MikaStars39/nano-eval huggingface dataset:
A spherical blackbody with a radius $r$ and temperature $T$ is surrounded by a concentric spherical shell with a radius $R$, both sides of the shell being black. Try to prove that the ratio by which this radiation shield reduces the cooling rate of the sphere (assuming the space between the shell and the object is evacuated, with no conductive heat loss) is determined by $a R^{2} / ( R^{2} + b r^{2} )$, and find the coefficients $a$ and $b$ as ___.

Options:
A. $$
a=2, \ \ b=3.
$$
B. $$
a=4, \ \ b=3.
$$
C. $$
a=2, \ \ b=1.
$$
D. $$
a=1, \ \ b=2.
$$
E. $$
a=0, \ \ b=2.
$$
F. $$
a=2, \ \ b=0.
$$
G. $$
a=3, \ \ b=2.
$$
H. $$
a=0, \ \ b=1.
$$
I. $$
a=3, \ \ b=4.
$$
J. $$
a=1, \ \ b=1.
$$
Answer: J
A spherical blackbody asteroid composed of rock, situated far from the solar system, is thus unaffected by solar radiation. Due to the presence of radioactive elements, there is a constant rate of heat generation inside the planet, $\dot{q}=3 \times 10^{-1} \, \text{cal} / (\text{g} \cdot \text{s})$. The density of the rock is $\rho = 3.5 \, \text{g} / \text{cm}^3$, and its thermal conductivity is $k=5 \times 10^{-1} \, \text{cal} / (\text{cm} \cdot \text{s} \cdot \degree \text{C})$. The radius of the planet is $R=100 \, \text{km}$. Determine the central temperature and surface temperature of the planet as _____. (Assume a stable temperature field has been established.)

Options:
A. $$380K$$
B. $$360K$$
C. $$375K$$
D. $$400K$$
E. $$385K$$
F. $$390K$$
G. $$350K$$
H. $$372K$$
I. $$395K$$
J. $$365K$$
Answer: H
When the atmospheric pressure is equal to 30.26 inches of mercury, what is the reading on a barometer using carbon tetrachloride as the measuring liquid at 68 degrees Fahrenheit ?

Options:
A. $$
2 0. 7 5 \mathrm{f t}
$$
B. $$
1 6. 7 8 \mathrm{f t}
$$
C. $$
2 4. 8 8 \mathrm{f t}
$$
D. $$
1 5. 6 3 \mathrm{f t}
$$
E. $$
1 9. 4 3 \mathrm{f t}
$$
F. $$
2 5. 1 6 \mathrm{f t}
$$
G. $$
2 2. 5 9 \mathrm{f t}
$$
H. $$
1 8. 8 2 \mathrm{f t}
$$
I. $$
1 7. 9 1 \mathrm{f t}
$$
J. $$
2 3. 4 0 \mathrm{f t}
$$
Answer: H
Air with a total flow rate of 20,000 ft³/s (0.072 lbₒ/f₃) passes through two propellers with a diameter of 6.5 feet. These propellers are installed on an aircraft flying at 150 miles per hour through still air. What is the horsepower input for each propeller, neglecting vortex losses ?

Options:
A. $$
2 1 0 0 h p
$$
B. $$
1 9 9 4 h p
$$
C. $$
1 7 5 0 h p
$$
D. $$
1 8 2 0 h p
$$
E. $$
2 0 5 0 h p
$$
F. $$
2 1 5 0 h p
$$
G. $$
2 0 0 0 h p
$$
H. $$
2 2 5 0 h p
$$
I. $$
1 8 9 0 h p
$$
J. $$
1 6 6 0 h p
$$
Answer: B
A box truck with dimensions 8 feet wide, 10 feet high, and 35 feet long travels at a speed of 60 km/h in air at 50°F, assuming the front of the truck is round (with airflow not separating at the front and sides). It is also assumed that the roof and sides are relatively smooth. Considering practical factors, there is sufficient surface roughness, and a turbulent boundary layer appears at the front. What is shear stress at the trailing edge?

Options:
A. $$
0. 0 2 0 0 1 2 \mathrm{b f} / \mathrm{f t}^{2}
$$
B. $$
0. 0 1 9 0 1 \mathrm{l b f} / \mathrm{f t}^{2}
$$
C. $$
0. 0 2 2 0 1 5 \mathrm{b f} / \mathrm{f t}^{2}
$$
D. $$
0. 0 1 7 0 1 4 \mathrm{b f} / \mathrm{f t}^{2}
$$
E. $$
0. 0 3 0 0 1 9 \mathrm{b f} / \mathrm{f t}^{2}
$$
F. $$
0. 0 1 8 0 1 3 \mathrm{b f} / \mathrm{f t}^{2}
$$
G. $$
0. 0 2 1 0 1 0 \mathrm{b f} / \mathrm{f t}^{2}
$$
H. $$
0. 0 1 6 0 1 8 \mathrm{b f} / \mathrm{f t}^{2}
$$
I. $$
0. 0 2 3 0 1 6 \mathrm{b f} / \mathrm{f t}^{2}
$$
J. $$
0. 0 1 5 0 2 1 \mathrm{b f} / \mathrm{f t}^{2}
$$
Answer: B
A rectangular channel, 2m wide, has a uniform flow discharge of 4.2 m³/s when the water depth is 0.5m. If the bend radius of the channel is 10m, what are the maximum and minimum water depths at the inner and outer channel walls?

Options:
A. $$0.4 \mathrm{m},\ 0.25 \mathrm{m},\ 0.95 \mathrm{m},\ 0.4 \mathrm{m}$$
B. $$0.8 \mathrm{m},\ 0.16 \mathrm{m},\ 0.84 \mathrm{m},\ 0.8 \mathrm{m}$$
C. $$0.6 \mathrm{m},\ 0.20 \mathrm{m},\ 0.7 \mathrm{m},\ 0.6 \mathrm{m}$$
D. $$0.6 \mathrm{m},\ 0.10 \mathrm{m},\ 0.8 \mathrm{m},\ 0.6 \mathrm{m}$$
E. $$0.5 \mathrm{m},\ 0.14 \mathrm{m},\ 0.86 \mathrm{m},\ 0.5 \mathrm{m}$$
F. $$0.7 \mathrm{m},\ 0.15 \mathrm{m},\ 0.85 \mathrm{m},\ 0.7 \mathrm{m}$$
G. $$0.65 \mathrm{m},\ 0.22 \mathrm{m},\ 0.78 \mathrm{m},\ 0.65 \mathrm{m}$$
H. $$0.45 \mathrm{m},\ 0.30 \mathrm{m},\ 1.0 \mathrm{m},\ 0.45 \mathrm{m}$$
I. $$0.55 \mathrm{m},\ 0.23 \mathrm{m},\ 0.77 \mathrm{m},\ 0.55 \mathrm{m}$$
J. $$0.35 \mathrm{m},\ 0.18 \mathrm{m},\ 0.9 \mathrm{m},\ 0.35 \mathrm{m}$$
Answer: E
Two large water tanks are connected by a pipe that is 15 meters long with a diameter of 100 mm (f = 0.02). The difference in water level elevation between them is 2 meters. If a valve that was initially closed suddenly opens, how long will it take for the water flow to reach 1/4, 1/2, and 3/4 of the steady flow rate? Assume that the water surface elevations remain unchanged and that the entrance is square.

Options:
A. $0.677s,\ 1.28s,\ 2.297s$
B. $0.567s,\ 1.20s,\ 2.177s$
C. $0.547s,\ 1.30s,\ 2.197s$
D. $0.617s,\ 1.18s,\ 2.227s$
E. $0.487s,\ 1.14s,\ 2.097s$
F. $0.597s,\ 1.44s,\ 2.257s$
G. $0.627s,\ 1.24s,\ 2.347s$
H. $0.657s,\ 1.38s,\ 2.367s$
I. $0.577s,\ 1.240s,\ 2.197s$
J. $0.687s,\ 1.34s,\ 2.397s$
Answer: I
A model pump has a diameter of 7.4 inches, a rotational speed of 3600 revolutions per minute, a head of 125 feet, and a discharge rate of 3.0 cubic feet per second. When the model pump and the prototype pump have the same head and a size ratio of 1:10, assuming the efficiency of the prototype pump is 90%, what is the input horsepower?

