\, {\frac{1} {5}} \mathrm{e}^{-| x |/5} \,, \quad x \, \in\,{R}
$$
J. $$
f ( x ) \,=\, {\frac{1} {2}} \mathrm{e}^{-| x |} \,, \quad x \, \in\,{R}
$$
Answer: J
Ag underwent deformation of 26%. The measured values are $\Delta E_{V} \approx 16.7 \mathrm{~J/mol}$, $\sigma=4 \times 10^{-5} \mathrm{~J/cm}^{2}$. It is known that $A_{r}=107.9$. With $\rho=10.49 \mathrm{~g/cm}^{3}$, find out how large L should be to achieve arch-out nucleation.

Options:
A. $$\approx2. 5 9\times1 0^{-4} ~ c m$$
B. $$\approx1. 4 8\times1 0^{-8} ~ c m$$
C. $$\approx9. 2 1\times1 0^{-8} ~ c m$$
D. $$\approx7. 6 4\times1 0^{-9} ~ c m$$
E. $$\approx5. 8 2\times1 0^{-6} ~ c m$$
F. $$\approx6. 2 5\times1 0^{-7} ~ c m$$
G. $$\approx1. 7 2\times1 0^{-9} ~ c m$$
H. $$\approx4. 9 3\times1 0^{-5} ~ c m$$
I. $$\approx8. 0 8\times1 0^{-6} ~ c m$$
J. $$\approx3. 1 7\times1 0^{-7} ~ c m$$
Answer: H
A damped spring-mass system has a mass $m = 17.5$ kg, spring constant $k = 70$ N/cm, and damping coefficient $c = 0.7$ N·s/cm. Calculate the system's ratio of two successive amplitudes $\eta$.

Options:
A. $$2.25$$
B. $$1.88$$
C. $$1.95$$
D. $$1.50$$
E. $$1.60$$
F. $$2.05$$
G. $$2.10$$
H. $$1.65$$
I. $$2.15$$
J. $$1.75$$
Answer: B
A 1×1×1 cube is stretched in one direction so that its length in that direction changes from 1 to $1+\varepsilon$. Calculate the change in the volume of the cube is ().

Options:
A. $$
\Delta V=\varepsilon\left( 3-2 \mathbf{v} \right)
$$
B. $$
\Delta V=\varepsilon\left( 2-2 \mathbf{v} \right)
$$
C. $$
\Delta V=\varepsilon\left( \mathbf{v}-1 \right)
$$
D. $$
\Delta V=\varepsilon\left( 1-3 \mathbf{v} \right)
$$
E. $$
\Delta V=\varepsilon\left( \mathbf{v}+2 \right)
$$
F. $$
\Delta V=\varepsilon\left( 1-\mathbf{v}^2 \right)
$$
G. $$
\Delta V=\varepsilon\left( 2+\mathbf{v}^2 \right)
$$
H. $$
\Delta V=\varepsilon\left( 1-2 \mathbf{v} \right)
$$
I. $$
\Delta V=\varepsilon\left( 2+\mathbf{v} \right)
$$
J. $$
\Delta V=\varepsilon\left( 1+\mathbf{v} \right)
$$
Answer: H
A certain axial load-bearing inner transverse wall is two stories high and has a thickness of $240 \text{mm}$. It is constructed using MU15 autoclaved fly ash bricks and M5 mixed mortar, with the masonry construction quality control grade being level C. The static calculation scheme is the rigid scheme, and the floor height is $3.3 \text{ m}$. What is the design value of the load-bearing capacity ( $\text{kN/m}$ ) of the second-story wall? (Which of the following values is it closest to?)
Hint: The length of the interior wall is greater than $6.6 \text{ m}$.

Options:
A. $$230$$
B. $$320$$
C. $$390$$
D. $$350$$
E. $$260$$
F. $$300$$
G. $$310$$
H. $$200$$
I. $$280$$
J. $$240$$
Answer: I
The circular water tank built with MU15 fired common clay bricks and M10 cement mortar (constructed with three stretchers and one header, with masonry construction quality control grade of $\mathbf{B}$) has an internal circumferential tensile force of $73 \text{ kN/m}$. Which of the following options is correct for selecting the tank wall thickness?

Options:
A. $$6 4 0 \mathrm{m m}$$
B. $$8 3 0 \mathrm{m m}$$
C. $$7 9 0 \mathrm{m m}$$
D. $$3 5 0 \mathrm{m m}$$
E. $$4 9 0 \mathrm{m m}$$
F. $$5 6 0 \mathrm{m m}$$
G. $$4 0 0 \mathrm{m m}$$
H. $$6 7 0 \mathrm{m m}$$
I. $$2 9 0 \mathrm{m m}$$
J. $$5 8 0 \mathrm{m m}$$
Answer: E
When the wind vibration coefficient at the roof height of $100 \mathrm{m}$ is known to be $\beta_{100} = 1.55$, The design value of the wind load perpendicular to the building surface at the roof height, denoted as $ w $ (in $\mathrm{kN/m^2}$), is closest to which of the following values?

Options:
A. 2.601
B. 1.832
C. 1.695
D. 1.987
E. 2.789
F. 1.425
G. 1.974
H. 2.056
I. 2.345
J. 2.150
Answer: G
A simply supported single-span beam bridge with a standard span of 30 meters is located on a secondary highway. The superstructure consists of 5 precast prestressed concrete T-section beams, each measuring $29.94 \mathrm{m}$ in length and 2.0 meters in height. The natural frequency (fundamental frequency) of the bridge's main beam structure is $f=4.5 \mathrm{Hz}$. The question is, the impact coefficient $\mu$ for the effects of vehicles on the bridge is closest to which of the following values (Hz)?

