MikaStars39/nano-eval huggingface dataset:
Under a total pressure of 101.3 kPa and a temperature of 273 K, component A diffuses from the gas phase bulk through a gas film with a thickness of 0.015 m to the surface of the catalyst, where an instantaneous chemical reaction A→3B occurs. The resulting gas B leaves the catalyst surface and diffuses through the gas film back into the gas phase bulk. It is known that the partial pressure of component A on the gas phase bulk side of the gas film is 22.5 kPa, and the diffusion coefficient of component A in component B is 1. $8 5 \times 10^{-5} \, \mathrm{m}^{2} \, / \mathrm{s}$. Calculate the mass transfer fluxes $N_{\mathrm{A}}$ and $N_{\mathrm{B}}$ for components A and B.

Options:
A. $$
N_{\mathrm{A}}=1. 0 3 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 1 0 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
B. $$
N_{\mathrm{A}}=0. 9 8 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-2. 9 5 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
C. $$
N_{\mathrm{A}}=1. 0 2 2 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 0 6 6 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
D. $$
N_{\mathrm{A}}=1. 0 1 2 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 0 3 6 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
E. $$
N_{\mathrm{A}}=0. 9 9 9 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-2. 9 9 7 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
F. $$
N_{\mathrm{A}}=1. 5 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-4. 5 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
G. $$
N_{\mathrm{A}}=1. 1 5 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 4 5 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
H. $$
N_{\mathrm{A}}=1. 2 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 6 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
I. $$
N_{\mathrm{A}}=1. 1 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 3 0 0 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
J. $$
N_{\mathrm{A}}=1. 0 0 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \, ; \; \; N_{\mathrm{B}}=-3. 0 1 5 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
Answer: D
At 101.3 kPa and 27°C, acetone vapor mixed in the air is absorbed using clean water in a plate column. The mixed gas flow rate is 30 kmol/h, and the volume fraction of acetone is 0.01, with an absorbent flow rate of 100 kmol/h. If the required acetone recovery rate is no less than 95% (under operating conditions, the gas-liquid equilibrium relationship is $Y_{\mathrm{e}} = 2.53X$), calculate the required number of theoretical stages.

Options:
A. 9.612
B. 7.034
C. 6.101
D. 8.245
E. 4.731
F. 10.559
G. 5.879
H. 3.906
I. 7.482
J. 5.366
Answer: C
A saturated soil sample was tested, with a measured wet soil mass of $185 \mathbf{g}$, a dry soil mass of $145 \mathbf{g}$, and a volume of $100 \mathrm{cm}^{3}$. The relative density of the soil particles is $d_{s}=2.70$. If the soil sample is compacted so that $\rho_{\mathrm{d}} = 1.65 \mathrm{g/cm}^{3}$, calculate how much the void ratio of the soil sample decreases.

Options:
A. $$
0. 2 2 1
$$
B. $$
0. 2 4 5
$$
C. $$
0. 2 0 9
$$
D. $$
0. 2 5 5
$$
E. $$
0. 1 8 7
$$
F. $$
0. 2 3 0
$$
G. $$
0. 1 9 0
$$
H. $$
0. 1 9 5
$$
I. $$
0. 2 0 2
$$
J. $$
0. 2 1 8
$$
Answer: I
A 12-meter thick saturated clay layer is subjected to an infinite uniformly distributed load of $P_{0}=140 \, \mathrm{kPa}$. The initial void ratio of the clay layer is $e_{1}=0.90$, the compression coefficient is $\alpha=0.4 \, \mathrm{MPa}^{-1}$, the compression modulus is $E_{s}=5.2 \, \mathrm{MPa}$, and the permeability coefficient is $k=1.8 \, \mathrm{cm/a}$. It has drainage on both sides. Calculate the ground settlement after one year of loading.($C_{\mathrm{v}} = \frac{k ( 1 + e_{1})}{\alpha\gamma_{\mathrm{w}}}$, $U_{t}=1-{\frac{8}{\pi^{2}}} \mathrm{e}^{-{\frac{\pi^{2}}{4}} T_{v}}$)

Options:
A. $$
1 8 9 . 7 6 {\mathrm{m m}}
$$
B. $$
1 6 4 . 5 6 {\mathrm{m m}}
$$
C. $$
2 0 1 . 4 2 {\mathrm{m m}}
$$
D. $$
1 6 1 . 0 5 {\mathrm{m m}}
$$
E. $$
1 8 2 . 1 1 {\mathrm{m m}}
$$
F. $$
1 9 5 . 8 3 {\mathrm{m m}}
$$
G. $$
1 5 3 . 4 2 {\mathrm{m m}}
$$
H. $$
1 7 4 . 6 8 {\mathrm{m m}}
$$
I. $$
1 6 9 . 9 0 {\mathrm{m m}}
$$
J. $$
1 7 7. 3 7 {\mathrm{m m}}
$$
Answer: J
A retaining wall has a height of $H = 5 \mathrm{m}$. The back of the wall is smooth and vertical, and the backfill soil is level and consists of dry sand. The unit weight of the sand is $\gamma = 19 \mathrm{kN/m^{3}}$, and the internal friction angle is $\varphi = 30^{\circ}$. There is a surcharge of $15 \mathrm{kN/m^{2}}$ on the surface of the backfill soil. Calculate the magnitude of the active earth pressure $E_{a}$ acting on the retaining wall is__.

Options:
A. $$
1 1 0. 5 \mathrm{k N / m}
$$
B. $$
1 0 3. 1 \mathrm{k N / m}
$$
C. $$
9 5. 4 \mathrm{k N / m}
$$
D. $$
9 8. 7 \mathrm{k N / m}
$$
E. $$
9 2. 6 \mathrm{k N / m}
$$
F. $$
1 0 0. 3 \mathrm{k N / m}
$$
G. $$
9 6. 8 \mathrm{k N / m}
$$
H. $$
1 0 5. 2 \mathrm{k N / m}
$$
I. $$
1 1 3. 3 \mathrm{k N / m}
$$
J. $$
1 0 7. 9 \mathrm{k N / m}
$$
Answer: B
The independent foundation under the column has a burial depth of $d = 1.8 \, \mathrm{m}$ and is subjected to an axial load of $F_{\mathrm{k}} = 2400 \, \mathrm{kN}$. The bearing soil layer is cohesive soil with $\gamma = 18 \, \mathrm{kN/m}^{3}$, $f_{\mathrm{ak}} = 150 \, \mathrm{kPa}$, $\eta_{\mathrm{b}} = 0.3$, and $\eta_{\mathrm{d}} = 1.6$. Determine the length of the base edge of this foundation is__.

Options:
A. 4m
B. 4.5m
C. 8m
D. 2.5m
E. 3m
F. 5m
G. 3.5m
H. 5.5m
I. 7m
J. 6m
Answer: A
In a seismic zone with an intensity of $8$, sand needs to be compacted to a relative density $D_{r}=0.7$ or higher. Tests show that the maximum dry density of sand from a certain site is $\rho_{\mathrm{dmax}}=1.96 \mathrm{g/cm}^{3}$ and the minimum dry density is $\rho_{\mathrm{dmin}}=1.46 \mathrm{g/cm}^{3}$. What dry density must this sand be compacted to in order to meet seismic requirements? (Specific gravity of sand $G_{s}=2.65$.)

Options:
A. $$
1. 6 7 \mathrm{g / c m}^{3}
$$
B. $$
1. 6 9 \mathrm{g / c m}^{3}
$$
C. $$
1. 8 0 \mathrm{g / c m}^{3}
$$
D. $$
1. 8 2 \mathrm{g / c m}^{3}
$$
E. $$
1. 8 3 \mathrm{g / c m}^{3}
$$
F. $$
1. 7 8 \mathrm{g / c m}^{3}
$$
G. $$
1. 8 1 \mathrm{g / c m}^{3}
$$
H. $$
1. 7 4 \mathrm{g / c m}^{3}
$$
I. $$
1. 7 5 \mathrm{g / c m}^{3}
$$
J. $$
1. 7 6 \mathrm{g / c m}^{3}
$$
Answer: F
The average energy loss rate of an ultra-relativistic $\mu$ meson when passing through $x \ \mathrm{g m} \cdot \mathrm{c m}^{-2}$ in material is given by the formula $\mathrm{d} E / \mathrm{d} x = a + b E$, where $a = 2.5 \ \mathrm{MeV \cdot gm^{-1} \cdot cm^{2}}$ is the ionization loss rate, and the second term represents the radiative energy loss. Calculate the average range of a 5000 GeV $\mu$ meson in rock with a density of 3 $\mathrm{g m} \cdot \mathrm{c m}^{-3}$, where the critical energy for the $\mu$ meson is $1000 \ \mathrm{GeV}$.