Options:
A. $$
4 2 0 0 \mathrm{h p}
$$
B. $$
4 5 5 0 \mathrm{h p}
$$
C. $$
4 4 7 5 \mathrm{h p}
$$
D. $$
5 1 9 0 \mathrm{h p}
$$
E. $$
5 0 8 0 \mathrm{h p}
$$
F. $$
5 3 2 5 \mathrm{h p}
$$
G. $$
3 5 2 5 \mathrm{h p}
$$
H. $$
3 7 6 5 \mathrm{h p}
$$
I. $$
4 7 3 0 \mathrm{h p}
$$
J. $$
4 9 0 0 \mathrm{h p}
$$
Answer: I
Experiments have measured that a germanium sample does not exhibit any Hall effect. Given that the electron mobility in germanium is $\mu_{n} = 3500 \text{ cm}^2 / (\text{V} \cdot \text{s})$, and the hole mobility is $\mu_{p} = 1400 \text{ cm}^2 / (\text{V} \cdot \text{s})$, what proportion of the total current in the sample is due to the electron current?

Options:
A. $\frac{5}{12}$
B. $\frac{1}{4}$
C. $\frac{2}{7}$
D. $\frac{1}{3}$
E. $\frac{3}{5}$
F. $\frac{7}{10}$
G. $\frac{5}{8}$
H. $\frac{1}{2}$
I. $\frac{3}{8}$
J. $\frac{4}{9}$
Answer: C
Assuming the effective masses of electrons and holes are equal, the band gap of silicon is 1.12 eV. The mobilities of electrons and holes are $0.135 \, \mathrm{cm}^2/\mathrm{(V \cdot s)}$ and $0.048 \, \mathrm{cm}^2/\mathrm{(V \cdot s)}$, respectively. What is the Seebeck coefficient of intrinsic silicon at room temperature?

Options:
A. $$
- 7 5 9 ( \mathrm{\mu V} / \mathrm{K} )
$$
B. $$
- 1 0 2 0 ( \mathrm{\mu V} / \mathrm{K} )
$$
C. $$
- 1 0 6 2 ( \mathrm{\mu V} / \mathrm{K} )
$$
D. $$
- 9 9 4 ( \mathrm{\mu V} / \mathrm{K} )
$$
E. $$
- 9 4 8 ( \mathrm{\mu V} / \mathrm{K} )
$$
F. $$
- 7 2 8 ( \mathrm{\mu V} / \mathrm{K} )
$$
G. $$
- 5 7 0 ( \mathrm{\mu V} / \mathrm{K} )
$$
H. $$
- 6 9 8 ( \mathrm{\mu V} / \mathrm{K} )
$$
I. $$
- 6 4 3 ( \mathrm{\mu V} / \mathrm{K} )
$$
J. $$
- 8 0 5 ( \mathrm{\mu V} / \mathrm{K} )
$$
Answer: E
A $\mathbf{p}$-type silicon with a hole concentration of $10^{16} \mathrm{cm}^{-3}$ has a cold junction temperature of 0°C and a hot junction temperature of 50°C. Assuming long acoustic wave scattering, what is the thermoelectric electromotive force?

Options:
A. $$
2. 2 ( \mathrm{m V} )
$$
B. $$
2. 5 ( \mathrm{m V} )
$$
C. $$
3. 2 ( \mathrm{m V} )
$$
D. $$
3. 8 ( \mathrm{m V} )
$$
E. $$
3. 5 ( \mathrm{m V} )
$$
F. $$
4. 1 ( \mathrm{m V} )
$$
G. $$
5. 3 ( \mathrm{m V} )
$$
H. $$
2. 9 ( \mathrm{m V} )
$$
I. $$
4. 4 ( \mathrm{m V} )
$$
J. $$
1. 7 ( \mathrm{m V} )
$$
Answer: D
The metallurgical junction area of a gate-controlled $\mathrm{p}^{+} \mathrm{n}$ diode is $10^{-3} \mathrm{cm}^{2}$, and the overlap area between the gate and the $\mathbf{n}$ region is $10^{-3} \mathrm{cm}^{2}$. The substrate impurity concentration is $10^{16} \mathrm{cm}^{-3}$, the junction depth is 5 μm, and the oxide layer thickness is $0.2 \mu\mathrm{m}$. The carrier lifetime $\tau=1 \mu s$, the surface recombination velocity $s_{0}=5 \mathrm{cm/s}$, and the flat-band voltage is $-2 \mathrm{V}$. What are the gate voltages when the substrate surface is intrinsic and strongly inverted, respectively, when the junction voltage is zero at room temperature?

Options:
A. $$
- 6. 8 ( \mathrm{V} )
$$
B. $$
- 3. 2 ( \mathrm{V} )
$$
C. $$
1. 9 ( \mathrm{V} )
$$
D. $$
- 1. 8 ( \mathrm{V} )
$$
E. $$
- 8. 3 ( \mathrm{V} )
$$
F. $$
- 4. 0 ( \mathrm{V} )
$$
G. $$
0. 7 ( \mathrm{V} )
$$
H. $$
- 2. 5 ( \mathrm{V} )
$$
I. $$
- 7. 5 ( \mathrm{V} )
$$
J. $$
- 5. 5 ( \mathrm{V} )
$$
Answer: J
A uniformly doped n-type silicon sample has a donor density $N_{\mathrm{D}} = 2.8 \times 10^{16} \, \mathrm{cm}^{-3}$. Assume there are acceptor-type surface states on the sample surface, with energy levels that are continuously and uniformly distributed between the valence band maximum and the conduction band minimum, with a density of $N_{s} = 6.0 \times 10^{11} \, \mathrm{cm}^{-2} \cdot \mathrm{eV}^{-1}$. What is the surface potential $V_{s}$?

Options:
A. $$
- 0. 5 0 \mathrm{V}
$$
B. $$
- 0. 4 0 \mathrm{V}
$$
C. $$
- 0. 2 2 \mathrm{V}
$$
D. $$
- 0. 7 2 \mathrm{V}
$$
E. $$
- 0. 9 5 \mathrm{V}
$$
F. $$
- 0. 1 4 \mathrm{V}
$$
G. $$
- 0. 3 5 \mathrm{V}
$$
H. $$
- 0. 4 8 \mathrm{V}
$$
I. $$
- 0. 8 9 \mathrm{V}
$$
J. $$
- 0. 6 1 \mathrm{V}
$$
Answer: G
Assume a Schottky diode composed of a certain metal and the crystal plane of n-type silicon, where the barrier height on the semiconductor side after contact is known to be $0.50 \mathrm{eV}$, $N_{\mathrm{D}}=10^{15} \mathrm{cm}^{-3}$, $N_{\mathrm{c}}=2.8 \times 10^{19} \mathrm{cm}^{-3}$, electron affinity $X=4.05 \mathrm{eV}$, $I_{\mathrm{p}}=10 \mu\mathrm{m}$, $D_{p}=15 \mathrm{cm^{2}/s}$, $n_{i}=1.5 \times 10^{10} \mathrm{cm^{-3}}$, $A^{*}=252 \mathrm{A/cm^{2}K^{2}}$ (Richardson constant). What is the minority carrier injection ratio?

Options:
A. $$
4. 5 \times1 0^{-6}
$$
B. $$
9. 3 \times1 0^{-7}
$$
C. $$
1. 2 \times1 0^{-4}
$$
D. $$
6. 4 \times1 0^{-7}
$$
E. $$
8. 9 \times1 0^{-5}
$$
F. $$
5. 6 \times1 0^{-4}
$$
G. $$
2. 8 \times1 0^{-5}
$$
H. $$
2. 1 \times1 0^{-9}
$$
I. $$
7. 1 \times1 0^{-8}
$$
J. $$
3. 7 \times1 0^{-6}
$$
Answer: J
Given a silicon junction with an n-Si side having a resistivity of $\rho_{\mathrm{n}}=10 \Omega\cdot\mathrm{cm}$ and a p-Si side with a resistivity of $\rho_{\mathrm{p}}=0.01 \Omega\cdot\mathrm{cm}$, and known mobilities of $\mu_{\mathrm{n}}=100 \mathrm{~cm}^{2}/(\mathrm{V\cdot s})$ and $\mu_{\mathrm{p}}=300 \mathrm{~cm}^{2}/(\mathrm{V\cdot s})$, what are the barrier height and width at room temperature?