Options:
A. 0.29
B. 0.25
C. 0.28
D. 0.35
E. 0.22
F. 0.27
G. 0.20
H. 0.24
I. 0.30
J. 0.32
Answer: B
A certain bridge is located in a seismic zone with a seismic intensity of 7 (peak ground acceleration is $0.15g$). The structure consists of multiple spans with 16m simply supported prestressed concrete hollow slab beams. The pier cap is a single-span double-cantilever rectangular structure, and neoprene bearing pads are used as supports. The expansion joint width is 80mm. What value is the minimum width (mm) of the pier cap beam of this bridge closest to?
Hint: Consider the calculative span of the beam as $15.5m$.

Options:
A. 1620
B. 1650
C. 1830
D. 1750
E. 1580
F. 1720
G. 1675
H. 1855
I. 1605
J. 1690
Answer: B
Let water at 293K flow through spherical benzoic acid particles in a fixed bed, with a particle diameter of 4mm and a superficial water velocity of 0.25m/s. If the benzoic acid concentration at entry point $a$ is $c_{\mathrm{A1}}=0$, and at exit point $\sigma$, the benzoic acid concentration is $c_{A2}=0.8 c_{A}$ (where $c_{A}$ is the saturation concentration of benzoic acid in water), calculate the required height of the bed layer.
It is known that at 293K, the viscosity and density of the benzoic acid solution are $1 \times 10^{-3} \mathrm{~Pa \cdot s}$ and $1000 \mathrm{~kg/m^3}$, respectively. The diffusion coefficient of benzoic acid in water is $0.77 \times 10^{-9} \mathrm{~m}^2/\mathrm{s}$. The porosity of the bed layer is $\mathbf{c=0.45}$.

Options:
A. 6.32m
B. 0.88m
C. 4.71m
D. 9.06m
E. 1.96m
F. 8.15m
G. 5.43m
H. 7.24m
I. 2.85m
J. 3.59m
Answer: J
At 30°C and 101.3 kPa, ammonia gas mixed in the air is absorbed using a packed column. The packing used is random ceramic rings with a specific surface area of 300 $m^2$/ $m^3$ and a diameter of 15 mm. The average partial pressure of ammonia in the mixed gas is known to be 6.0 kPa, the empty tower mass velocity of the gas is $G = 3.0 \mathbf{kg}/(\mathbf{m}^2\cdot\mathbf{s})$; under operating conditions, the diffusion coefficient of ammonia in air is $1.98\times 10^{-5}\mathrm{m}^2/$s, the viscosity of the gas is $1.86\times10^{-5}$ Pa·s, and the density is 1.14 kg/m³. Calculate the gas film absorption coefficient $k_{\mathrm{G}}$.

Options:
A. $k_{G}=3.40\times10^{-5}kmol/(m^{2}\cdot s\cdot kPa)$
B. $k_{G}=1.55\times10^{-5}kmol/(m^{2}\cdot s\cdot kPa)$
C. $k_{G}=2.00\times10^{-7}kmol/(m^{2}\cdot s\cdot kPa)$
D. $k_{G}=4.50\times10^{-5}kmol/(m^{2}\cdot s\cdot kPa)$
E. $k_{G}=9.90\times10^{-6}kmol/(m^{2}\cdot s\cdot kPa)$
F. $k_{G}=7.80\times10^{-6}kmol/(m^{2}\cdot s\cdot kPa)$
G. $k_{G}=2.20\times10^{-5}kmol/(m^{2}\cdot s\cdot kPa)$
H. $k_{G}=1.80\times10^{-4}kmol/(m^{2}\cdot s\cdot kPa)$
I. $k_{G}=5.12\times10^{-6}kmol/(m^{2}\cdot s\cdot kPa)$
J. $k_{G}=1.00\times10^{-5}kmol/(m^{2}\cdot s\cdot kPa)$
Answer: B
In the rectifying section of the tray distillation column, it is measured that: the operating vapor-liquid ratio is 1.25, the gas phase composition entering the $i$th theoretical plate is $\mathbf{y}_{i+1}=0.712$, the liquid phase composition leaving the $i$th plate is $x_{i}=0.65$, and the average relative volatility of the system is $\alpha=1.8$. Try to find the liquid phase composition entering the $i$th plate $x_{i-1}$.

Options:
A. 0.6852
B. 0.7105
C. 0.7221
D. 0.7250
E. 0.7821
F. 0.6710
G. 0.7993
H. 0.6934
I. 0.6523
J. 0.7400
Answer: C
In a continuous operation distillation column, a benzene-toluene mixture is separated. Under total reflux conditions, the liquid phase compositions on adjacent trays are measured to be 0.28, 0.41, and 0.57, respectively. The average relative volatility of the benzene-toluene mixture under operating conditions can be taken as 2.5. Calculate the murphree efficiency $E_{M L}$ for the lower two trays among the three layers.