Options:
A. 4.6km
B. 3.8km
C. 1.1km
D. 5.1km
E. 5.2km
F. 2.4km
G. 6.3km
H. 1.7km
I. 2.9km
J. 0.9km
Answer: F
$A B$ and $C D$ are two identical rods, each with a mass of $m$ and a length of $l$. A rope is tightly stretched between $E F$ with $A E = D F = l / n$. The ground is smooth.What is the tension in the rope and the forces acting on the ends of the rods ?

Options:
A. $T=\frac{gMl\tan\alpha}{(2m-n)}$
B. $T=\frac{(M+n)m\sin\alpha}{2g}$
C. $T=\frac{mlg\tan\beta}{(2n-M)}$
D. $T=\frac{2Mgl\cos\theta}{(n-m)}$
E. $T=\frac{Mng\sin\alpha}{l(2-m)}$
F. $T=\frac{mng\cos\beta}{l(M-2)}$
G. $T=\frac{nml\sin\theta}{2(M-g)}$
H. $T=\frac{(M+m)ng\cot\alpha}{2(n-1)}$
I. $T=\frac{Ml\sin\beta}{n(2-m)}$
J. $T=\frac{2mgn\sin\theta}{(M-l)}$
Answer: H
The reducer consists of a fixed gear 1, two internally meshing gears 2 and 3 consolidated into one piece, and a gear 4 affixed to the driven shaft. The number of teeth on each gear is known to be $z_{1}=30$, $z_{2}=80$, $z_{3}=70$, $z_{4}=20$, and the driving shaft rotates at an angular speed of $n_{I}=1200 \ r/\mathrm{min}$.What is the rotational speed of the driven shaft ?

Options:
A. $$
n_{I I}=-4 2 0 ~ \mathrm{r} / \mathrm{m i n}.
$$
B. $$
n_{I I}=-4 0 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
C. $$
n_{I I}=-3 8 0 ~ \mathrm{r} / \mathrm{m i n}.
$$
D. $$
n_{I I}=-3 1 0 ~ \mathrm{r} / \mathrm{m i n}.
$$
E. $$
n_{I I}=-3 7 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
F. $$
n_{I I}=-3 9 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
G. $$
n_{I I}=-4 1 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
H. $$
n_{I I}=-3 0 0 ~ \mathrm{r} / \mathrm{m i n}.
$$
I. $$
n_{I I}=-2 8 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
J. $$
n_{I I}=-3 2 5 ~ \mathrm{r} / \mathrm{m i n}.
$$
Answer: E
A particle with mass $m$ falls to the ground without an initial velocity. What is its equation of motion? The air resistance is proportional to the square of the velocity, with a proportionality coefficient equal to $k$.

Options:
A. $$
x=\frac{m} {g} \operatorname{a r c t a n} \sqrt{\frac{k g} {m}} t.
$$
B. $$
x=\frac{g} {m} \operatorname{l n} \operatorname{s i n} \sqrt{\frac{k m} {g}} t.
$$
C. $$
x=\frac{g} {k} \operatorname{l n} \operatorname{t a n h} \sqrt{\frac{m k} {g}} t.
$$
D. $$
x=\frac{m} {k} \operatorname{l n} \operatorname{c o s h} \sqrt{\frac{g k} {m}} t.
$$
E. $$
x=\frac{k} {m} \operatorname{a r c c o s} \sqrt{\frac{g m} {k}} t.
$$
F. $$
x=\frac{g} {m} \operatorname{a r c s i n} \sqrt{\frac{k m} {g}} t.
$$
G. $$
x=\frac{k} {g} \operatorname{l n} \operatorname{c o s h} \sqrt{\frac{m g} {k}} t.
$$
H. $$
x=\frac{k} {m} \operatorname{l n} \operatorname{s i n h} \sqrt{\frac{g m} {k}} t.
$$
I. $$
x=\frac{m} {k} \operatorname{l n} \operatorname{s i n} \sqrt{\frac{g k} {m}} t.
$$
J. $$
x=\frac{g} {k} \operatorname{l n} \operatorname{c o s h} \sqrt{\frac{m k} {g}} t.
$$
Answer: D
In a discharge tube, single-charged bromine ions are obtained and accelerated under a potential difference of 10,000 volts before entering a magnetic field with a strength of 12,000 Oersteds, perpendicular to the electric field. Calculate the linear separation of bromine isotopes with mass numbers 79 and 81 after they are deflected by 180° in the magnetic field.

Options:
A. 0.226 cm
B. 0.246 cm
C. 0.286 cm
D. 0.256 cm
E. 0.206 cm
F. 0.266 cm
G. 0.216 cm
H. 0.196 cm
I. 0.276 cm
J. 0.236 cm
Answer: J
The plateau slope of the Geiger-Müller counter tube is 5%, with a plateau length of 250 volts. When the operating voltage is higher than or at 175 volts, compared to higher than or at 50 volts, by how much does the count rate increase?

Options:
A. 2.5%
B. 6.5%
C. 1.0%
D. 7.0%
E. 3.0%
F. 3.5%
G. 5.0%
H. 4.0%
I. 1.5%
J. 0.5%
Answer: A
The energy released by the K$^{42}$ nucleus is 3.5 million electron volts of $\beta$ particles hitting a thin-walled Geiger-Müller counter tube with a diameter of 20 millimeters. If the $\beta$ particles penetrate the counter tube vertically, how many pairs of ions will be produced in the gas within the counter tube? (The partial pressure of hydrogen in the tube is 100 mmHg) .

Options:
A. 19 pairs.
B. 22 pairs.
C. 30 pairs.
D. 12 pairs.
E. 26 pairs.
F. 18 pairs.
G. 28 pairs.
H. 15 pairs.
I. 20 pairs.
J. 24 pairs.
Answer: I
Move the 25-curie cobalt source from the storage location along the unprotected transport track to the container waiting for irradiation. If the control station is 2 meters away from the transport track and the transfer takes 3 minutes, how much should the shielding material reduce the physical dose rate to ensure safe operation during the transfer of $\mathrm{Co}^{60}$?

Options:
A. 8 times
B. 4 times
C. 8.5 times
D. 6 times
E. 5 times
F. 12 times
G. 8.4 time
H. 7 times
I. 3 times
J. 9 times
Answer: A
In a sealed ampoule containing 1 curie of radium with a volume of 100 milliliters, how much time will it take for the pressure to double? Assume that the initial pressure inside the ampoule is 1 atmosphere.

Options:
A. 600 years
B. 980 years
C. 1000 years
D. 432 years
E. 890 years
F. 534 years
G. 750 years
H. 700 years
I. 267 years
J. 320 years
Answer: F
Ten hours after irradiation ceased, the radioactivity of the sample in which Ba$^{140}$ and its decay product La$^{140}$ coexist is $2 \times 10^{3}$ counts per minute. Assuming the counting efficiencies of Ba$^{140}$ and La$^{140}$ are the same, calculate the counting rate of the Ba$^{140}$ sample immediately after irradiation stopped.

Options:
A. 1830 pulses/minute
B. 1600 pulses/minute
C. 1455 pulses/minute
D. 1890 pulses/minute
E. 2100 pulses/minute
F. 1645 pulses/minute
G. 1983 pulses/minute
H. 1572 pulses/minute
I. 2020 pulses/minute
J. 1764 pulses/minute
Answer: J
In a cyclotron, P$^{32}$ is prepared via the P$^{31}$(d,p)P$^{32}$ reaction. When deuterons are used to bombard for 100 hours with a current intensity of 10 microamperes, the ion utilization coefficient in this nuclear reaction is proportional to the effective cross-section, and the production yield is $3×10^4$. Determine the radioactivity of the P$^{32}$ preparation (how many times per minute does β decay occur?).