Options:
A. $$
0. 6 3 ( \mathrm{e V} ),\ 3. 5 4 \times1 0^{-4} ( \mathrm{\, c m} )
$$
B. $$
0. 8 1 ( \mathrm{e V} ),\ 2. 4 6 \times1 0^{-4} ( \mathrm{\, c m} )
$$
C. $$
0. 6 7 ( \mathrm{e V} ),\ 4. 0 2 \times1 0^{-4} ( \mathrm{\, c m} )
$$
D. $$
0. 8 5 ( \mathrm{e V} ),\ 2. 9 4 \times1 0^{-4} ( \mathrm{\, c m} )
$$
E. $$
0. 5 9 ( \mathrm{e V} ),\ 1. 1 8 \times1 0^{-4} ( \mathrm{\, c m} )
$$
F. $$
0. 7 6 ( \mathrm{e V} ),\ 1. 2 6 \times1 0^{-4} ( \mathrm{\, c m} )
$$
G. $$
0. 6 1 ( \mathrm{e V} ),\ 3. 8 1 \times1 0^{-4} ( \mathrm{\, c m} )
$$
H. $$
0. 7 8 ( \mathrm{e V} ),\ 1. 5 0 \times1 0^{-4} ( \mathrm{\, c m} )
$$
I. $$
0. 7 0 ( \mathrm{e V} ),\ 1. 4 3 \times1 0^{-4} ( \mathrm{\, c m} )
$$
J. $$
0. 7 3 ( \mathrm{e V} ),\ 1. 7 9 \times1 0^{-4} ( \mathrm{\, c m} )
$$
Answer: F
An $\mathbf{n}$-type semiconductor silicon has a doping concentration of $N_{\mathrm{D}}=10^{15} \, \mathrm{cm}^{-3}$ and a minority carrier lifetime $\tau_{p}=5 \, \mu s$. If due to external influences all the minority carriers are removed (for instance, near a reverse-biased pn junction), what is the generation rate of electron-hole pairs at this time? (Assume $n_{i}=1.5 \times 10^{10} \, \mathrm{cm}^{-3}$).

Options:
A. $$
-1. 2 \times1 0^{1 0} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
B. $$
-1. 1 \times1 0^{1 3} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
C. $$
-1. 6 \times1 0^{1 1} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
D. $$
-1. 4 \times1 0^{1 2} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
E. $$
-1. 8 \times1 0^{1 1} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
F. $$
-1. 9 \times1 0^{1 2} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
G. $$
-1. 3 \times1 0^{1 1} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
H. $$
-1. 3 \times1 0^{1 0} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
I. $$
-1. 7 \times1 0^{1 3} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
J. $$
-1. 5 \times1 0^{1 2} [ 1 / ( \mathrm{c m \cdot s} ) ]
$$
Answer: G
In a non-degenerate $\mathrm{p}$-type silicon substrate, a certain concentration of indium is present, with a measured hole concentration at room temperature of $p_{0} = 1.1 \times 10^{16} \, \mathrm{cm}^{-3}$. At room temperature, the silicon's $N_{\mathrm{v}} = 1.04 \times 10^{19} \, \mathrm{cm}^{-3}$. The known concentration of boron is $N_{A1} = 10^{16} \, \mathrm{cm}^{-3}$, with its ionization energy $\Delta E_{\mathrm{A1}} = E_{\mathrm{A1}} - E_{\mathrm{v}} = 0.046 \, \mathrm{eV}$. The ionization energy for indium is $\Delta E_{A2} = E_{A2} - E_{\tau} = 0.16 \, \mathrm{eV}$. What is the concentration of indium in this semiconductor?

Options:
A. $$
4. 1 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
B. $$
1. 5 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
C. $$
5. 3 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
D. $$
3. 0 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
E. $$
1. 2 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
F. $$
1. 0 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
G. $$
2. 2 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
H. $$
3. 5 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
I. $$
2. 4 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
J. $$
2. 8 \times1 0^{1 5} \mathrm{c m}^{-3}
$$
Answer: G
Set the lattice constant of a two-dimensional square grid to $a$. If the electron energy can be expressed as
$$
E ( \, k \, )={\frac{h^{2} ( \, k_{x}^{2} \,+\, k_{y}^{2} \, )} {2 m_{n}^{*}}} \,,
$$
what is the density of states?

Options:
A. $$
4 \pi S \frac{2 m_{n}^{*}} {2 h^{2}}
$$
B. $$
8 \pi S \frac{m_{n}^{*}} {h^{2}}
$$
C. $$
4 \pi S \frac{m_{n}^{*}} {2 h^{2}}
$$
D. $$
4 \pi S \frac{m_{n}^{*}} {h^{2}}
$$
E. $$
2 \pi S \frac{m_{n}^{*}} {h^{2}}
$$
F. $$
4 \pi S \frac{m_{n}^{*}} {h^{2} S}
$$
G. $$
4 \pi S \frac{h^{2}} {m_{n}^{*}}
$$
H. $$
4 \pi \frac{m_{n}^{*}} {S h^{2}}
$$
I. $$
\pi S \frac{m_{n}^{*}} {2 h^{2}}
$$
J. $$
4 \pi S \frac{2 m_{n}^{*}} {h^{2}}
$$
Answer: D
The electric power of an electric furnace is 1KW, the temperature of the heating wire is 847°C, and the diameter is 1mm. The efficiency of the electric furnace is 0.96. Try to determine the shortest length of the furnace wire required.

Options:
A. $$
5.27m
$$
B. $$
2.74m
$$
C. $$
2.91m
$$
D. $$
4.18m
$$
E. $$
3.89m
$$
F. $$
3.42m
$$
G. $$
3.61m
$$
H. $$
1.83m
$$
I. $$
4.56m
$$
J. $$
2.38m
$$
Answer: G
Given: A square solar collector, placed horizontally, with a side length of 1.1 m. The heat-absorbing surface is directly exposed to the air, with an emissivity $\mathcal{E} = 0.2$, and no intermediate layers. The absorptivity for solar energy is $\alpha_s = 0.9$. When the solar incident radiation is $G = 800 \mathrm{W/m}^2$, the measured temperature of the heat-absorbing surface is 90°C, and the ambient temperature is 30°C. The sky can be regarded as a black body at 23 K. The efficiency of the collector is defined as the ratio of the solar energy absorbed by the collector to the solar incident radiation.
Find: The efficiency of this solar collector.

Options:
A. $$
16.8\%
$$
B. $$
15.7\%
$$
C. $$
17.3\%
$$
D. $$
23.9\%
$$
E. $$
19.7\%
$$
F. $$
22.1\%
$$
G. $$
21.2\%
$$
H. $$
24.5\%
$$
I. $$
18.5\%
$$
J. $$
20.4\%
$$
Answer: E
Given the vector $A = a_{x} x^{2} + a_{y} x y$ in the Cartesian coordinate system, find the expression of this vector in the spherical coordinate system is ().

Options:
A. $$
a_{\theta} R^{2} \operatorname{c o s}^{3} \theta\operatorname{s i n} \varphi+a_{\phi} R^{3} \operatorname{s i n} \theta\operatorname{c o s}^{2} \varphi
$$
B. $$
a_{\phi} R^{4} \operatorname{s i n} \theta\operatorname{c o s}^{3} \varphi+a_{r} R^{2} \operatorname{c o s} \theta\operatorname{s i n}^{2} \varphi
$$
C. $$
a_{\phi} R^{3} \operatorname{c o s} \theta\operatorname{s i n}^{3} \varphi+a_{k} R \operatorname{s i n} \theta\operatorname{c o s}^{2} \varphi
$$
D. $$
a_{r} R \operatorname{c o s} \theta\operatorname{c o s}^{2} \varphi+a_{\theta} R^{3} \operatorname{s i n}^{3} \theta\operatorname{s i n} \varphi
$$
E. $$
a_{k} R^{2} \operatorname{s i n}^{3} \theta\operatorname{c o s} \varphi+a_{\theta} R^{2} \operatorname{s i n}^{2} \theta\operatorname{c o s} \theta\operatorname{c o s} \varphi
$$
F. $$
a_{k} R^{2} \operatorname{s i n} \theta\operatorname{s i n}^{3} \varphi+a_{\theta} R^{4} \operatorname{c o s} \theta\operatorname{s i n}^{2} \varphi
$$
G. $$
a_{r} R^{4} \operatorname{c o s} \theta\operatorname{s i n}^{2} \varphi+a_{\phi} R \operatorname{s i n}^{3} \theta\operatorname{s i n} \varphi
$$
H. $$
a_{k} R \operatorname{c o s} \theta\operatorname{s i n}^{3} \varphi+a_{\theta} R^{3} \operatorname{s i n}^{4} \theta\operatorname{c o s} \varphi
$$
I. $$
a_{\theta} R \operatorname{s i n} \theta\operatorname{c o s}^{3} \varphi+a_{\phi} R^{3} \operatorname{s i n}^{4} \theta\operatorname{c o s} \theta
$$
J. $$
a_{r} R^{3} \operatorname{c o s}^{2} \theta\operatorname{s i n} \varphi+a_{\phi} R^{2} \operatorname{s i n} \theta\operatorname{c o s}^{2} \varphi
$$
Answer: E
Assume that the air above a certain city can be represented as an empty box model with a length and width of 100 km each, and a height of 1.0 km. Clean air flows in from one side at a velocity of 4 m/s. Suppose a certain air pollutant is entering the box at a total emission rate of 10.0 kg/s, with a degradation reaction rate constant of 0.20 h⁻¹. Assuming complete mixing and that the wind speed suddenly drops to 1 m/s, estimate the concentration of the pollutant after 2 hours is ().