Options:
A. $$
E_{\mathrm{M L 1}}=0. 7 1 6 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 7 5
$$
B. $$
E_{\mathrm{M L 1}}=0. 7 1 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 7 0 0
$$
C. $$
E_{\mathrm{M L 1}}=0. 8 0 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 3 5
$$
D. $$
E_{\mathrm{M L 1}}=0. 6 6 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 7 2 8
$$
E. $$
E_{\mathrm{M L 1}}=0. 6 9 5 \,, \, \, \, E_{\mathrm{M L 2}}=0. 7 1 0
$$
F. $$
E_{\mathrm{M L 1}}=0. 7 0 5 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 8 5
$$
G. $$
E_{\mathrm{M L 1}}=0. 8 2 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 5 0
$$
H. $$
E_{\mathrm{M L 1}}=0. 7 8 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 4 0
$$
I. $$
E_{\mathrm{M L 1}}=0. 7 2 5 \,, \, \, \, E_{\mathrm{M L 2}}=0. 7 0 5
$$
J. $$
E_{\mathrm{M L 1}}=0. 8 1 0 \,, \, \, \, E_{\mathrm{M L 2}}=0. 6 6 5
$$
Answer: A
In an atmospheric counter-current rotary dryer, a certain crystalline material is dried. Fresh air with a temperature of $t_{0}=25 \mathrm{°C}$ and a relative humidity of $\varphi_{0}=55$% is heated by a preheater to a temperature of $t_{1}=85 \mathrm{°C}$ before being introduced into the dryer, with the leaving air temperature being $t_{2}=30 \mathrm{°C}$. The preheater uses 180 kPa saturated steam to heat the air, and the total heat transfer coefficient of the preheater is $50 \mathbf{W} / (\mathbf{m}^{2} \cdot \mathbf{K})$, with negligible heat loss. The initial temperature of the wet material is $\theta_{1}=24 \mathrm{°C}$, with a wet basis moisture content of $w_{1}=0.037$; after drying, the temperature rises to $\theta_{2}=60 \mathrm{°C}$ and the wet basis moisture content decreases to $\boldsymbol{w}_{2}=0.002$. The flow rate of the dried product is $G_{2}=1000 \mathrm{kg} / \mathrm{h}$. The specific heat capacity of the absolutely dry material is $c_{s}=1.507 \mathrm{kJ}/(\mathrm{kg} \cdot \mathrm{°C})$. The diameter of the rotary dryer is $D=1.3 \mathrm{m}$, and its length is $Z=7 \mathrm{m}$. The convective-radiative heat transfer coefficient for the exterior wall of the dryer to the air is $35 \mathrm{kJ}/(\mathrm{m}^{3} \cdot \mathrm{h} \cdot \mathrm{°C})$. Determine the heat transfer area of the preheater.

Options:
A. 21.67m²
B. 15.72m²
C. 20.30m²
D. 24.11m²
E. 17.53m²
F. 23.19m²
G. 18.89m²
H. 16.88m²
I. 19.04m²
J. 22.45m²
Answer: G
Water at a temperature of 280K flows through a circular tube with an inner diameter of 50mm at a velocity of 1.5m/s, with cinnamic acid coated on the inner wall surface. It is known that the $S_c$ (Schmidt number) of cinnamic acid when dissolved in water is $2920$. Try to calculate the fully developed convective mass transfer coefficient using the Reynolds, Prandtl-Taylor, von Kármán, and Colburn analogy relations.

Options:
A. $$
2. 1 5 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
B. $$
8. 5 6 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
C. $$
1. 9 2 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
D. $$
5. 3 3 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
E. $$
4. 8 9 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
F. $$
3. 0 4 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
G. $$
6. 7 7 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
H. $$
7. 1 1 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
I. $$
0. 6 8 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
J. $$
9. 4 2 \times1 0^{-5} {\mathrm{m}} / {\mathrm{s}}
$$
Answer: C
A mixture of hydrogen (component A) and air (component B) at a total pressure of 101.3 kPa and a temperature of 273 K diffuses through a capillary with a diameter of 5 nm and a length of 0.3 m. It is known that the partial pressures of hydrogen at the two ends of the capillary are $p_{\mathrm{A 1}}=2.6$ kPa and $p_{\mathsf{A 2}}=1.3$ kPa, respectively. Under the diffusion conditions, the viscosity of hydrogen is $0.845 \times 10^{-5} \, \mathrm{Pa} \cdot \mathrm{s}$. Calculate the diffusion flux of hydrogen $N_{\mathrm{A}}$.

Options:
A. $$
N_{\mathrm{A}}=6. 1 7 5 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
B. $$
N_{\mathrm{A}}=5. 2 1 9 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
C. $$
N_{\mathrm{A}}=4. 5 7 6 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
D. $$
N_{\mathrm{A}}=6. 2 0 3 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
E. $$
N_{\mathrm{A}}=6. 0 6 1 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
F. $$
N_{\mathrm{A}}=5. 8 3 2 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
G. $$
N_{\mathrm{A}}=5. 9 4 3 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
H. $$
N_{\mathrm{A}}=4. 8 0 3 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
I. $$
N_{\mathrm{A}}=5. 4 0 3 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
J. $$
N_{\mathrm{A}}=5. 0 3 9 \times1 0^{-6} \mathrm{~ k m o l / ( m^{2} ~ · ~ s )}
$$
Answer: I
Given that the natural unit weight of a soil sample $\gamma=19.0 \mathrm{kN/m}^{3}$, the relative density of the soil particles $d_{s}=2.71$, and the water content $w=23.7\%$, try to calculate the degree of saturation, void ratio, dry unit weight, and saturated unit weight of the soil sample.