Options:
A. $$
1.2 \cdot 10^{11} \, \beta \text{ particles/min}
$$
B. $$
3.5 \cdot 10^{11} \, \beta \text{ particles/min}
$$
C. $$
1.7 \cdot 10^{11} \, \beta \text{ particles/min}
$$
D. $$
2.9 \cdot 10^{11} \, \beta \text{ particles/min}
$$
E. $$
1.5 \cdot 10^{11} \, \beta \text{ particles/min}
$$
F. $$
2.2 \cdot 10^{11} \, \beta \text{ particles/min}
$$
G. $$
4.0 \cdot 10^{11} \, \beta \text{ particles/min}
$$
H. $$
2.7 \cdot 10^{11} \, \beta \text{ particles/min}
$$
I. $$
3.1 \cdot 10^{11} \, \beta \text{ particles/min}
$$
J. $$
2.0 \cdot 10^{11} \, \beta \text{ particles/min}
$$
Answer: F
If the total amount of lead ions in the solution is 10 $^{20}$, the radioactivity of the solution is 1000 counts/min, and the radioactivity on the surface of the precipitate is 10 $^{6}$ counts/min, find the surface area of Pb$^{2+}$ in the solution containing P. It is known that the effective surface area occupied by one atom can be expressed by the following formula:
$s=[M/(a∙N∙P)]^{2/3}$
where M is the molecular weight, a is the number of gram-atoms of the atom in 1 gram-molecule of solid substance, N is Avogadro's number, and P is the density.

Options:
A. 2.10 $\cdot 10^{4}$$cm^{2}$
B. 8.07 $\cdot 10^{3}$$cm^{2}$
C. 1.45 $\cdot 10^{3}$$cm^{2}$
D. 4.11 $\cdot 10^{4}$$cm^{2}$
E. 9.23 $\cdot 10^{3}$$cm^{2}$
F. 1.32 $\cdot 10^{2}$$cm^{2}$
G. 6.67 $\cdot 10^{2}$$cm^{2}$
H. 3.25 $\cdot 10^{5}$$cm^{2}$
I. 7.98 $\cdot 10^{1}$$cm^{2}$
J. 5.64 $\cdot 10^{2}$$cm^{2}$
Answer: C
Add heavy water with a total radioactivity of 200 curies to an underground well. Three years later, take water samples from this area and measure using a gas-filled counting tube; the radioactivity is 10 pulses per minute higher than the background. Given that the volume of the counting tube is 200 cm $^{3}$, and the tritium in the water is introduced into the tube in the form of hydrogen gas, with a pressure of 10 mmHg and a counting efficiency of 100%, calculate: What is the storage capacity of the groundwater?

Options:
A. 90,000 tons
B. 95,000 tons
C. 55,000 tons
D. 100,000 tons
E. 85,000 tons
F. 60,000 tons
G. 80,000 tons
H. 65,000 tons
I. 70,000 tons
J. 75,000 tons
Answer: G
The spectral term $2 \mathrm{D} \frac{3}{2}$ of the $^{209}Bi$ atom has a hyperfine splitting with 4 components, and the ratio of the intervals between adjacent components is $4 : 5 : 6$. Find the spin quantum number of this atomic nucleus is____.

Options:
A. $$
\frac{1} {2}
$$
B. $$
\frac{13} {2}
$$
C. $$
\frac{12} {2}
$$
D. $$
\frac{15} {2}
$$
E. $$
\frac{7} {2}
$$
F. $$
\frac{5} {2}
$$
G. $$
\frac{3} {2}
$$
H. $$
\frac{9} {2}
$$
I. $$
\frac{8} {2}
$$
J. $$
\frac{11} {2}
$$
Answer: H
The neutrons in the nucleus are in the $2 \mathbf{f}_{7 / 2}$ state, with the maximum number of neutrons that can be filled in this state being _____.

Options:
A. $$
8
$$
B. $$
14
$$
C. $$
10
$$
D. $$
20
$$
E. $$
18
$$
F. $$
4
$$
G. $$
12
$$
H. $$
6
$$
I. $$
16
$$
J. $$
2
$$
Answer: A
Phytic acid is ().

Options:
A. Nucleotide sequences coding for mitochondrial proteins
B. Protein subunits forming aquatic vertebrate scales
C. Ionic compounds embedding cellular chloroplasts
D. Hydrolytic enzymes secreted by bacterial spores
E. Polymeric aldehydes binding to protein receptors
F. Storage macromolecules in eukaryotic cell nuclei
G. Complex lipids present in fungal cell membranes
H. Acidic polysaccharides found in plant photosynthesis cells
I. Lipid bilayers in animal nerve tissue membranes
J. Cell wall components of Gram-positive bacteria
Answer: J
A high-voltage single-core cable is 20 meters long, with $\tan\delta_{2}=0.005$ and $\varepsilon_{r}=3.8$. Currently, 1 meter of it has partial damage, and the $\tan\delta$ at that section has increased to 0.05, denoted as $\tan\delta_1$. The $\varepsilon_{r}$ remains essentially unchanged. What should the $\tan\delta_{2}$ of the cable be at this time?

Options:
A. $$\tan\delta=0.046$$
B. $$\tan\delta=0.047$$
C. $$\tan\delta=0.053$$
D. $$\tan\delta=0.049$$
E. $$\tan\delta=0.052$$
F. $$\tan\delta=0.045$$
G. $$\tan\delta=0.044$$
H. $$\tan\delta=0.050$$
I. $$\tan\delta=0.051$$
J. $$\tan\delta=0.048
$$
Answer: J
An overhead transmission line $\mathrm{A}$, with a wave impedance $Z_{1}=500\, \Omega$, is connected via a cable with a wave impedance $Z_{0}=50\, \Omega$ to another overhead line $\mathrm{B}$ with a wave impedance $Z_{2}=400\, \Omega$. An infinite length rectangular wave with amplitude $U = 100\, \mathrm{kV}$ travels along line $\mathrm{A}$. What is the voltage at point O, where line $\mathrm{A}$ connects with the cable, after 2 reflections?

Options:
A. $$
4 3. 0\mathrm{k V}
$$
B. $$
5 1. 5\mathrm{k V}
$$
C. $$
4 8. 9\mathrm{k V}
$$
D. $$
5 2. 0\mathrm{k V}
$$
E. $$
3 5. 5\mathrm{k V}
$$
F. $$
4 4. 8\mathrm{k V}
$$
G. $$
4 1. 3\mathrm{k V}
$$
H. $$
4 0. 0\mathrm{k V}
$$
I. $$
4 5. 1\mathrm{k V}
$$
J. $$
3 9. 7\mathrm{k V}
$$
Answer: G
For a $330 \mathrm{kV}$ line with a total length of $540 \mathrm{km}$, the positive sequence impedance is $Z_{1}=310 \Omega$, and the zero sequence impedance is $Z_{0} = 660 \Omega$. The positive sequence wave velocity is $v_{1} = 3 \times 10^{5} \, \mathrm{km/s}$, and the zero sequence wave velocity is $v_{0}=2/3 \, v_{1}$. Given that the power source voltage is $E$, and assuming a single-phase grounding occurs at the midpoint of phase $\mathrm{A}$ on a no-load line, what is the increase in voltage at the non-fault phase at the end of the line?

Options:
A. $$ 3. 5 2 E $$
B. $$ 2. 8 3 E $$
C. $$ 0. 9 4 E $$
D. $$
1. 2 8 E
$$
E. $$ 8. 0 9 E $$
F. $$ 9. 3 0 E $$
G. $$ 6. 4 2 E $$
H. $$ 5. 1 7 E $$
I. $$ 1. 7 5 E $$
J. $$ 4. 6 1 E $$
Answer: D
A certain $500 \mathrm{kV}$ line is $400 \mathrm{km}$ long, $\sin \lambda = 0.41$. The line surge impedance is $Z = 260 \Omega$. The line is open-circuited at the end with no parallel reactor. The ratio of the steady-state power frequency voltage at the line end to the source voltage is $\beta = 1.2$. It is required to limit the switching overvoltage factor $K \leq 2.0$. What is the resistance value $R$ of the resistor in parallel with the circuit breaker?