Options:
A. $$
3. 5 0 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
B. $$
9. 7 5 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
C. $$
5. 0 0 \times1 0^{-3} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
D. $$
2. 3 0 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
E. $$
7. 2 5 \times1 0^{-3} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
F. $$
4. 5 0 \times1 0^{-3} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
G. $$
8. 0 0 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
H. $$
1. 1 5 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
I. $$
6. 0 0 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
J. $$
4. 0 0 \times1 0^{-2} \mathrm{m g} / \mathrm{m}^{3} \circ
$$
Answer: H
A boiler discharges flue gas through a chimney with an internal diameter of 3.5 meters, with a discharge rate of \(3.5 \times 10^5 \, \text{m}^3/\text{h}\). At an average flue gas temperature of 260°C, its average density is \(0.6 \, \text{kg/m}^3\) and its average viscosity is \(2.8 \times 10^{-4} \, \text{Pa}\cdot \text{s}\). The atmospheric temperature is 20°C and the average density within the chimney height range is \(1.15 \, \text{kg/m}^3\). To overcome the resistance of coal ash, the pressure at the chimney base is 245 Pa lower than the ground atmospheric pressure. How tall does this chimney need to be? Assume a roughness of 5 mm.

Options:
A. $$
4 4. 8 5 \mathrm{m}.
$$
B. $$
3 7. 5 4 \mathrm{m}.
$$
C. $$
4 1. 8 9 \mathrm{m}.
$$
D. $$
5 5. 4 8 \mathrm{m}.
$$
E. $$
3 9. 7 3 \mathrm{m}.
$$
F. $$
4 9. 9 2 \mathrm{m}.
$$
G. $$
6 0. 1 1 \mathrm{m}.
$$
H. $$
5 2. 3 7 \mathrm{m}.
$$
I. $$
4 7. 6 4 \mathrm{m}.
$$
J. $$
4 3. 0 6 \mathrm{m}.
$$
Answer: I
If a steel pipe with an outer diameter of 70mm, a length of 3m, and an outer surface temperature of $227°C$ is placed in a brick trench with a cross-section of $0.3 \, \mathrm{m} \times 0.3 \, \mathrm{m}$, where the brick wall temperature is 27°C, and the emissivities of the steel pipe and the brick wall are 0.8 and 0.93 respectively, determine the radiation heat loss of the pipe.(assuming the radiation losses from the two ends of the pipe can be neglected and the blackness of the copper tube is 0.8 ).

Options:
A. $$
1. 3 5 {\times} 1 0^{3} \mathrm{W}
$$
B. $$
1. 6 8 {\times} 1 0^{3} \mathrm{W}
$$
C. $$
1. 0 5 {\times} 1 0^{3} \mathrm{W}
$$
D. $$
1. 4 2 {\times} 1 0^{3} \mathrm{W}
$$
E. $$
3. 7 9 {\times} 1 0^{3} \mathrm{W}
$$
F. $$
9. 9 2 {\times} 1 0^{3} \mathrm{W}
$$
G. $$
2. 3 3 {\times} 1 0^{3} \mathrm{W}
$$
H. $$
1. 2 0 {\times} 1 0^{3} \mathrm{W}
$$
I. $$
1. 8 5 {\times} 1 0^{3} \mathrm{W}
$$
J. $$
2. 6 7 {\times} 1 0^{3} \mathrm{W}
$$
Answer: D
At a temperature of 25°C and a pressure of \(1.013 \times 10^{5} \text{Pa F}\), an oxygen bubble with an initial diameter of \(0.1 \text{cm}\) is submerged in stirred pure water. After 7 minutes, the bubble's diameter decreases to \(0.054 \text{cm}\). Calculate the mass transfer coefficient of the system is (). The saturation concentration of oxygen in water is \(1.5 \times 10^{-3} \text{mol/L}\).

Options:
A. $$
1. 5 5 \times1 0^{-5} {\mathrm{m / s}}
$$
B. $$
1. 6 4 \times1 0^{-5} {\mathrm{m / s}}
$$
C. $$
1. 3 8 \times1 0^{-5} {\mathrm{m / s}}
$$
D. $$
1. 4 9 \times1 0^{-5} {\mathrm{m / s}}
$$
E. $$
1. 7 0 \times1 0^{-5} {\mathrm{m / s}}
$$
F. $$
1. 3 3 \times1 0^{-5} {\mathrm{m / s}}
$$
G. $$
1. 5 2 \times1 0^{-5} {\mathrm{m / s}}
$$
H. $$
1. 6 1 \times1 0^{-5} {\mathrm{m / s}}
$$
I. $$
1. 5 0 \times1 0^{-5} {\mathrm{m / s}}
$$
J. $$
1. 4 7 \times1 0^{-5} {\mathrm{m / s}}
$$
Answer: D
Spherical particles with a diameter of $0.1 \, \text{mm}$ are suspended in water, with a particle volume fraction of 0.1. When filtered under a constant pressure difference of $9.81 \times 10^{3} \, \text{Pa}$, an incompressible filter cake forms with a porosity of 0.6, and the resistance of the filter medium can be neglected. Calculate the filtration time required to obtain $1.5 \, \text{m}^{3}$ of filtrate per square meter of filter area is ().

Options:
A. $$
7 9 2s
$$
B. $$
4 9 6s
$$
C. $$
4 8 9s
$$
D. $$
3 5 0s
$$
E. $$
6 2 4s
$$
F. $$
3 7 5s
$$
G. $$
5 5 0s
$$
H. $$
5 0 8s
$$
I. $$
6 1 0s
$$
J. $$
5 9 1s
$$
Answer: H
A stainless steel rotor flow meter $( \rho_{steel}=7920 \mathrm{kg}/\mathrm{m}^{3} )$ has a measurement range of $250 \sim 2500 \mathrm{L}/\mathrm{h}$. When measuring carbon tetrachloride ( $\rho_{\mathrm{CCl_{4}}}=1590 \mathrm{kg}/\mathrm{m}^{3}$ ), what is the maximum measurable flow rate?

Options:
A. $$
1 8 9 5 \mathrm{L} / \mathrm{h}
$$
B. $$
2 0 5 0 \mathrm{L} / \mathrm{h}
$$
C. $$
2 1 0 0 \mathrm{L} / \mathrm{h}
$$
D. $$
1 7 2 0 \mathrm{L} / \mathrm{h}
$$
E. $$
2 2 5 0 \mathrm{L} / \mathrm{h}
$$
F. $$
2 5 5 0 \mathrm{L} / \mathrm{h}
$$
G. $$
2 3 0 0 \mathrm{L} / \mathrm{h}
$$
H. $$
1 9 0 0 \mathrm{L} / \mathrm{h}
$$
I. $$
1 5 0 0 \mathrm{L} / \mathrm{h}
$$
J. $$
1 6 5 5 \mathrm{L} / \mathrm{h}
$$
Answer: A
A plate-and-frame filter press operates under constant pressure to filter a water suspension with a solid content of 0.1 kg solid per kg of suspension. The porosity of the filter cake is $\varepsilon = 0.4$; the density of the particles is $\rho_{\mathrm{p}} = 5000 \mathrm{kg/m}^{3}$, and the initial specific filtration resistance $q_{\mathrm{e}} = 0$. After filtering for 10 minutes, 1.2 m³ of filtrate is collected. Question: What is the volume of the filter cake after filtering for 1 hour?