Options:
A. $$
8 3. 1 \%
$$
$$
0. 7 2
$$
$$
1 6. 0 5 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 5 1 \mathrm{k N} / \mathrm{m}^{3}
$$
B. $$
8 0. 2 \%
$$
$$
0. 7 5
$$
$$
1 6. 1 0 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 2 5 \mathrm{k N} / \mathrm{m}^{3}
$$
C. $$
8 4. 5 \%
$$
$$
0. 7 6
$$
$$
1 5. 3 6 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 6 9 \mathrm{k N} / \mathrm{m}^{3}
$$
D. $$
8 2. 3 \%
$$
$$
0. 8 0
$$
$$
1 4. 8 2 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 3 0 \mathrm{k N} / \mathrm{m}^{3}
$$
E. $$
8 2. 9 \%
$$
$$
0. 7 9
$$
$$
1 4. 9 5 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 8. 9 9 \mathrm{k N} / \mathrm{m}^{3}
$$
F. $$
7 9. 6 \%
$$
$$
0. 8 3
$$
$$
1 5. 0 2 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 7 3 \mathrm{k N} / \mathrm{m}^{3}
$$
G. $$
7 8. 9 \%
$$
$$
0. 6 8
$$
$$
1 5. 7 4 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 8. 8 7 \mathrm{k N} / \mathrm{m}^{3}
$$
H. $$
8 0. 7 \%
$$
$$
0. 7 3
$$
$$
1 6. 2 4 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
2 0. 0 5 \mathrm{k N} / \mathrm{m}^{3}
$$
I. $$
8 1. 5 \%
$$
$$
0. 7 4
$$
$$
1 5. 9 0 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
2 0. 1 2 \mathrm{k N} / \mathrm{m}^{3}
$$
J. $$
8 5. 1 \%
$$
$$
0. 7 1
$$
$$
1 5. 6 8 \mathrm{k N} / \mathrm{m}^{3}
$$
$$
1 9. 8 8 \mathrm{k N} / \mathrm{m}^{3}
$$
Answer: C
During the construction of a certain earth dam, the relative density of the material used for the dam is $d_{s}=2.70$, with a natural water content of 10%. The dry density of the loose soil when placed on the dam is $\gamma_{\mathrm{d}} = 12 \mathrm{kN} / \mathrm{m}^{3}$. After compaction, the saturation level is required to reach 95%, with a dry density of $16.8 \mathrm{kN}/\mathrm{m}^{3}$. If the daily dam fill volume is $5000 \mathrm{m}^{3}$, how much additional water is needed in total?

Options:
A. $$
1 5 0 \mathrm{t}
$$
B. $$
1 0 4 0 \mathrm{t}
$$
C. $$
9 0 0 \mathrm{t}
$$
D. $$
9 5 5 \mathrm{t}
$$
E. $$
1 1 0 0 \mathrm{t}
$$
F. $$
1 0 8 0 \mathrm{t}
$$
G. $$
1 2 0 0 \mathrm{t}
$$
H. $$
8 5 0 \mathrm{t}
$$
I. $$
1 3 5 0 \mathrm{t}
$$
J. $$
7 5 0 \mathrm{t}
$$
Answer: D
An unconfined compression test was conducted on a certain saturated soft clay, yielding a shear strength of 80 kPa. If the same soil sample undergoes a triaxial unconsolidated undrained shear test with a confining pressure of 180 kPa, at what vertical stress will the sample fail?

Options:
A. $$
8 0 k P a
$$
B. $$
2 2 0 k P a
$$
C. $$
1 6 0 k P a
$$
D. $$
2 0 0 k P a
$$
E. $$
2 4 0 k P a
$$
F. $$
1 2 0 k P a
$$
G. $$
1 4 0 k P a
$$
H. $$
1 0 0 k P a
$$
I. $$
1 8 0 k P a
$$
J. $$
2 8 0 k P a
$$
Answer: A
A certain retaining wall has a height of 10.0m, with a vertical and smooth back face, and a horizontal fill surface behind the wall. A uniform load $q = 20 \mathrm{kPa}$ acts on the fill. The fill consists of two layers: the upper layer is medium sand with a unit weight $\gamma_{1} = 18.5 \mathrm{kN/m^{3}}$, an internal friction angle $\varphi_{1} = 30^{\circ}$, and a thickness $h_{1} = 3.0 \mathrm{m}$; the lower layer is coarse sand with $\gamma_{2} = 19.0 \mathrm{kN/m^{3}}$, $\varphi_{2} = 35^{\circ}$. The groundwater level is located 6.0m from the top of the wall. The saturated unit weight of the submerged coarse sand is $\gamma_{\mathrm{sat}} = 20.0 \mathrm{kN/m^{3}}$. Calculate the total active earth pressure and water pressure acting on this retaining wall is().

Options:
A. $$
4 2 0 \mathrm{k N / m}
$$
$$
85 \mathrm{k N / m}
$$
B. $$
2 7 0 \mathrm{k N / m}
$$
$$
75 \mathrm{k N / m}
$$
C. $$
3 6 0 \mathrm{k N / m}
$$
$$
90 \mathrm{k N / m}
$$
D. $$
4 0 5 \mathrm{k N / m}
$$
$$
88 \mathrm{k N / m}
$$
E. $$
2 9 5 \mathrm{k N / m}
$$
$$
78 \mathrm{k N / m}
$$
F. $$
3 1 0 \mathrm{k N / m}
$$
$$
82 \mathrm{k N / m}
$$
G. $$
3 3 0 \mathrm{k N / m}
$$
$$
77 \mathrm{k N / m}
$$
H. $$
3 1 5 \mathrm{k N / m}
$$
$$
80 \mathrm{k N / m}
$$
I. $$
3 2 5 \mathrm{k N / m}
$$
$$
83 \mathrm{k N / m}
$$
J. $$
3 0 5 \mathrm{k N / m}
$$
$$
95 \mathrm{k N / m}
$$
Answer: H
The wall is a vertically smooth retaining wall, 6m high, with a horizontal fill surface. On top of it, there is a vertical uniform load $q=20 \, \text{kN/m}^2$, with fill having properties $\gamma=18 \, \text{kN/m}^3, \; c=16 \, \text{kPa}, \; \varphi=22^\circ$. the depth of potential cracks in the fill is().