Options:
A. $$ 730~\Omega
$$
B. $$ 560~\Omega
$$
C. $$ 670~\Omega
$$
D. $$ 710~\Omega
$$
E. $$ 840~\Omega
$$
F. $$ 880~\Omega
$$
G. $$ 920~\Omega
$$
H. $$ 788~\Omega
$$
I. $$ 900~\Omega
$$
J. $$ 640~\Omega
$$
Answer: H
A certain high-voltage laboratory's power frequency test transformer's rated voltage is 500kV, with a high-voltage lead 4m above the ground. To prevent corona discharge, what should be the radius of the lead (considering a surface roughness factor of $0.7 \sim 0.8$)?

Options:
A. $$11~cm$$
B. $$10~cm$$
C. $$4~cm$$
D. $$15~cm$$
E. $$6~cm$$
F. $$17~cm$$
G. $$8~cm$$
H. $$3~cm$$
I. $$9~cm$$
J. $$12~cm$$
Answer: E
Under atmospheric conditions of $p=99.5 \text{kPa}$, a dry-bulb temperature of 30°C, and a wet-bulb temperature of 27.5°C, the 50% breakdown voltage of a rod-to-plate gap under positive standard lightning impulse voltage is measured to be 540 kV. What will its breakdown voltage be under standard conditions?

Options:
A. $$
4 9 4. 3 7 k V
$$
B. $$
5 2 0. 8 1 k V
$$
C. $$
5 1 4. 9 5 k V
$$
D. $$
5 2 1. 4 5 k V
$$
E. $$
5 3 0. 7 1 k V
$$
F. $$
5 1 7. 8 8 k V
$$
G. $$
5 0 1. 5 2 k V
$$
H. $$
5 2 8. 0 3 k V
$$
I. $$
5 3 2. 9 6 k V
$$
J. $$
5 0 3. 6 4 k V
$$
Answer: A
The dielectric between certain coaxial cylindrical electrodes is $\mathrm{SF}_{6}$ gas, and its breakdown field strength $E_{\mathrm{b}}$ follows a Gumbel distribution, with distribution parameters $\eta\!=\! 177 \mathrm{kV/cm}, \ \gamma\!=\! 5.67 \mathrm{kV/cm}$. If the electrode length is increased by 100 times, what is the reduction ratio of the withstand field strength?

Options:
A. $$
7 6. 2 2 \%
$$
B. $$
3 4. 9 5 \%
$$
C. $$
2 9. 8 1 \%
$$
D. $$
1 6. 9 2 \%
$$
E. $$
5 0. 4 8 \%
$$
F. $$
4 5. 0 0 \%
$$
G. $$
3 8. 1 4 \%
$$
H. $$
4 8. 5 6 \%
$$
I. $$
2 0. 3 7 \%
$$
J. $$
6 1. 7 2 \%
$$
Answer: D
A bubble of air has mixed into mercury barometer A, causing its reading to be lower than the actual atmospheric pressure. When the accurate barometer reading is 0.102 MPa, its reading is only 0.0997 MPa, and the distance from the surface of the mercury inside the tube to the top of the tube is 80 mm. What should the actual atmospheric pressure be when this barometer reads 0.0978 MPa?
( Assume the temperature of the air remains constant. )

Options:
A. $$
p=0. 1 0 1 0 \mathrm{~ M P a}
$$
B. $$
p=0. 0 9 8 5 \mathrm{~ M P a}
$$
C. $$
p=0. 0 9 9 7 \mathrm{~ M P a}
$$
D. $$
p=0. 1 0 3 5 \mathrm{~ M P a}
$$
E. $$
p=0. 0 9 5 3 \mathrm{~ M P a}
$$
F. $$
p=0. 1 0 2 9 \mathrm{~ M P a}
$$
G. $$
p=0. 0 9 4 7 \mathrm{~ M P a}
$$
H. $$
p=0. 0 9 6 9 \mathrm{~ M P a}
$$
I. $$
p=0. 0 9 2 9 \mathrm{~ M P a}
$$
J. $$
p=0. 1 0 0 2 \mathrm{~ M P a}
$$
Answer: C
Under low temperature conditions, the walls of a vacuum container can adsorb gas molecules, a process known as "cryopumping." It is a simple method to improve vacuum levels. Consider a spherical container with a radius of 0.1 m, where a 1 cm² area on the container wall is cooled to the temperature of liquid nitrogen (77 K), while the rest of the container remains at 300 $\mathbf{K}$. Initially, the water vapor pressure inside the container is 1.3 Pa. Assume that every water molecule hitting this small area can be adsorbed or condensed onto it. How much time is required to reduce the pressure in the container to 1.3 x $10^{-4}$ Pa?

Options:
A. $$9.85s$$
B. $$4.75s$$
C. $$8.30s$$
D. $$2.60s$$
E. $$5.90s$$
F. $$3.40s$$
G. $$7.15s$$
H. $$1.25s$$
I. $$6.05s$$
J. $$0.50s$$
Answer: D
The inner layer outer diameter of the Dewar flask's interlayer is 10.0 cm, and the inner diameter of the outer layer is $10.6 \ \mathrm{cm}$. The flask contains a mixture of ice and water, and the room temperature outside the flask is 25 $\mathbf{°C}$. The Dewar flask's height is 24.0 cm. If the interlayer is filled with nitrogen gas at 10° Pa, approximately estimate the amount of heat flowing into the Dewar flask per second due to thermal conduction by the gas.
( Take the effective diameter of nitrogen molecule as $3.1 \times 10^{-10} \mathrm{~m}$. )

Options:
A. $$
\bf1 2. 1 ~ {\bf J}
$$
B. $$
\bf16.3~{\bf w}
$$
C. $$
\bf17.8~{\bf w}
$$
D. $$
\bf9.2~{\bf w}
$$
E. $$
\bf13.4~{\bf w}
$$
F. $$
\bf2.5~{\bf w}
$$
G. $$
\bf18.6~{\bf w}
$$
H. $$
\bf15.7~{\bf w}
$$
I. $$
\bf10.9~{\bf w}
$$
J. $$
\bf14.0~{\bf w}
$$
Answer: A
A $1 \mathrm{~m}^{3}$ adiabatic container is filled with air at the same pressure as the standard atmospheric pressure outside, but the wall of the container has a crack. If the container is slowly heated from 0°C to 20°C, how much heat is absorbed by the gas?
( Given that the specific heat capacity of air at constant pressure is $c_{p}=0.99 \mathrm{~kJ ~} \cdot \mathrm{~kg}^{-1} \cdot \mathrm{~K}^{-1}$, the molar mass of air is $M=0.029 \mathrm{~kg} \cdot \mathrm{~mol}^{-1}$, and the heat capacity ratio $\gamma=1.41$. )

Options:
A. $$3.5kJ$$
B. $$6.3kJ$$
C. $$5.8kJ$$
D. $$5.2kJ$$
E. $$4.2kJ$$
F. $$4.0kJ$$
G. $$4.7kJ$$
H. $$3.1kJ$$
I. $$2.9kJ$$
J. $$6.0kJ$$
Answer: G
Hydrogen can be divided into orthohydrogen (with two proton spins oriented parallel to each other) and parahydrogen (with two proton spins oriented anti-parallel to each other) based on the different orientations of the two proton spins. Parahydrogen molecules have one spin state, while orthohydrogen molecules have three spin states. At the temperature of liquid hydrogen (20 K), all molecules are parahydrogen, whereas at room temperature, hydrogen is randomly distributed among the four spin states of orthohydrogen and parahydrogen. Now, if 1 mol of parahydrogen is taken out from a liquid hydrogen container and placed into a 300 $\mathbf{K}$ room, it will slowly and irreversibly transform into hydrogen with four spin states. What is the total change in entropy?

Options:
A. $$8.30R$$
B. $$6.90R$$
C. $$13.00R$$
D. $$14.22R$$
E. $$12.15R$$
F. $$10.87R$$
G. $$5.75R$$
H. $$7.65R$$
I. $$11.45R$$
J. $$9.56R$$
Answer: F
Combine equal volume copper and aluminum blocks, with temperatures $T_{1}=273 \; \mathrm{K}$ and $T_{2}=373 \; \mathrm{K}$ respectively, ensuring that they do not exchange heat with the surroundings. If the densities of copper and aluminum are $\rho_{1}=8.5 \times 10^{3} \; \mathrm{kg/m}^{3}$ and $\rho_{2}=2.6 \times 10^{3} \; \mathrm{kg/m}^{3}$ respectively, and their specific heat capacities are $c_{1}=376 \; \mathrm{J/(kg \cdot K)}$ and $c_{2}=920 \; \mathrm{J/(kg \cdot K)}$ respectively, what is the relative change in their total volume when they reach thermal equilibrium ?