Options:
A. $0.45m^3$
B. $0.25m^3$
C. $0.30m^3$
D. $0.22m^3$
E. $0.15m^3$
F. $0.50m^3$
G. $0.20m^3$
H. $0.18m^3$
I. $0.11m^3$
J. $0.35m^3$
Answer: I
Using a leaf filter to filter a water suspension of a certain solid powder, the mass fraction of the solid content in the suspension is 4%, and the density of the solid is $2500 \mathrm{kg}/\mathrm{m}^{3}$. The operating temperature is 20°C, and the filter cake is incompressible, with a water content of 30% (mass fraction). Currently, each filtration takes 30 minutes, producing a filter cake volume of 0.4 $\mathrm{m}^{3}$, with an operational pressure difference of 0.15 MPa. The filtration constant $K=7.5 \times 10^{-5} \,\mathrm{m^{2}/s}$, and $q_{e}=3.226 \times 10^{-4}\,\mathrm{m^{3}/m^{2}}$. To maintain the same amount of filtrate in 30 minutes if the leaf filter becomes partially clogged over time, reducing the filtration area by 19.3%, what should the operational pressure difference be (MPa)?.

Options:
A. 0.28MPa
B. 0.25MPa
C. 0.18MPa
D. 0.20MPa
E. 0.33MPa
F. 0.23MPa
G. 0.19MPa
H. 0.30MPa
I. 0.21MPa
J. 0.27MPa
Answer: F
To filter a certain suspension using a plate-and-frame filter press, the filtration area is $10 \mathrm{m}^{2}$, the resistance of the medium can be ignored, and the filter cake is incompressible, with $K=2.5\times10^{-4}\,\mathrm{m}^{2}/\mathrm{s}$. If at the end of filtration, the volume of the filtrate is $V=5\,\mathrm{m}^{3}$, and it is then washed with 0.5 $m^3$ of clean water (with $\Delta p$ and $\mu$ the same as at the end of filtration), what is the washing rate?

Options:
A. $$ 9 . 1 5 \times 1 0 ^{-5} $$
B. $$
6. 2 5 \times1 0^{-4}
$$
C. $$ 6 . 0 0 \times 1 0 ^{-5} $$
D. $$ 1 . 2 0 \times 1 0 ^{-3} $$
E. $$ 4 . 7 5 \times 1 0 ^{-4} $$
F. $$ 2 . 5 0 \times 1 0 ^{-3} $$
G. $$ 1 . 5 0 \times 1 0 ^{-4} $$
H. $$ 7 . 9 0 \times 1 0 ^{-4} $$
I. $$ 8 . 0 1 \times 1 0 ^{-4} $$
J. $$ 5 . 0 3 \times 1 0 ^{-4} $$
Answer: B
Airflow containing small particles removes fine particles in the dust-settling chamber (Stokes region). The smallest particles that can be 100% removed are particles of $50\mu\mathrm{m}$. If the gas flow rate $q_{V}$ is doubled, what is the smallest particle size that can be 100% removed at this time?

Options:
A. $$
4 4. 8 \mu\mathrm{m}
$$
B. $$
1 2. 5 \mu\mathrm{m}
$$
C. $$
7 0. 7 \mu\mathrm{m}
$$
D. $$
5 1. 1 \mu\mathrm{m}
$$
E. $$
2 9. 7 \mu\mathrm{m}
$$
F. $$
9 8. 2 \mu\mathrm{m}
$$
G. $$
6 2. 9 \mu\mathrm{m}
$$
H. $$
1 5. 3 \mu\mathrm{m}
$$
I. $$
3 5. 4 \mu\mathrm{m}
$$
J. $$
8 5. 6 \mu\mathrm{m}
$$
Answer: C
A gravity dust fall chamber measuring 2m in length, 2m in width, and 1m in height is used to process dust-laden gas at a rate of $3000 \mathrm{m}^{3}/\mathrm{h}$. The density of the dust particles is known to be $3000 \mathrm{kg}/\mathrm{m}^{3}$, the gas density is 1.5 $kg/{m}^{3}$, and the gas viscosity $\mu = 2 \times 10^{-5} \,\mathrm{Pa}\cdot\!\mathrm{s}$. The dust particles can be considered spherical, uniformly distributed in the gas. If four horizontal baffles are installed in the dust fall chamber, dividing it evenly into 5 layers each 200mm high, what is the smallest particle diameter that can theoretically be removed 100%?

Options:
A. 0.01234mm
B. 0.05123mm
C. 0.04056mm
D. 0.02259mm
E. 0.04321mm
F. 0.03098mm
G. 0.05987mm
H. 0.02567mm
I. 0.06572mm
J. 0.07890mm
Answer: D
In a certain packed tower, air is used to remove toluene from water. The water contains toluene at a concentration of $60\operatorname{mg}/\operatorname{kg}$ (mass ratio), and now we want to reduce the toluene concentration in the water to $2\mathrm{mg}/\mathrm{kg}$. The packed tower operates at 20°C and 1.1 atm. The equilibrium relation is given by $p_{\mathrm{tol}}=256x$, where $p_{\mathrm{tol}}$ is the partial pressure of toluene in the gas phase, in atm, and $x$ is the mole fraction of toluene in the liquid phase. What is the minimum air flow rate required when the water flow rate is $6\mathrm{m}^{3}$/h?

Options:
A. 1. 325kmol/h
B. 1. 365kmol/h
C. 1. 345kmol/h
D. 1. 405kmol/h
E. 1. 295kmol/h
F. 1. 415kmol/h
G. 1. 385kmol/h
H. 1. 355kmol/h
I. 1. 395kmol/h
J. 1. 375kmol/h
Answer: G
Using clear water to counter-currently absorb the soluble components in a mixed gas, the concentration of the soluble components in the mixed gas is 0.05, the gas outlet concentration is 0.02, and the absorbent liquid outlet concentration is 0.098 (all in mole fractions). Within the operational range, the gas-liquid equilibrium relationship is $y=0.5x$. It is known that this absorption process is controlled by gas phase resistance, and the overall mass transfer coefficient $K_{y}a\propto G^{0.8}$. Calculate the mole fraction of the liquid at the bottom of the column $x_{out}$ when the liquid flow rate is doubled?

Options:
A. 0.0564
B. 0.0722
C. 0.0812
D. 0.0896
E. 0.0651
F. 0.0608
G. 0.0753
H. 0.0547
I. 0.0785
J. 0.0639
Answer: B
In a countercurrent operation absorption tower, ammonia is absorbed from a mixed gas of ammonia and air. The flow rate of the mixed gas per unit tower cross-section is $0.036\mathrm{kmol} / ({m^{2}} \cdot\mathrm{s} )$, containing 2% ammonia (by volume). The fresh absorbent is a water solution containing 0.0003 (mole fraction) of ammonia, added from the top of the tower. The required ammonia recovery rate must not be lower than 91%. The design uses a liquid-to-gas ratio that is 1.3 times the minimum liquid-to-gas ratio. The phase equilibrium relationship for the ammonia-water-air system is $y = 1.2x$. Given that the overall gas-phase mass transfer coefficient $K_{y} a$ is 0.0483 kmol/($m^{3} \cdot s$), determine the required tower height $H$.

Options:
A. 6.72m
B. 7.34m
C. 9.47m
D. 5.89m
E. 4.65m
F. 5.56m
G. 4.29m
H. 6.08m
I. 8.13m
J. 5.02m
Answer: J
24-year-old woman, experienced amenorrhea for 41 days, tested positive for pregnancy, and underwent suction curettage 10 days ago. Today, she suddenly collapsed to the ground, with a body temperature of 37.5°C, blood pressure of 75/52.5 mmHg, and pulse of 100/min. There is significant tenderness and rebound tenderness in the lower abdomen, slight vaginal bleeding, marked cervical motion tenderness, the cervix is closed, the uterus is slightly enlarged and slightly soft, and there seems to be a poorly defined mass on the right side with tenderness. White blood cell count is 10x10⁹/L, with neutrophils at 0.70. The most accurate diagnosis is?

Options:
A. Endometriosis with acute rupture of endometriotic cyst
B. Rupture of the right fallopian tube due to ectopic pregnancy
C. Pelvic inflammatory disease with severe complications
D. Tubo-ovarian abscess with significant peritoneal irritation
E. Acute appendicitis with pelvic involvement and hemorrhage
F. Rupture of an ovarian cyst causing acute abdominal pain
G. Incomplete abortion with retained products of conception
H. Ovarian torsion with resultant hemorrhagic necrosis
I. Hemorrhagic corpus luteum cyst rupture leading to shock
J. Perforation of the uterus following recent curettage
Answer: B
A 35-year-old woman has not conceived in 5 years of marriage, with increased menstrual flow over the past 3 years and worsening dysmenorrhea. A gynecological examination reveals two nodules the size of soybeans palpable at the uterine fundus ligaments, with obvious tenderness. A mass approximately 5cm x 6cm, partially solid and partially cystic with limited mobility, is palpable in the area of the right adnexa. The most effective auxiliary examination method to clarify the diagnosis is ().