Options:
A. $$
1. 3 6 \mathrm{m}
$$
B. $$
2. 1 8 \mathrm{m}
$$
C. $$
2. 4 7 \mathrm{m}
$$
D. $$
2. 5 5 \mathrm{m}
$$
E. $$
1. 6 4 \mathrm{m}
$$
F. $$
1. 7 3 \mathrm{m}
$$
G. $$
2. 6 1 \mathrm{m}
$$
H. $$
1. 4 9 \mathrm{m}
$$
I. $$
2. 3 8 \mathrm{m}
$$
J. $$
1. 5 2 \mathrm{m}
$$
Answer: J
A saturated clay layer with a thickness of $6 \mathrm{m}$ is underlain by an incompressible impermeable layer. The vertical consolidation coefficient of the clay layer is known to be $C_{v} = 0.0045 \mathrm{cm^{2}/s}$, and the unit weight is $\gamma = 16.8 \mathrm{kN/m^{3}}$. Over the clay layer is a thin permeable sand layer, and an infinite uniformly distributed load $p = 120 \mathrm{kPa}$ is instantaneously applied on the surface. When the degree of consolidation is 50%, the time factor for a rectangular initial pore pressure distribution curve is 0.2, and for a triangular initial pore pressure distribution curve, it is 0.3. If the clay layer has already completed consolidation under its self-weight before the load $p$ is applied, calculate the time required to reach a 50% degree of consolidation is__.

Options:
A. $$ 1. 1 5 \mathrm{y e a r}
$$
B. $$ 1. 4 9 \mathrm{y e a r}
$$
C. $$ 0. 9 8 \mathrm{y e a r}
$$
D. $$ 0. 6 2 \mathrm{y e a r}
$$
E. $$ 0. 2 6 \mathrm{y e a r}
$$
F. $$ 0. 8 4 \mathrm{y e a r}
$$
G. $$ 1. 0 3 \mathrm{y e a r}
$$
H. $$ 0. 5 1 \mathrm{y e a r}
$$
I. $$ 1. 3 7 \mathrm{y e a r}
$$
J. $$ 0. 7 9 \mathrm{y e a r}
$$
Answer: H
Pulley A and $B$ are situated on the same horizontal line, with a distance $A B = l$. The rope CAEBD passes over the pulleys, with weights of $p$ hanging from each end of the rope at points $C$ and $D$, and a weight of $P$ hanging at point $E$. Assuming no friction in the pulleys and neglecting the sizes of the pulleys and the weight of the rope.What is the distance $x$ from point $E$ to the straight line $A B$ in the state of equilibrium ?

Options:
A. $$
x=\frac{2 P l} {\sqrt{4 P^{2}-p^{2}}}
$$
B. $$
x=\frac{P l} {3 \sqrt{4 p^{2}-P^{2}}}
$$
C. $$
x=\frac{3 P l} {2 \sqrt{4 p^{2}-P^{2}}}
$$
D. $$
x=\frac{P l} {2 \sqrt{p^{2}+4 P^{2}}}
$$
E. $$
x=\frac{P l} {\sqrt{p^{2}-P^{2}}}
$$
F. $$
x=\frac{2 pl} {\sqrt{4 p^{2}+P^{2}}}
$$
G. $$
x=\frac{P l} {2 \sqrt{3 p^{2}-P^{2}}}
$$
H. $$
x=\frac{P l} {4 \sqrt{p^{2}+P^{2}}}
$$
I. $$
x=\frac{P l} {2 \sqrt{4 p^{2}-P^{2}}}
$$
J. $$
x=\frac{P l} {2 \sqrt{4 p^{2}+P^{2}}}
$$
Answer: I
A homogeneous rod rests with its lower end on a rough surface, and its upper end is held by hand, forming an angle $\theta_{0}$ with the ground. Upon release, the rod falls, but the lower end does not slide.What is the force exerted by the rod on the ground at the instant it is released ?

Options:
A. $$N=mg+\frac12mg\cos^2\theta_0.$$
B. $$N=mg-\frac13mg\sin^2\theta_0.$$
C. $$N=mg+\frac14mg\tan^2\theta_0.$$
D. $$N=mg-\frac45mg\sin^2\theta_0.$$
E. $$N=mg+\frac38mg\sin^2\theta_0.$$
F. $$N=mg+\frac34mg\sin^2\theta_0.$$
G. $$N=mg+\frac23mg\cos^2\theta_0.$$
H. $$N=mg-\frac34mg\cos^2\theta_0.$$
I. $$N=mg-\frac12mg\tan^2\theta_0.$$
J. $$N=mg-\frac25mg\cos^2\theta_0.$$
Answer: H
Cone 1, with a vertex angle of 60°, rolls purely on the inner wall of hollow cone 2, which has a vertex angle of 120°. At the same time, cone 2 rotates about the fixed vertical axis $O_{1} O_{2}$ at a constant angular velocity $\omega=3 \ \mathrm{rad/s}$. Point $B$ on the edge of the base of cone 1 is on diameter $BC$, which lies within the same vertical plane as the axis $O_{1} O_{2}$. The speed of point $B$ remains constant at $60 \, \mathrm{cm/s}$, and its direction is perpendicular to the plane $O B C$ shown in the diagram. It is also known that $O B = O C = 20 \ \mathrm{cm}$ and $\angle C O D = 30^{\circ}$.What is the magnitude of the absolute acceleration of points $B$ and $C$ on cone 1 ?