Options:
A. $$
- 5. 5 \times1 0^{-3}
$$
B. $$
- 7. 9 \times1 0^{-4}
$$
C. $$
- 1. 1 \times1 0^{-4}
$$
D. $$
- 8. 9 \times1 0^{-4}
$$
E. $$
- 4. 6 \times1 0^{-2}
$$
F. $$
- 2. 7 \times1 0^{-3}
$$
G. $$
- 3. 2 \times1 0^{-4}
$$
H. $$
- 6. 8 \times1 0^{-2}
$$
I. $$
- 1. 3 \times1 0^{-5}
$$
J. $$
- 9. 5 \times1 0^{-4}
$$
Answer: D
A spherical soap bubble, which is filled with air, the air quality is not counted, the bubble is a vacuum, its radius is $r_0$ when equilibrium, due to the disturbance, the soap bubble does a small radial expansion, contraction vibration. What is its vibration period ?
( The quality and surface strength coefficient of the soap bubble are known to be $m$ and $\sigma$ respectively, and the air temperature in the bubble remains unchanged during the vibration process. )

Options:
A. $$
\frac{\sigma}{\sqrt{8 \pi m}}$$
B. $$
\sqrt{\frac{8 m} {\pi \sigma}}$$
C. $$
\sqrt{\frac{\pi m} {8 \sigma}}
$$
D. $$
\sqrt{\frac{8 \sigma} {\pi m}}$$
E. $$
\frac{8 \sigma}{\sqrt{\pi m}}$$
F. $$
\sqrt{\frac{\pi \sigma} {8 m}}$$
G. $$
\sqrt{\frac{m^2 \pi} {8 \sigma}}$$
H. $$
\sqrt{\frac{8 \pi \sigma }{m}}$$
I. $$
\frac{m}{\sqrt{8 \pi \sigma}}$$
J. $$
\pi \sqrt{\frac{8 m}{ \sigma}}$$
Answer: C
The natural frequency of a one-degree-of-freedom mechanical vibration system is 15 $\mathbf{k} \mathbf{Hz}$, with a mass of $0.1 \ g$. If the effective value of the external force applied to the system is 100 dyne, what is the amplitude of the vibration velocity when the frequency is 100 Hz?

Options:
A. $$
y_{\mathrm{m}} \ =\ 7 0^{-4} \ \mathrm{m / s_{}}
$$
B. $$
u_{\mathrm{m}} \ =\ 5 0^{-4} \ \mathrm{m / s_{}}
$$
C. $$
u_{\mathrm{n}} \ =\ 4 0^{-4} \ \mathrm{m / s_{}}
$$
D. $$
u_{\mathrm{m}} \ =\ 9 0^{-4} \ \mathrm{m / s_{}}
$$
E. $$
w_{\mathrm{m}} \ =\ 3 0^{-4} \ \mathrm{m / s_{}}
$$
F. $$
u_{\mathrm{p}} \ =\ 1 0^{-2} \ \mathrm{m / s_{}}
$$
G. $$
v_{\mathrm{m}} \ =\ 2 0^{-4} \ \mathrm{m / s_{}}
$$
H. $$
z_{\mathrm{m}} \ =\ 8 0^{-4} \ \mathrm{m / s_{}}
$$
I. $$
x_{\mathrm{m}} \ =\ 6 0^{-4} \ \mathrm{m / s_{}}
$$
J. $$
u_{\mathrm{m}} \ =\ 1 0^{-4} \ \mathrm{m / s_{}}
$$
Answer: J
A steel wire with a length of 1 m and a cross-sectional area of $1.0 \times 10^{-5} \mathrm{~m}^{2}$ has a mass block of $2.0 \ \mathrm{kg}$ attached to its lower end. If the system is considered as a simple harmonic oscillator, what is the fundamental frequency of the vertical vibration of the mass block? When the system is considered as a rod fixed at one end with a mass block at the other, what is the fundamental frequency of the system's free longitudinal vibration? Prove that when $k L < 0.2$, the fundamental frequency can be simplified to $\omega_{0}=\sqrt{\frac{s}{m}}$, where $s$ is the elastic constant?

Options:
A. $f_{0} \;=\; 128 \; \mathrm{Hz} \, ;$ given $\operatorname{sin} ( k L ) \,=\, 14 k L {\Rightarrow} f_{0} \, \circ$
B. $f_{0} \;=\; 176 \; \mathrm{Hz} \, ;$ given $\operatorname{tan} ( k L ) \,=\, 26 k L {\Rightarrow} f_{0} \, \circ$
C. $f_{0} \;=\; 134 \; \mathrm{Hz} \, ;$ given $\operatorname{cot} ( k L ) \,=\, 16 k L {\Rightarrow} f_{0} \, \circ$
D. $f_{0} \;=\; 160 \; \mathrm{Hz} \, ;$ given $\operatorname{sec} ( k L ) \,=\, 30 k L {\Rightarrow} f_{0} \, \circ$
E. $f_{0} \;=\; 170 \; \mathrm{Hz} \, ;$ given $\operatorname{cot} ( k L ) \,=\, 24 k L {\Rightarrow} f_{0} \, \circ$
F. $f_{0} \;=\; 150 \; \mathrm{Hz} \, ;$ given $\operatorname{cot} ( k L ) \,=\, 28 k L {\Rightarrow} f_{0} \, \circ$
G. $f_{0} \;=\; 138 \; \mathrm{Hz} \, ;$ given $\operatorname{csc} ( k L ) \,=\, 20 k L {\Rightarrow} f_{0} \, \circ$
H. $f_{0} \;=\; 156 \; \mathrm{Hz} \, ;$ given $\operatorname{cot} ( k L ) \,=\, 26 k L {\Rightarrow} f_{0} \, \circ$
I. $f_{0} \;=\; 164 \; \mathrm{Hz} \, ;$ given $\operatorname{cos} ( k L ) \,=\, 18 k L {\Rightarrow} f_{0} \, \circ$
J. $f_{0} \;=\; 142 \; \mathrm{Hz} \, ;$ given $\operatorname{tan} ( k L ) \,=\, 22 k L {\Rightarrow} f_{0} \, \circ$
Answer: H
A circular membrane has a radius of $0.01 \mathrm{~m}$, a surface density of $0.20 \ \mathrm{kg/m}^{2}$, and a tension of 4000 N/m. When it vibrates at its fundamental frequency, the displacement amplitude at the center of the membrane is $0.01 \ \mathrm{cm}$. Determine the following: what is the fundamental frequency? What is the maximum volume of air displaced when the circular membrane vibrates?

Options:
A. $$f=4.20kHz; 1.10\times10^{-2}cm^{3}$$
B. $$f=5.42kHz; 1.36 \times1 0^{-2}cm^{3}$$
C. $$f=4.50kHz; 1.90\times10^{-2}cm^{3}$$
D. $$f=7.00kHz; 1.36\times10^{-2}cm^{3}$$
E. $$f=6.10kHz; 1.70\times10^{-2}cm^{3}$$
F. $$f=5.10kHz; 1.80\times10^{-2}cm^{3}$$
G. $$f=6.20kHz; 1.40\times10^{-2}cm^{3}$$
H. $$f=5.00kHz; 1.50\times10^{-2}cm^{3}$$
I. $$f=5.42kHz; 2.00\times10^{-2}cm^{3}$$
J. $$f=6.50kHz; 1.20\times10^{-2}cm^{3}$$
Answer: B
What is the amplitude of temperature change caused by an 80 dB plane sound wave in air at 20°C and standard atmospheric pressure?