Options:
A. Biopsy of uterine lining
B. Blood hormone testing
C. Pelvic X-ray
D. Computed tomography
E. Laparoscopy
F. Cervical swab analysis
G. Ovarian cyst aspiration
H. Abdominal MRI
I. Hysterosalpingography
J. Pelvic ultrasound
Answer: E
Water at $1.5 MPa$ and 150 °C undergoes adiabatic throttling through a throttle valve, reducing its pressure to $200 kPa$. The velocity entering the throttle valve is 5 m/s, and the pipe diameters before and after throttling are equal. What is the velocity of the fluid after throttling?

Options:
A. 200.9 m $/ s$
B. 207.1 m $/ s$
C. 201.3 m $/ s$
D. 206.4 m $/ s$
E. 199.8 m $/ s$
F. 212.0 m $/ s$
G. 210.5 m $/ s$
H. 215.4 m $/ s$
I. 203.6 m $/ s$
J. 208.7 m $/ s$
Answer: D
Assuming the total amount of carboxyl groups in the original mixture is 2 mol, among which 1.0% is acetic acid, without any other factors affecting the molar fraction of functional groups, a polyester with $M_{n}=5000$ is synthesized from 1 mol of butanediol and 1 mol of adipic acid. What is the required degree of reaction $p$ to achieve the same number average polymerization degree?

Options:
A. $$
p \!=\! 0. 7 2 5
$$
B. $$
p \!=\! 0. 8 4 3
$$
C. $$
p \!=\! 0. 8 8 9
$$
D. $$
p \!=\! 0. 9 3 2
$$
E. $$
p \!=\! 0. 5 4 8
$$
F. $$
p \!=\! 0. 9 1 7
$$
G. $$
p \!=\! 0. 6 7 4
$$
H. $$
p \!=\! 0. 9 8 1
$$
I. $$
p \!=\! 0. 7 5 2
$$
J. $$
p \!=\! 0. 6 2 9
$$
Answer: H
Compounds tetra-n-propylammonium chloride and tri-n-propylammonium chloride are identified by _____.

Options:
A. NaOH aqueous solution
B. NaCl aqueous solution
C. KOH aqueous solution
D. H2SO4 aqueous solution
E. HCl aqueous solution
F. Na2CO3 aqueous solution
G. CH3COOH aqueous solution
H. NH4Cl aqueous solution
I. H2O2 aqueous solution
J. NaHCO3 aqueous solution
Answer: A
Slider $A$ moves along a guide rail in a vertical plane. The shape of the guide rail is a hyperbola, and its equation is $xy = 36 (\mathrm{m}^{2})$. Assuming that the speed of the slider is a constant $v = 10$ m/s, what are the horizontal and vertical acceleration components of the slider when $x = 6$ m?

Options:
A. $a_x = 11.56\mathrm{m}/\mathrm{s}^{2}$
$a_y = 11.56\mathrm{m}/\mathrm{s}^{2}$
B. $a_x = 10.50\mathrm{m}/\mathrm{s}^{2}$
$a_y = 10.50\mathrm{m}/\mathrm{s}^{2}$
C. $a_x = 9.06\mathrm{m}/\mathrm{s}^{2}$
$a_y = 9.06\mathrm{m}/\mathrm{s}^{2}$
D. $a_x = 9.21\mathrm{m}/\mathrm{s}^{2}$
$a_y = 9.21\mathrm{m}/\mathrm{s}^{2}$
E. $a_x = 10.63\mathrm{m}/\mathrm{s}^{2}$
$a_y = 10.63\mathrm{m}/\mathrm{s}^{2}$
F. $a_x = 8.56\mathrm{m}/\mathrm{s}^{2}$
$a_y = 8.56\mathrm{m}/\mathrm{s}^{2}$
G. $a_x = 7.42\mathrm{m}/\mathrm{s}^{2}$
$a_y = 7.42\mathrm{m}/\mathrm{s}^{2}$
H. $a_x = 8.34\mathrm{m}/\mathrm{s}^{2}$
$a_y = 8.34\mathrm{m}/\mathrm{s}^{2}$
I. $a_x = 6.28\mathrm{m}/\mathrm{s}^{2}$
$a_y = 6.28\mathrm{m}/\mathrm{s}^{2}$
J. $a_x = 5.97\mathrm{m}/\mathrm{s}^{2}$
$a_y = 5.97\mathrm{m}/\mathrm{s}^{2}$
Answer: H
At a certain moment, point $P$ is moving along a plane curve, and its position can be determined by polar coordinates. At this instant, $r = 2 \, \mathrm{m}$, $\theta = 60^\circ$, $v_r = 3 \, \mathrm{m/s}$, $v_\theta = 4 \, \mathrm{m/s}$, $a_r = -10 \, \mathrm{m/s}^2$, $a_\theta = -5 \, \mathrm{m/s}^2$. Find the radius of curvature $\rho$ of the trajectory at this moment.

Options:
A. $$
10m
$$
B. $$
5m
$$
C. $$
7m
$$
D. $$
4.5m
$$
E. $$
3m
$$
F. $$
6m
$$
G. $$
8m
$$
H. $$
12m
$$
I. $$
11m
$$
J. $$
9m
$$
Answer: B
Establish a new temperature scale, with the symbol $\mathrm{^{\circ}N}$ representing the temperature unit (its absolute temperature scale is represented by $\mathrm{{^\circ Q}}$ as the temperature unit). It is stipulated that the freezing point and boiling point of pure water are 100°N and 1000°N. Find:
If the absolute zero of this temperature scale is the same as the zero of the thermodynamic temperature scale, what would be the reading on its absolute temperature scale when it reads $0^{\circ} \mathrm{N}$ ?

Options:
A. $$
1789.645^{\circ} \mathrm{Q}
$$
B. $$
2587.321^{\circ} \mathrm{Q}
$$
C. $$
2358.385^{\circ} \mathrm{Q}
$$
D. $$
1245.678^{\circ} \mathrm{Q}
$$
E. $$
2156.774^{\circ} \mathrm{Q}
$$
F. $$
3102.589^{\circ} \mathrm{Q}
$$
G. $$
2947.853^{\circ} \mathrm{Q}
$$
H. $$
2879.762^{\circ} \mathrm{Q}
$$
I. $$
1123.456^{\circ} \mathrm{Q}
$$
J. $$
2034.198^{\circ} \mathrm{Q}
$$
Answer: C
Benzene at 30°C flows through the inner tube of a double-pipe heat exchanger at a rate of 4500 kg·$h^{-1}$, with the temperature rising to 50°C. The specifications of the heat exchanger tubes are as follows: the outer tube is $\phi$ 7mm×3mm, and the inner tube is $\phi$ 38mm×2.5mm. Toluene, with a density of 830 kg·$m^{-3}$, flows through the annular space, entering at 72°C and exiting at 38°C. Determine the convective heat transfer coefficient of the tube wall for toluene.

Options:
A. 1250W$\cdot m^{-2}\cdot °C^{-1}$
B. 1425W$\cdot m^{-2}\cdot °C^{-1}$
C. 950W$\cdot m^{-2}\cdot °C^{-1}$
D. 1190W$\cdot m^{-2}\cdot °C^{-1}$
E. 1342W$\cdot m^{-2}\cdot °C^{-1}$
F. 1035W$\cdot m^{-2}\cdot °C^{-1}$
G. 1470W$\cdot m^{-2}\cdot °C^{-1}$
H. 1263W$\cdot m^{-2}\cdot °C^{-1}$
I. 1300W$\cdot m^{-2}\cdot °C^{-1}$
J. 1100W$\cdot m^{-2}\cdot °C^{-1}$
Answer: H
In a 1-2 type shell-and-tube heat exchanger with a heat transfer area of 5 m$^{2}$, hot water outside the tubes is cooled by cold water inside the tubes. The heat transfer coefficient $K=1.4\times10^3$ W·m$^{-2}$·K$^{-1}$. The flow rates and inlet temperatures of the cold and hot water are as follows: $q_{m,2}=1\times10^4$ kg·h$^{-1}$, $q_{m+1}=5\times10^3$ kg·h$^{-1}$, $T_1^{\prime}=20$°C, $T_1=100$°C. What is the heat transfer calculated using the logarithmic mean temperature difference method?