Options:
A. $$
w_{B}=4 9 0 \ \mathrm{c m / s^2}, w_{C}=3 0 5 \ \mathrm{c m / s^2}.
$$
B. $$
w_{B}=5 2 0 \ \mathrm{c m / s^2}, w_{C}=3 2 5 \ \mathrm{c m / s^2}.
$$
C. $$
w_{B}=4 9 7 \ \mathrm{c m / s^2}, w_{C}=3 1 6 \ \mathrm{c m / s^2}.
$$
D. $$
w_{B}=5 1 0 \ \mathrm{c m / s^2}, w_{C}=3 0 0 \ \mathrm{c m / s^2}.
$$
E. $$
w_{B}=4 7 0 \ \mathrm{c m / s^2}, w_{C}=3 5 0 \ \mathrm{c m / s^2}.
$$
F. $$
w_{B}=4 9 8 \ \mathrm{c m / s^2}, w_{C}=3 1 5 \ \mathrm{c m / s^2}.
$$
G. $$
w_{B}=4 8 5 \ \mathrm{c m / s^2}, w_{C}=3 2 0 \ \mathrm{c m / s^2}.
$$
H. $$
w_{B}=5 0 5 \ \mathrm{c m / s^2}, w_{C}=3 3 0 \ \mathrm{c m / s^2}.
$$
I. $$
w_{B}=4 8 0 \ \mathrm{c m / s^2}, w_{C}=3 6 0 \ \mathrm{c m / s^2}.
$$
J. $$
w_{B}=5 0 0 \ \mathrm{c m / s^2}, w_{C}=3 4 0 \ \mathrm{c m / s^2}.
$$
Answer: C
A weight with a mass of $m = 1.75 \ \mathrm{kg}$ is hung inside a box with a vertical spring. The spring has a stiffness coefficient of $c = 0.88 \ \mathrm{kN/m}$. The box is placed on a table that vibrates in the vertical direction. The equation for the table's vibration is $x = 0.225 \sin 3t$ (where $x$ is measured in cm). What is the absolute amplitude of the weight's vibration?

Options:
A. $$
x=0. 2 9 1 0 \mathrm{~ c m}
$$
B. $$
x=0. 2 6 4 2 \mathrm{~ c m}
$$
C. $$
x=0. 1 7 8 3 \mathrm{~ c m}
$$
D. $$
x=0. 3 5 0 9 \mathrm{~ c m}
$$
E. $$
x=0. 1 8 2 7 \mathrm{~ c m}
$$
F. $$
x=0. 3 0 5 8 \mathrm{~ c m}
$$
G. $$
x=0. 2 2 5 4 \mathrm{~ c m}
$$
H. $$
x=0. 2 1 4 5 \mathrm{~ c m}
$$
I. $$
x=0. 2 7 6 1 \mathrm{~ c m}
$$
J. $$
x=0. 3 2 9 7 \mathrm{~ c m}
$$
Answer: G
The element with a half-life of 30 days, Cm$^{2+1}$, emits an $\alpha$ particle with an energy of 6.25 MeV. Calculate the heat released from a micro-test tube containing a 2 mg solution of the salt of Cm$^{2+1}$.

Options:
A. 3.58 joules/second.
B. 0.54 calories/minute.
C. 1.02 joules/minute.
D. 0.88 calories/second.
E. 1.35 joules/minute.
F. 2.16 joules/second.
G. 0.69 calories/second.
H. 0.71 calories/minute.
I. 4.33 calories/hour.
J. 3.42 calories/hour.
Answer: G
Under the same conditions, two samples of the same cobalt-60 $\gamma$-radioactive solution were measured. The radioactivity of a 0.1 ml sample was measured at 350 counts per minute, and the radioactivity of a 3.0 ml sample was measured at 9900 counts per minute. Question: What is the resolving time of the counter tube? Assume that the resolving time of other parts of the counter apparatus and the self-absorption effect can be ignored.

Options:
A. $$
6 \cdot 6 1 0 pulses/min
$$
B. $$
6 \cdot 6 0 0 pulses/min
$$
C. $$
4 \cdot 6 0 0 pulses/sec
$$
D. $$
6 \cdot 7 0 0 pulses/sec
$$
E. $$
6 \cdot 6 0 5 counts/min
$$
F. $$
5 \cdot 6 0 0 pulses/min
$$
G. $$
6 \cdot 5 0 5 pulses/sec
$$
H. $$
7 \cdot 6 0 0 counts/min
$$
I. $$
5 \cdot 6 7 0 counts/sec
$$
J. $$
6 \cdot 6 5 0 counts/min
$$
Answer: B
The capacitor of Lauritsen's electrometer is 5 picofarads. In the ionization chamber, there are 100 $\alpha$ particles, each losing 3.9 million electron volts of energy per second. Try to calculate how much time is needed for the potential of the electrometer to drop from 200 volts to 190 volts?

Options:
A. 20 seconds
B. 18 seconds
C. 35 seconds
D. 45 seconds
E. 22 seconds
F. 40 seconds
G. 30 seconds
H. 28 seconds
I. 15 seconds
J. 25 seconds
Answer: J
If at a distance of $x$ meters from a lead container with a thickness of 10 cm containing a cobalt source, a Roentgen dosimeter indicates a dose rate of $0.78 \times 10^{-2}$ R/hour, and at $x + 0.5$ meters, it is $0.195 \times 10^{-2}$ R/hour, find the radioactivity of the cobalt source. Neglect the absorption of gamma rays by air.

Options:
A. 0.5 Curie
B. 10 Curies
C. 15 Curies
D. 2 Curies
E. 1 Curie
F. 0.8 Curie
G. 3 Curies
H. 5 Curies
I. 0.2 Curie
J. 20 Curies
Answer: E
Given: The concentration of argon in the atmosphere is much higher than that of other inert gases, which can be explained by the decay of the naturally radioactive element $\mathbf{K}^{40}$ to
$$
(\mathrm{Ar}^{40})
$$
. In argon, 99.63% of the component is
$$
\mathbf{Ar}^{40}
$$
, which confirms the correctness of the above hypothesis. It is possible that not all of the argon generated from the decay of $\mathbf{K}^{40}$ enters the atmosphere. It is noted that the content of $\mathbf{K}^{40}$ in the Earth's crust is approximately $4.9 \times 10^{17}$ tons. Try to calculate the amount (%) of argon that has dissipated into the atmosphere through the crust's fractures over the geophysical age of the Earth (approximately $4.46 \times 10^{9}$ years).