Options:
A. $$
3. 0 \times1 0^{-2} \mathrm{~ K}
$$
B. $$
2. 3 \times1 0^{-4} \mathrm{~ K}
$$
C. $$
1. 1 \times1 0^{-6} \mathrm{~ K}
$$
D. $$
4. 8 \times1 0^{-5} \mathrm{~ K}
$$
E. $$
8. 9 \times1 0^{-4} \mathrm{~ K}
$$
F. $$
7. 4 \times1 0^{-2} \mathrm{~ K}
$$
G. $$
1. 5 \times1 0^{-3} \mathrm{~ K}
$$
H. $$
5. 2 \times1 0^{-3} \mathrm{~ K}
$$
I. $$
6. 1 \times1 0^{-6} \mathrm{~ K}
$$
J. $$
9. 7 \times1 0^{-5} \mathrm{~ K}
$$
Answer: B
A plane sound wave is incident perpendicularly on the boundary plane between air and an infinite fluid with unknown characteristic impedance. If it is known that half of the sound energy is reflected, find the unknown characteristic impedance. If $\frac{1}{4}$ of the energy is reflected, what is the unknown characteristic impedance?

Options:
A. $$
74.0 \mathrm{~ Rayl.} \,, 131.8 \mathrm{~ Rayl.}
$$
B. $$
69.6 \mathrm{~ Rayl.} \,, 143.7 \mathrm{~ Rayl.}
$$
C. $$
68.5 \mathrm{~ Rayl.} \,, 145.0 \mathrm{~ Rayl.}
$$
D. $$
67.9 \mathrm{~ Rayl.} \,, 148.2 \mathrm{~ Rayl.}
$$
E. $$
69.2 \mathrm{~ Rayl.} \,, 142.1 \mathrm{~ Rayl.}
$$
F. $$
72.6 \mathrm{~ Rayl.} \,, 136.5 \mathrm{~ Rayl.}
$$
G. $$
70.8 \mathrm{~ Rayl.} \,, 140.0 \mathrm{~ Rayl.}
$$
H. $$
72.0 \mathrm{~ Rayl.} \,, 135.2 \mathrm{~ Rayl.}
$$
I. $$
71.2 \mathrm{~ Rayl.} \,, 138.3 \mathrm{~ Rayl.}
$$
J. $$
73.4 \mathrm{~ Rayl.} \,, 132.9 \mathrm{~ Rayl.}
$$
Answer: I
If a plane sound wave with a frequency of 20 kHz is required to enter steel from water without reflection, try to determine the thickness and sound speed of the intervening plastic layer (with a density of $1500 \ \mathrm{kg/m}^{3}$). If the thickness of the plastic layer is infinitely large, what is the sound intensity reflection coefficient for normally incident waves?

Options:
A. 0.34 m; 5450 m/s, 0.3
B. 0.28 m; 5558 m/s, 0.7
C. 0.26 m; 5630 m/s, 0.8
D. 0.32 m; 5520 m/s, 0.5
E. 0.30 m; 5480 m/s, 0.9
F. 0.27 m; 5570 m/s, 0.4
G. 0.31 m; 5500 m/s, 0.8
H. 0.33 m; 5535 m/s, 0.6
I. 0.29 m; 5600 m/s, 0.6
J. 0.25 m; 5605 m/s, 0.5
Answer: B
The temperature of the air inside a ventilation duct with a radius of 0.1 m is 50°C. It is desired to install a low-pass filter with a radius $a \left( \, a > 0.1 \, \mathrm{m} \, \right)$ in the middle of this duct, in order to reduce the sound intensity level of a 120 Hz plane sound wave by 13 dB. The question is: What should be the length and radius of the filter to most effectively meet the above filtering requirements? How much does this filter reduce the sound intensity level of a 60 Hz plane sound wave?

Options:
A. $$
0. 8 1 \ \mathrm{m}, 0. 1 5 \ \mathrm{m} ;\,-\, 6. 2 \ \mathrm{d B}
$$
B. $$
1. 1 0 \ \mathrm{m}, 0. 2 6 \ \mathrm{m} ;\,-\, 4. 6 \ \mathrm{d B}
$$
C. $$
0. 5 8 \ \mathrm{m}, 0. 1 8 \ \mathrm{m} ;\,-\, 8. 9 \ \mathrm{d B}
$$
D. $$
0. 7 8 \ \mathrm{m}, 0. 1 9 \ \mathrm{m} ;\,-\, 9. 1 \ \mathrm{d B}
$$
E. $$
0. 7 5 \ \mathrm{m}, 0. 2 9 \ \mathrm{m} ;\,-\, 1 0. 2 \ \mathrm{d B}
$$
F. $$
0. 6 3 \ \mathrm{m}, 0. 2 5 \ \mathrm{m} ;\,-\, 9. 4 \ \mathrm{d B}
$$
G. $$
0. 7 1 \ \mathrm{m}, 0. 2 2 \ \mathrm{m} ;\,-\, 3. 8 \ \mathrm{d B}
$$
H. $$
1. 0 2 \ \mathrm{m}, 0. 3 1 \ \mathrm{m} ;\,-\, 5. 7 \ \mathrm{d B}
$$
I. $$
0. 6 7 \ \mathrm{m}, 0. 3 0 \ \mathrm{m} ;\,-\, 2. 5 \ \mathrm{d B}
$$
J. $$
0. 9 9 \ \mathrm{m}, 0. 3 3 \ \mathrm{m} ;\,-\, 7. 3 \ \mathrm{d B}
$$
Answer: E
For a piston sound source with a radius of 0.12 m mounted on an infinitely large rigid baffle, emitting sound waves at a frequency of 2000 Hz, find the beamwidth where the sound pressure level decreases by 6 dB. (Operating in air)

Options:
A. $$
2 5^{\circ} \times2=5 0^{\circ}
$$
B. $$
2 8^{\circ} \times2=5 6^{\circ}
$$
C. $$
2 0^{\circ} \times2=4 0^{\circ}
$$
D. $$
3 2^{\circ} \times2=6 4^{\circ}
$$
E. $$
4 5^{\circ} \times2=9 0^{\circ}
$$
F. $$
3 5^{\circ} \times2=7 0^{\circ}
$$
G. $$
3 6^{\circ} \times2=7 2^{\circ}
$$
H. $$
3 0^{\circ} \times2=6 0^{\circ}
$$
I. $$
3 8^{\circ} \times2=7 6^{\circ}
$$
J. $$
4 0^{\circ} \times2=8 0^{\circ}
$$
Answer: H
At a not-so-high position above the ground, a sound source emits sound waves at 500 Hz. Assuming the sound waves expand spherically in the half-space above the ground, without considering the sound absorption by the ground, try to calculate the air's viscous absorption coefficient. To produce a sound intensity level of 60 dB (reference 20 μPa) at 300 m, what should be the output sound power in watts when there is no absorption by the air and when there is viscous absorption?

Options:
A. 5.12x10 $^{-3}$dB/m;0.65W,0.95W
B. 6.79x10 $^{-3}$dB/m;0.60W,1.10W
C. 9.21x10 $^{-3}$dB/m;0.50W,1.20W
D. 5.98x10 $^{-3}$dB/m;0.57W,1.30W
E. 7.88x10 $^{-3}$dB/m;0.48W,1.08W
F. 7.05x10 $^{-3}$dB/m;0.45W,1.15W
G. 6.25x10 $^{-3}$dB/m;0.62W,1.12W
H. 8.98x10 $^{-3}$dB/m;0.56W,1.05W
I. 4.32x10 $^{-3}$dB/m;0.70W,1.00W
J. 8.54x10 $^{-3}$dB/m;0.55W,1.25W
Answer: H
An ideal dynamic speaker, driven by a 100 mV constant voltage source, produces 2 $\mathbf{w}$ of acoustic power on an acoustic impedance of $4 \times 10^{4} \mathrm{~ Pa \cdot s / m^{3}}$. The diaphragm has an area of 0.01 m². If it is used as a microphone and the measured diaphragm velocity is 0.1 $\mathrm{m / s}$, determine its open-circuit output voltage.

Options:
A. 0.45V
B. 1.67V
C. 1.15V
D. 1.49V
E. 1.32V
F. 0.28V
G. 0.98V
H. 0.75V
I. 0.13V
J. 0.60V
Answer: I
The source level of the transducer, with a working frequency of 1 kHz, is 210 dB (reference value 1 μPa). After emitting sound pulse 1, the reverberation level is 80 dB. Assuming the water volume contributing to the reverberation is $1.0\times 10 ^{8} m ^{3}$, find the scattering intensity.