Options:
A. $269kW$
B. $723kW$
C. $512kW$
D. $347kW$
E. $248kW$
F. $384kW$
G. $612kW$
H. $158kW$
I. $459kW$
J. $303kW$
Answer: A
Under conditions of 5°C and normal pressure, the solubility of ethylene oxide in water is measured, assuming that the equilibrium data conform to Henry's Law within the experimental range. What is the equilibrium relationship in the form of $Y=f(X)$ when the experimental data is $x=0.0301$ (mole fraction) and the vapor phase equilibrium partial pressure is $p=12.73k$Pa?

Options:
A. $$Y=\frac{mX}{1+(1+mX)}=\frac{5.17X}{1+2.17X}$$
B. $$Y=\frac{mX}{1+(1-mX)}=\frac{4.17X}{1-3.17X}$$
C. $$Y=\frac{mX}{1-(1+mX)}=\frac{3.17X}{1+4.17X}$$
D. $$Y=\frac{mX}{1+(1+mX)}=\frac{7.17X}{1+3.17X}$$
E. $$Y=\frac{mX}{1+(1+mX)}=\frac{9.17X}{1+7.17X}$$
F. $$Y=\frac{mX}{1+(1-mX)}=\frac{8.17X}{1-7.17X}$$
G. $$Y=\frac{mX}{1-(1+mX)}=\frac{0.17X}{1+8.17X}$$
H. $$Y=\frac{mX}{1+(1-mX)}=\frac{6.17X}{1-4.17X}$$
I. $$Y=\frac{mX}{1-(1-mX)}=\frac{1.17X}{1-6.17X}$$
J. $$Y=\frac{mX}{1-(1-mX)}=\frac{2.17X}{1-5.17X}$$
Answer: B
In the liquid-phase reaction A+B$\xrightarrow k$R+S, it is known that $-r_{A}=k_{c}c_{A}^{2},k_{c}=2\mathrm{I}_{c}\bullet\mathrm{mol}^{-1}\bullet\mathrm{s}^{-1},c_{A,0}= lmol·L^{-1}$. If the reaction is carried out in two equal-volume continuous stirred-tank reactors in series, what is the conversion rate when the average residence time is 2 seconds?

Options:
A. 57%
B. 74%
C. 35%
D. 52%
E. 45%
F. 80%
G. 63%
H. 61%
I. 69%
J. 39%
Answer: I
Rod $AB$, which is 10 cm long, undergoes planar motion with accelerations at both endpoints directed toward each other along the rod. Given $a_{A} = 10 \ \mathrm{cm/s^{2}}$ and $a_{B} = 20 \ \mathrm{cm/s^{2}}$, what are the angular velocity and angular acceleration of the rod ?

Options:
A. $$\frac{3}{2} \mathrm{~ r a d / s, ~} 1$$
B. $$4 \mathrm{~ r a d / s, ~} 0$$
C. $$\sqrt{3} \mathrm{~ r a d / s, ~} 0$$
D. $$3 \mathrm{~ r a d / s, ~} 1$$
E. $$\sqrt{5} \mathrm{~ r a d / s, ~} 0$$
F. $$\sqrt{2} \mathrm{~ r a d / s, ~} 1$$
G. $$1 \mathrm{~ r a d / s, ~} 2$$
H. $$\frac{1}{2} \mathrm{~ r a d / s, ~} 2$$
I. $$\sqrt{2} \mathrm{~ r a d / s, ~} 2$$
J. $$2 \mathrm{~ r a d / s, ~} 0$$
Answer: C
A steel ball bearing falls onto a horizontal steel plate at a 45° angle and bounces off forming a 60° angle with the vertical line. What is the coefficient of restitution for the collision ?

Options:
A. $$0. 7 0$$
B. $$0. 5 3$$
C. $$0. 6 5$$
D. $$0. 5 8$$
E. $$0. 5 0$$
F. $$0. 8 0$$
G. $$0. 7 5$$
H. $$0. 4 9$$
I. $$0. 7 2$$
J. $$0. 6 2$$
Answer: D
The main component of an accelerometer is an inertial mass, which is connected to the casing by a linear spring and is immersed in a viscous fluid. The amplitude-frequency curve of the accelerometer exhibits a resonance peak, with the corresponding frequency of the resonance peak being $\omega_{0} = 100$ rad/s. The relative height of the resonance peak (i.e., the ratio of the resonance peak to the amplitude at $\omega=0$ on the amplitude-frequency curve) is equal to 1.4. When calibrating the accelerometer, it was found that if the measurement axis of the accelerometer is installed vertically and then inverted 180°, the output signal proportional to the displacement of the inertial mass will change by 5B. Now, the accelerometer is mounted on a movable base that undergoes random vibrations along a certain axis, and the measurement axis of the accelerometer is aligned with this axis. Assuming that the random acceleration of the base's vibration can be considered as white noise, what is the intensity of the white noise when the mean square value of the AC component of the accelerometer's output signal reaches $100 B^{2}$ ?

Options:
A. $$
B^{2}=5 6 \ \mathrm{m^{2} / s^{3}}.
$$
B. $$
B^{2}=4 8 \ \mathrm{m^{2} / s^{3}}.
$$
C. $$
B^{2}=5 0 \ \mathrm{m^{2} / s^{3}}.
$$
D. $$
B^{2}=4 9 \ \mathrm{m^{2} / s^{3}}.
$$
E. $$
B^{2}=6 0 \ \mathrm{m^{2} / s^{3}}.
$$
F. $$
B^{2}=5 3 \ \mathrm{m^{2} / s^{3}}.
$$
G. $$
B^{2}=5 1 \ \mathrm{m^{2} / s^{3}}.
$$
H. $$
B^{2}=5 5 \ \mathrm{m^{2} / s^{3}}.
$$
I. $$
B^{2}=5 7 \ \mathrm{m^{2} / s^{3}}.
$$
J. $$
B^{2}=5 8 \ \mathrm{m^{2} / s^{3}}.
$$
Answer: F
A smooth flat plate with a length of 3 m and a width of 1 m flies at a constant speed of $V=50 \mathrm{m/s}$ with no angle of attack. It is known that the value of air's $\nu$ is 15 mm/s, and the flow within the boundary layer transitions from laminar to turbulent at 0.9 m from the leading edge.The drag force on one side of the plate is ().

Options:
A. 0.00301
B. 0.00478
C. 0.00315
D. 0.00375
E. 0.00150
F. 0.00256
G. 0.00185
H. 0.00124
I. 0.00426
J. 0.00208
Answer: J
The water depth at the beach is 1m, and in the distance, the rising tide wave is 2m above the water surface. the propagation speed of the tidal wave, $D$, and the movement speed of the tidal water $V_{f}$ is ().

Options:
A. $D$=7.70m/s, $V_{f}$ =5.00m/s
B. $D$=7.67m/s,
$V_{f}$ =5.11m/s
C. $D$=7.65m/s, $V_{f}$ =5.25m/s
D. $D$=7.50m/s, $V_{f}$ =5.10m/s
E. $D$=7.60m/s, $V_{f}$ =5.00m/s
F. $D$=7.55m/s, $V_{f}$ =5.20m/s
G. $D$=8.10m/s, $V_{f}$ =5.15m/s
H. $D$=7.80m/s, $V_{f}$ =5.05m/s
I. $D$=8.05m/s, $V_{f}$ =5.30m/s
J. $D$=8.00m/s, $V_{f}$ =5.50m/s
Answer: B
All the triple-sealed containers are equipped with vacuum gauges, and their readings are the same, $p_{1}=p_{2}=p_{3}=20kPa$ (vacuum degree). The gas pressure $\rho$ in the innermost container is ().

Options:
A. 443m
B. 526m
C. 305m
D. 212m
E. 382m
F. 331m
G. 198m
H. 449m
I. 474m
J. 509m
Answer: H
A uniformly charged plastic sphere with a diameter of $r = 0.01 \ \mathrm{m}$ and a total charge of $q = 10^{-8} \ \mathrm{C}$ is suspended using an insulating string, with its lowest point 0.01 m above the surface of a saltwater container. As a result, we observe a slight bulge on the water surface underneath the sphere. The surface tension of the water can be neglected, and the density of the saltwater is taken to be $\rho = 1000 \ \mathrm{kg/m}^3$. What is the height of the bulge on the water's surface?