Options:
A. $$
\sim2. 7 \%
$$
B. $$
\sim4. 2 \%
$$
C. $$
\sim8. 3 \%
$$
D. $$
\sim5. 4 \%
$$
E. $$
\sim9. 8 \%
$$
F. $$
\sim3. 9 \%
$$
G. $$
\sim7. 5 \%
$$
H. $$
\sim0. 3 \%
$$
I. $$
\sim1. 6 \%
$$
J. $$
\sim6. 1 \%
$$
Answer: I
Using neutrons from a Ra--Be source, target the same volume of $\mathrm{CCl}_{4}$ (density $d = 1.595$) and $\mathrm{CS}_{2}$ (density $d = 1.263$), the $\mathrm{S}^{32} (n, \, p) \mathrm{P}^{32}$ reaction occurs with an effective cross-section of 0.138 barns, and the $\mathrm{Cl}^{35} (n, \alpha) \mathrm{P}^{32}$ reaction occurs with an effective cross-section of 0.022 barns. Calculate: how many times greater is the yield of $\mathbf{P}^{32}$ generated from the CS$_2$ target compared to that generated from the
$\mathrm{CCl}_{4}$
target?

Options:
A. 2.8 times
B. 5.7 times
C. 8.6 times
D. 5.2 times
E. 9.4 times
F. 4.1 times
G. 7.9 times
H. 6.3 times
I. 3.1 times
J. 4.5 times
Answer: H
For a strontium salt solution labeled with Sr$^{89}$, the specific radioactivity is 2 mCi/ml. If 0.2 ml of the solution is used to prepare a sample and the counting efficiency is 0.1, how many times must the original solution be diluted to achieve a radioactivity of 1000 counts per minute in a beta counting tube?

Options:
A. 90 times
B. 85 times
C. 89 times
D. 79 times
E. 88 times
F. 84 times
G. 92 times
H. 91 times
I. 82 times
J. 95 times
Answer: C
If the specific radioactivity of the phosphate used during topdressing is 10 $^{6}$ counts/min per gram, and the sample obtained from the plant ash after 45 days of growth has a radioactivity of 1250 counts/min, with samples in both cases made into 20 mg of magnesium pyrophosphate, determine the percentage of phosphorus absorbed by the plant from the soil.

Options:
A. 75%
B. 20%
C. 50%
D. 10%
E. 33%
F. 15%
G. 25%
H. 60%
I. 45%
J. 40%
Answer: C
Irradiate a 100 mg silver foil with a Ra-Be neutron source for 10 minutes. Measurements begin 8 minutes after irradiation stops, with a count of 262 pulses within 5 minutes. Given that the counting efficiency is 0.186 and the effective cross-section for Ag$^{107}$ neutron capture is 44.5x10 $^{-24}$ cm$^2$, determine the neutron flux intensity of the source and the number of Ag$^{108}$ atoms produced.

Options:
A. 2.3 $\cdot 10^{-9}$ grams
9.9 $\cdot 10^{4}$ neutrons per square centimeter $\cdot$ second
B. 9.5 $\cdot 10^{-8}$ grams
3.3 $\cdot 10^{3}$ neutrons per square centimeter $\cdot$ second
C. 7.7 $\cdot 10^{-9}$ grams
5.4 $\cdot 10^{4}$ neutrons per square centimeter $\cdot$ second
D. 1.1 $\cdot 10^{-7}$ grams
8.7 $\cdot 10^{2}$ neutrons per square centimeter $\cdot$ second
E. 8.1 $\cdot 10^{-7}$ grams
2.6 $\cdot 10^{3}$ neutrons per square centimeter $\cdot$ second
F. 4.6 $\cdot 10^{-8}$ grams
7.0 $\cdot 10^{2}$ neutrons per square centimeter $\cdot$ second
G. 5.2 $\cdot 10^{-8}$ grams
4.9 $\cdot 10^{4}$ neutrons per square centimeter $\cdot$ second
H. 6.0 $\cdot 10^{-8}$ grams
1.2 $\cdot 10^{3}$ neutrons per square centimeter $\cdot$ second
I. 8.8 $\cdot 10^{-9}$ grams
1.5 $\cdot 10^{3}$ neutrons per square centimeter $\cdot$ second
J. 3.4 $\cdot 10^{-9}$ grams
2.8 $\cdot 10^{3}$ neutrons per square centimeter $\cdot$ second
Answer: I
To penetrate the Coulomb barrier of a light nucleus, the order of magnitude of the minimum energy that a proton must have is____.

Options:
A. $$
\mathrm{0.1 ~ M e V}
$$
B. $$
\mathrm{10 ~ k e V}
$$
C. $$
\mathrm{100 ~ M e V}
$$
D. $$
\mathrm{1 ~ G e V}
$$
E. $$
\mathrm{2 ~ G e V}
$$
F. $$
\mathrm{500 ~ k e V}
$$
G. $$
\mathrm{50 ~ M e V}
$$
H. $$
\mathrm{1 ~ M e V}
$$
I. $$
\mathrm{5 ~ k e V}
$$
J. $$
\mathrm{200 ~ M e V}
$$
Answer: H
Given that the wavenumber difference between adjacent lines in the far-infrared pure rotational spectrum of an NaCl molecule is $0.28 \mathrm{cm}^{-1}$, what is the ratio of the number of NaCl molecules in the ground state to those in the first and second rotationally excited states at a temperature of 300K? It is known that $k=8.617 \times 10^{-5} \mathrm{eV} \cdot \mathrm{K}^{-1}$ and $hc=1240 \mathrm{eV} \cdot \mathrm{nm}$.