Options:
A. -115dB
B. -85dB
C. -100dB
D. -75dB
E. -110dB
F. -120dB
G. -90dB
H. -80dB
I. -105dB
J. -95dB
Answer: J
A Helmholtz resonator has a cylindrical neck with both ends open, with a neck length and diameter of 1 cm each. If the resonance chamber is spherical and the resonance frequency is to be 400 Hz, what must the radius of the sphere be?

Options:
A. 0.037m
B. 0.033m
C. 0.045m
D. 0.040m
E. 0.031m
F. 0.032m
G. 0.028m
H. 0.030m
I. 0.034m
J. 0.036m
Answer: I
A stationary $\pi^{+}$ meson decays into a muon and a neutrino, with their respective rest masses being $m_{\pi0}, m_{\mu0}$, and zero. Give the kinetic energies $T_{\mu}$ of the muon and $T_{\mathrm{v}}$ of the neutrino.

Options:
A. $$
\frac{( m_{\mu0}+m_{\pi0} )^{2}} {2 m_{\pi0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}+m_{\mu0}^{2}} {2 m_{\mu0}} c^{2}
$$
B. $$
\frac{( m_{\pi0}+m_{\mu0} )^{2}} {2 m_{\mu0}} c^{2}
$$
$$
\frac{m_{\mu0}^{2}+m_{\pi0}^{2}} {2 m_{\mu0}} c^{2}
$$
C. $$
\frac{( m_{\pi0}-m_{\mu0} )^{2}} {2 m_{\pi0}} c^{2}
$$
$$
\frac{m_{\mu0}^{2}-m_{\pi0}^{2}} {2 m_{\pi0}} c^{2}
$$
D. $$
\frac{( m_{\pi0}-m_{\mu0} )^{2}} {2 m_{\mu0}} c^{2}
$$
$$
\frac{m_{\mu0}^{2}+m_{\pi0}^{2}} {2 m_{\pi0}} c^{2}
$$
E. $$
\frac{( m_{\pi0}+m_{\mu0} )^{2}} {2 m_{\pi0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}-m_{\mu0}^{2}} {2 m_{\mu0}} c^{2}
$$
F. $$
\frac{( m_{\mu0}+m_{\pi0} )^{2}} {2 m_{\mu0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}-m_{\mu0}^{2}} {2 m_{\pi0}} c^{2}
$$
G. $$
\frac{( m_{\mu0}-m_{\pi0} )^{2}} {2 m_{\mu0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}+m_{\mu0}^{2}} {2 m_{\pi0}} c^{2}
$$
H. $$
\frac{( m_{\mu0}-m_{\pi0} )^{2}} {2 m_{\pi0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}-m_{\mu0}^{2}} {2 m_{\pi0}} c^{2}
$$
I. $$
\frac{( m_{\pi0}-m_{\mu0} )^{2}} {2 m_{\mu0}} c^{2}
$$
$$
\frac{m_{\pi0}^{2}-m_{\mu0}^{2}} {2 m_{\mu0}} c^{2}
$$
J. $$
\frac{( m_{\mu0}+m_{\pi0} )^{2}} {2 m_{\pi0}} c^{2}
$$
$$
\frac{m_{\mu0}^{2}-m_{\pi0}^{2}} {2 m_{\mu0}} c^{2}
$$
Answer: H
In the proton intersecting storage ring (ISR) at CERN, a proton-proton collision is achieved with an energy of $30 \mathrm{GeV}$. To achieve the same center-of-mass energy as the ISR using a proton accelerator to accelerate protons to bombard stationary protons, what should the energy of the proton be?

Options:
A. $$
1. 1 8 \times1 0^{3} \mathrm{G e V}
$$
B. $$
2. 0 5 \times1 0^{3} \mathrm{G e V}
$$
C. $$
1. 4 6 \times1 0^{3} \mathrm{G e V}
$$
D. $$
5. 9 3 \times1 0^{3} \mathrm{G e V}
$$
E. $$
2. 3 7 \times1 0^{3} \mathrm{G e V}
$$
F. $$
1. 9 2 \times1 0^{3} \mathrm{G e V}
$$
G. $$
4. 1 0 \times1 0^{3} \mathrm{G e V}
$$
H. $$
2. 8 5 \times1 0^{3} \mathrm{G e V}
$$
I. $$
3. 3 0 \times1 0^{3} \mathrm{G e V}
$$
J. $$
1. 6 7 \times1 0^{3} \mathrm{G e V}
$$
Answer: F
Calculate the threshold energy required to produce a $\mathrm{K^{-}}$ meson by bombarding a stationary proton target with a $\pi$ meson.

Options:
A. $$
1. 5 5 0 ( \mathrm{G e V} )
$$
B. $$
1. 3 9 6 ( \mathrm{G e V} )
$$
C. $$
1. 5 0 2 ( \mathrm{G e V} )
$$
D. $$
1. 5 1 7 ( \mathrm{G e V} )
$$
E. $$
1. 4 5 5 ( \mathrm{G e V} )
$$
F. $$
1. 4 7 8 ( \mathrm{G e V} )
$$
G. $$
1. 7 2 0 ( \mathrm{G e V} )
$$
H. $$
1. 6 2 3 ( \mathrm{G e V} )
$$
I. $$
1. 3 5 8 ( \mathrm{G e V} )
$$
J. $$
1. 4 8 3 ( \mathrm{G e V} )
$$
Answer: C
The mass of the $\mathrm{J} / \psi$ particle is $3.097 \mathrm{GeV} / c^{2}$, and its width is $63 \mathrm{keV} / c^{2}$. What is the average distance traversed by the $\mathrm{J} / \psi$ before it decays when its momentum is $100 \mathrm{GeV} / c$ in the decay process $\mathrm{J} / \psi \to \mathrm{e}^{+} + \mathrm{e}^{-}$?

Options:
A. $$
1. 0 1 2 \times1 0^{-1 0} ( \mathrm{m} )
$$
B. $$
4. 0 4 8 \times1 0^{-0 9} ( \mathrm{m} )
$$
C. $$
8. 0 5 5 \times1 0^{-1 3} ( \mathrm{m} )
$$
D. $$
5. 0 1 5 \times1 0^{-1 1} ( \mathrm{m} )
$$
E. $$
7. 0 2 0 \times1 0^{-1 2} ( \mathrm{m} )
$$
F. $$
2. 0 2 4 \times1 0^{-1 1} ( \mathrm{m} )
$$
G. $$
6. 0 0 8 \times1 0^{-1 0} ( \mathrm{m} )
$$
H. $$
1. 0 1 8 \times1 0^{-1 0} ( \mathrm{m} )
$$
I. $$
9. 0 9 0 \times1 0^{-1 4} ( \mathrm{m} )
$$
J. $$
3. 0 3 6 \times1 0^{-1 2} ( \mathrm{m} )
$$
Answer: A
From the summary of the skiing competition, it was found that 96% of the students met the standard requirements. It is known that this number has a 0.5% margin of error. What is the minimum number of students who participated in this skiing competition?

Options:
A. 29
B. 15
C. 20
D. 35
E. 31
F. 25
G. 23
H. 27
I. 40
J. 18
Answer: G
In a certain project, the measured compressional wave velocity of moderately weathered rock is $V_{\mathrm{p m}}=3185 \mathrm{m/s}$, the shear wave velocity is $V_{\mathrm{s}}=1603 \mathrm{m/s}$, the compressional wave velocity of the corresponding rock block is $V_{\mathrm{p r}}=5067 \mathrm{m/s}$, and the shear wave velocity is $V_{\mathrm{s}}=2438\, \mathrm{m/s}$; the rock's mass density is $\rho=2.64 \mathrm{g/cm}^{3}$, and the saturated uniaxial compressive strength is $R_{\mathrm{c}}=40 \mathrm{MPa}$. What is the basic quality index $BQ$ of this rock mass in terms of the following values?