Options:
A. $$
2. 7 \times10^{-4} \mathrm{~m}
$$
B. $$
2. 6 \times10^{-4} \mathrm{~m}
$$
C. $$
3. 2 \times10^{-4} \mathrm{~m}
$$
D. $$
2. 8 \times10^{-4} \mathrm{~m}
$$
E. $$
2. 4 \times10^{-4} \mathrm{~m}
$$
F. $$
3. 0 \times10^{-4} \mathrm{~m}
$$
G. $$
3. 1 \times10^{-4} \mathrm{~m}
$$
H. $$
2. 5 \times10^{-4} \mathrm{~m}
$$
I. $$
3. 3 \times10^{-4} \mathrm{~m}
$$
J. $$
2. 9 \times1 0^{-4} \mathrm{~ m}
$$
Answer: J
In a cylinder with no heat exchange with the outside, there is a very light piston closing off water with a mass of $m = 30 \, \text{g}$ at a temperature of 0 °C. At this moment, the piston is just above the water surface. Now, using an electric heater with a resistance of $r = 10 \, \Omega$ to heat the water, the heat absorption efficiency of the cylinder is $\eta = 80\%$. Given the external pressure is $p = 1 \times 10^{5} \, \text{Pa}$, with a current of $I = 2 \, \text{A}$ applied for a time of $t = 10 \, \text{min}$ and the cross-sectional area of the piston is $S = 1 \times 10^{-2} \, \text{m}^{2}$, what is the height $H$ that the piston can rise to?

Options:
A. $0.54\mathrm{~ m}$
B. $0.55\mathrm{~ m}$
C. $0.52\mathrm{~ m}$
D. $0.50\mathrm{~ m}$
E. $0.60\mathrm{~ m}$
F. $0.45\mathrm{~ m}$
G. $0.59\mathrm{~ m}$
H. $0.51\mathrm{~ m}$
I. $0.48\mathrm{~ m}$
J. $0.62\mathrm{~ m}$
Answer: H
The radius of the wire is $a$, and the radius of the cylinder is $b$. The thickness of the cylinder is negligible. A coaxial cable is composed of a long straight wire and a coaxial conductor cylinder surrounding it. The current $I$ flows through the cylinder and returns through the wire. In the cross-sections of both the wire and the cylinder, $I$ is uniformly distributed. What is the magnetic field capacity $W_{m}$ stored by this cable of length $l$ when $a = 1.0 \, \mathrm{mm}$, $b = 7.0 \, \mathrm{mm}$, $l = 1.00 \, \mathrm{m}$, and $I = 100 \, \mathrm{A}$?

Options:
A. $$
4. 0 \times1 0^{-3}~\mathrm{J}
$$
B. $$
4. 9 \times1 0^{-3}~\mathrm{J}
$$
C. $$
2. 5 \times1 0^{-3}~\mathrm{J}
$$
D. $$
5. 0 \times1 0^{-3}~\mathrm{J}
$$
E. $$
3. 1 \times1 0^{-3}~\mathrm{J}
$$
F. $$
6. 3 \times1 0^{-3}~\mathrm{J}
$$
G. $$
3. 4 \times1 0^{-3}~\mathrm{J}
$$
H. $$
0. 7 \times1 0^{-3}~\mathrm{J}
$$
I. $$
2. 2 \times1 0^{-3}~\mathrm{J}
$$
J. $$
1. 8 \times1 0^{-3}~\mathrm{J}
$$
Answer: I
A magnetic rod is 5.0 cm long, with a cross-sectional area of 1.0 cm² and a density of 7.9 g/cm³. Assume all the magnetic moments of the iron atoms in the rod are neatly aligned along the rod's length, with each iron atom having a magnetic moment of 1.8 × 10⁻²³ A·m². Given that the atomic weight of iron is 55.85 and Avogadro's constant is 6.022 × 10²³ mol⁻¹, when this ferromagnetic rod is placed in an external magnetic field B = 1.5 T and is perpendicular to B, what is the torque exerted by B that causes it to rotate?

Options:
A. $$
5~\mathrm{N} \cdot\mathrm{m}
$$
B. $$
0.8~\mathrm{N} \cdot\mathrm{m}
$$
C. $$
2~\mathrm{N} \cdot\mathrm{m}
$$
D. $$
1 2~\mathrm{N} \cdot\mathrm{m}
$$
E. $$
11~\mathrm{N} \cdot\mathrm{m}
$$
F. $$
9.2~\mathrm{N} \cdot\mathrm{m}
$$
G. $$
7.5~\mathrm{N} \cdot\mathrm{m}
$$
H. $$
4.5~\mathrm{N} \cdot\mathrm{m}
$$
I. $$
6.1~\mathrm{N} \cdot\mathrm{m}
$$
J. $$
3~\mathrm{N} \cdot\mathrm{m}
$$
Answer: D
An infinitely long straight cylindrical conductor with a radius of $R$ carries a current flowing along the axial direction. The current is uniformly distributed across the cross-section, and the current density is $j$. What is the magnetic field strength at a distance $r$ from the conductor's axis?

Options:
A. $$
B {=} \mu_{0} \left( \frac{R^{2}} {r^{2}} \right) j \times R, \quad r {>} R
$$
B. $$
B {=} \frac{1} {3} \mu_{0} \left( \frac{r} {R} \right) j \times r, \quad r {>} R
$$
C. $$
B {=} \frac{1} {2} \mu_{0} \left( \frac{r} {R} \right)^{2} j \times R, \quad r {>} R
$$
D. $$
B {=} 3 \mu_{0} \left( \frac{R} {r} \right)^{2} j \times R, \quad r {>} R
$$
E. $$
B {=} 2 \mu_{0} \left( \frac{R} {r} \right) j \times R, \quad r {>} R
$$
F. $$
B {=} \frac{1} {2} \mu_{0} \left( \frac{R} {r} \right)^{2} j \times r, \quad r {>} R
$$
G. $$
B {=} 2 \mu_{0} \left( \frac{R^{3}} {r} \right) j \times r, \quad r {>} R
$$
H. $$
B {=} \frac{3} {2} \mu_{0} \left( \frac{r} {R} \right)^{3} j \times r, \quad r {>} R
$$
I. $$
B {=} \frac{1} {2} \mu_{0} \left( \frac{R} {r^{2}} \right) j \times r, \quad r {>} R
$$
Answer: F
The uranium-235 nucleus can be considered as a sphere with a radius of $R = 9.2 \times 10^{-15} \, \mathrm{m}$, containing a total of 92 protons, each with a charge of $e = 1.6 \times 10^{-19} \, \mathrm{C}$. Assume that these charges are uniformly distributed within the sphere. How much energy is released when 1 kg of uranium-235 undergoes fission into such fragments?

Options:
A. $$
8. 1\times 1 0^{2 7}~\mathrm{M e V}
$$
B. $$
9. 2\times 1 0^{2 5}~\mathrm{M e V}
$$
C. $$
5. 9\times 1 0^{2 5}~\mathrm{M e V}
$$
D. $$
4. 3\times 1 0^{2 8}~\mathrm{M e V}
$$
E. $$
2. 5\times 1 0^{2 8}~\mathrm{M e V}
$$
F. $$
7. 4 \times1 0^{2 6}~\mathrm{M e V}
$$
G. $$
5. 5\times 1 0^{2 6}~\mathrm{M e V}
$$
H. $$
3. 7\times 1 0^{2 6}~\mathrm{M e V}
$$
I. $$
6. 8\times 1 0^{2 4}~\mathrm{M e V}
$$
J. $$
6. 6\times 1 0^{2 7}~\mathrm{M e V}
$$
Answer: F
The plates of a parallel plate capacitor are separated by $2.0\mathrm{mm}$, with a potential difference of $400\mathrm{V}$. Between the plates is a uniform glass sheet with a dielectric constant of $\varepsilon_{\mathrm{r}}=5.0$. Neglecting edge effects, what is the surface charge density of the polarized charge on the glass surface?

Options:
A. $$
- 3. 9 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
B. $$
- 4. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
C. $$
- 9. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
D. $$
- 5. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
E. $$
- 6. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
F. $$
- 10. 0 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
G. $$
- 2. 8 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
H. $$
- 1. 7 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
I. $$
- 8. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
J. $$
- 7. 1 \times1 0^{-6} \left( \mathrm{C / m^{2}} \right)
$$
Answer: J