Options:
A. $$
N_{0} : N_{1} : N_{2}\approx1 : 2. 9 2 : 4. 9 8
$$
B. $$
N_{0} : N_{1} : N_{2}\approx1 : 2. 8 9 : 4. 7 9
$$
C. $$
N_{0} : N_{1} : N_{2}\approx1 : 2. 9 7 : 4. 8 3
$$
D. $$
N_{0} : N_{1} : N_{2}\approx1 : 3. 2 0 : 4. 8 1
$$
E. $$
N_{0} : N_{1} : N_{2}\approx1 : 3. 0 1 : 4. 9 5
$$
F. $$
N_{0} : N_{1} : N_{2}\approx1 : 2. 9 0 : 5. 0 0
$$
G. $$
N_{0} : N_{1} : N_{2}\approx1 : 3. 0 5 : 4. 8 2
$$
H. $$
N_{0} : N_{1} : N_{2}\approx1 : 3. 1 0 : 4. 7 5
$$
I. $$
N_{0} : N_{1} : N_{2}\approx1 : 2. 9 6 : 4. 8 0
$$
J. $$
N_{0} : N_{1} : N_{2}\approx1 : 3. 0 2 : 4. 7 8
$$
Answer: I
At a height of 10 meters above the ground, a single wire with a diameter of 3 cm is suspended, and an effective value of 63.5 kV of power frequency alternating voltage is applied to the wire. Please calculate the maximum electric field strength on the surface of the wire. If the wire is replaced with a horizontally arranged double split conductor, keeping the total cross-sectional area of the two wires consistent with that of the single wire, and the distance between the wires is 30 cm, what is the maximum electric field strength on the surface of the wire?

Options:
A. $$
E_{\operatorname* {m a x}}=7. 3 5 0 k V / c m
$$
B. $$
E_{\operatorname* {m a x}}=4. 8 7 0 k V / c m
$$
C. $$
E_{\operatorname* {m a x}}=6. 5 4 0 k V / c m
$$
D. $$
E_{\operatorname* {m a x}}=6. 1 2 0 k V / c m
$$
E. $$
E_{\operatorname* {m a x}}=5. 0 9 0 k V / c m
$$
F. $$
E_{\operatorname* {m a x}}=5. 3 8 0 k V / c m
$$
G. $$
E_{\operatorname* {m a x}}=6. 9 0 0 k V / c m
$$
H. $$
E_{\operatorname* {m a x}}=5. 4 5 0 k V / c m
$$
I. $$
E_{\operatorname* {m a x}}=4. 9 5 0 k V / c m
$$
J. $$
E_{\operatorname* {m a x}}=4. 5 2 0 k V / c m
$$
Answer: H
When the distance $d \!=\! 0.1 \mathrm{cm}$ between parallel plate electrodes, the breakdown voltage is 4.6 kV. The gas is air under standard atmospheric conditions, with $A \!=\! 6460/\mathrm{cm}, \ B \!=\! 1.9 \times 10^{5} \mathrm{~V/cm}$. What is the ionization coefficient $\gamma$? When $d \!=\! 1.0 \mathrm{cm}$, the breakdown voltage is 31.6 kV. What is $\gamma$ again?

Options:
A. $$
0. 5 4 3 \times1 0^{-5},\ 0.290
$$
B. $$
4. 0 2 5 \times1 0^{-5},\ 0.639
$$
C. $$
3. 0 8 9 \times1 0^{-5},\ 0.206
$$
D. $$
2. 4 1 7 \times1 0^{-5},\ 0.145
$$
E. $$
9. 5 6 4 \times1 0^{-5},\ 0.829
$$
F. $$
5. 0 7 1 \times1 0^{-5},\ 0.315
$$
G. $$
1. 1 8 3 \times1 0^{-5},\ 0.702
$$
H. $$
8. 1 3 2 \times1 0^{-5},\ 0.218
$$
I. $$
6. 9 8 2 \times1 0^{-5},\ 0.507
$$
J. $$
7. 3 6 4 \times1 0^{-5},\ 0.582
$$
Answer: C
For a certain 10.5kV direct distribution pole, with a capacity of $10000 \mathrm{kW}$, its three-phase wave impedance $Z_{1}=380 \Omega$, and the overhead direct distribution line's three-phase wave impedance is $266 \Omega$. The $U_{50\%}$ of the line insulators is $80 \mathrm{kV}$. What should be the capacitance value installed on the busbar to ensure that the rise rate of the impulse voltage on the busbar does not exceed $5 \mathrm{kV} / \mu\mathrm{s}$?

Options:
A. $$
<0. 0 5 0 \mu\mathrm{F}
$$
B. $$
\ge0. 0 4 1 \mu\mathrm{F}
$$
C. $$
\ne0. 0 8 8 \mu\mathrm{F}
$$
D. $$
\ge0. 0 7 7 \mu\mathrm{F}
$$
E. $$
<0. 0 2 4 \mu\mathrm{F}
$$
F. $$
\ne0. 0 3 2 \mu\mathrm{F}
$$
G. $$
\ne0. 0 9 1 \mu\mathrm{F}
$$
H. $$
\leq0. 0 6 9 \mu\mathrm{F}
$$
I. $$
\ge0. 0 1 5 \mu\mathrm{F}
$$
J. $$
>0. 1 0 5 \mu\mathrm{F}
$$
Answer: B