Options:
A. 365
B. 310
C. 295
D. 410
E. 342
F. 275
G. 300
H. 287
I. 360
J. 328
Answer: B
The distribution of foundation soil layers in a certain excavation site and the groundwater level is 0.5m below the surface. The natural unit weight of layers ① and ② is $\gamma=19 \mathrm{kN/m}^{3}$, while the natural unit weight of the silty soil in layer ③ is 17.1 kN/m³. The triaxial consolidated undrained strength parameters are: $c_{\mathrm{eu}}=17.8 \mathrm{kPa}$, $\varphi_{\mathrm{eu}}=13.2°$. If a soil sample is taken from the upper part of layer ③ and is consolidated under its effective self-weight pressure (with an isotropic consolidation principal stress $\sigma_{3}=68 \mathrm{kPa}$), and then undergoes an unconsolidated undrained triaxial test (UU), which of the following options is its $c_M$ value closest to?

Options:
A. 41.7
B. 46.1
C. 42.6
D. 51.4
E. 48.8
F. 39.3
G. 38.7
H. 37.9
I. 44.2
J. 35.5
Answer: C
A deep plate load test was conducted at a site at $10 \mathrm{m}$, with a load plate diameter of 0.25m. The proportional limit is 250kPa, corresponding to a settlement of 2.5mm. The soil Poisson's ratio is 0.25. According to the "Geotechnical Engineering Investigation Standard" (GB 50021-2001) (2009 edition), the deformation modulus is ()${MPa}$.

Options:
A. 15.30
B. 11.65
C. 9.90
D. 9.45
E. 10.55
F. 7.25
G. 12.40
H. 14.20
I. 8.75
J. 13.80
Answer: E
The width of the strip foundation is $3.6 \mathrm{m}$, with the self-weight of the foundation and the weight of the soil on the foundation being $G_{\mathrm{k}}=100 \mathrm{kN/m}$. The vertical force transmitted from the superstructure to the top surface of the foundation is $F_{\mathrm{k}}=200 \mathrm{kN/m_{\mathrm{}}}$. The eccentricity of the resultant force $F_{\mathrm{k}}+G_{\mathrm{k}}$ is $0.4 \mathrm{m}$. Which of the following options should the characteristic value of the corrected foundation bearing capacity meet or exceed to satisfy the bearing capacity verification requirements?"

Options:
A. 142kPa
B. 116kPa
C. 90kPa
D. 160kPa
E. 104kPa
F. 98kPa
G. 130kPa
H. 120kPa
I. 126kPa
J. 92kPa
Answer: B
A gravity-type quay, constructed underwater at a certain port, is based on a strip foundation with a rubble bed foundation. The thickness of the rubble bed is $d_{1}=2.0 \mathrm{m}$, and the effective compressive width at the bottom surface of the rubble bed is $B_{\mathrm{e}}^{\prime}=12 \mathrm{m}$. The resultant tilt rate is $\operatorname{tan} \delta^{\prime}=0.203 \, (\delta^{\prime}=11.5°)$. The standard values of soil shear strength indicators within the stress zone below the rubble bed bottom surface are $\varphi_{\mathrm{kl}}=24°$, $c_{\mathrm{k}}=15 \mathrm{kPa}$. The standard value of natural unit weight is $\gamma_{\mathbf{k}}=18.5 \mathbf{kN} / \mathbf{m}^{3}$, and within the rubble bed range, the natural unit weight standard value is $\gamma_{\mathrm{kl}}=19 \mathrm{kN / m}^{3}$. The design value of the vertical resultant force acting on the rubble bed is $V_{d}^{\prime}=1760 \mathrm{kN}$. At this time, the resistance partial coefficient $\gamma_{n}$ is (). (Bearing capacity coefficients $N_{t}=3.3$, $N_{q}=6\,$)

Options:
A. 3.93
B. 2.56
C. 5.89
D. 2.84
E. 3.76
F. 3.21
G. 4.05
H. 6.32
I. 4.67
J. 5.12
Answer: D
The foundation dimensions of a certain building are $16 \mathrm{m} \times 32 \mathrm{m}$. The burial depth of the foundation base, measured from the natural ground surface, is 3.4m, while the stabilized groundwater level is at a depth of 1.0m. The average natural bulk density of the backfill above the foundation base is 19kN/m³. The vertical load values acting on the foundation base, corresponding to the quasi-permanent and standard load combinations, are 122880kN and 15360kN, respectively. According to the design requirements, the outdoor ground level will be generally raised by 1.0m after the construction of the superstructure. The additional pressure on the foundation base used for calculating ground deformation is closest to ( ) ${k P a}$.

Options:
A. 188.7kPa
B. 206.8kPa
C. 205.1kPa
D. 217.9kPa
E. 181.8kPa
F. 212.3kPa
G. 199.4kPa
H. 190.5kPa
I. 175.6kPa
J. 172.4kPa
Answer: G
The proposed design depth for the isolated foundation is $2.0 \mathrm{m}$. Given a foundation bearing capacity design value of $f_{\mathrm{a}}=226 \mathrm{kPa}$, an upper structure load of $N=1600 \mathrm{kN}$, $M=400 \mathrm{kN} \cdot \mathrm{m}$, and a base point load of $Q=50 \mathrm{kN}$, the most economically feasible base dimensions are approximately().

Options:
A. $$
3. 4 \mathrm{m} \times3. 6 \mathrm{m}
$$
B. $$
3. 8 \mathrm{m} \times3. 3 \mathrm{m}
$$
C. $$
3. 3 \mathrm{m} \times3. 7 \mathrm{m}
$$
D. $$
3. 9 \mathrm{m} \times3. 1 \mathrm{m}
$$
E. $$
3. 2 \mathrm{m} \times3. 8 \mathrm{m}
$$
F. $$
3. 7 \mathrm{m} \times3. 4 \mathrm{m}
$$
G. $$
4. 1 \mathrm{m} \times3. 0 \mathrm{m}
$$
H. $$
4. 0 \mathrm{m} \times3. 5 \mathrm{m}
$$
I. $$
3. 5 \mathrm{m} \times3. 0 \mathrm{m}
$$
J. $$
3. 6 \mathrm{m} \times3. 2 \mathrm{m}
$$
Answer: J
The site conditions of a certain construction location are as follows: From the surface to a depth of $0-12 \, \mathrm{m}$ is plastic state cohesive soil, with a single bridge static cone penetration ratio $p$ of 1200 kPa; below 12 m is dense coarse sand, with a penetration ratio of 5800 kPa. The site intends to use a bored pile foundation, with a pile length of 12 m, a pile diameter of 0.5 m, and a pile top embedding depth of 2.0 m. According to the Chinese "Technical Code for Building Pile Foundations" (JGJ 94-2008), the calculated standard value of the ultimate bearing capacity for a single pile is ( ) kN.

Options:
A. 1550.1kN
B. 1610.7kN
C. 1450.2kN
D. 1230.4kN
E. 2000.6kN
F. 1900.0kN
G. 2500.9kN
H. 1702.8kN
I. 1400.3kN
J. 1800.5kN
Answer: B
Given conditions: The dimensions of the column are $500 \mathrm{mm} \times 500 \mathrm{mm}$; the dimensions of the pile are $400 \mathrm{mm} \times 400 \mathrm{mm}$; the height of the cap is $h = 600 \mathrm{mm}$, $h_{0} = 450 \mathrm{mm}$, the design tensile strength value of the concrete cap is $f_{\mathrm{t}} = 1.27 \mathrm{MPa}$, and the bearing capacity of the corner pile for punching shear is () kN.

Options:
A. 612.45kN
B. 499.89kN
C. 521.19kN
D. 558.91kN
E. 546.74kN
F. 577.23kN
G. 489.52kN
H. 523.67kN
I. 574.36kN
J. 535.38kN
Answer: J
The subsurface of a certain construction site is planned to be reinforced using Cement Fly-Ash Gravel (CFG) piles. It is known that the foundation depth is 2.0m, the length of the CFG piles is 14.0m, the pile diameter is 500mm, and the pile body strength is $f_{\mathrm{c u}}=20 \mathrm{MPa}$. The reduction coefficient for the bearing capacity of the soil between piles is set at 0.8. According to the "Technical Code for Ground Treatment of Buildings" (JGJ 79-2002), if the characteristic value of the composite foundation bearing capacity is required to reach 180kPa, which option should be selected for the replacement rate $m$ of the CFG pile area?

Options:
A. 9.4%
B. 11.7%
C. 14.3%
D. 10.8%
E. 12.5%
F. 16.0%
G. 15.1%
H. 8.7%
I. 13.9%
J. 7.5%
Answer: B