MikaStars39/nano-eval huggingface dataset:
The corona is the millimeter-wave band radio wave radiation source of the Sun. Assuming the effective temperature of the radiation is \(T $\approx 10^{6}$, $\mathrm{K}$\), and the equivalent radius of the corona is \($r = 6.95 \times 10^{8}$$\mathrm{m}$). What is the radio radiation flux with a bandwidth of 1 MHz from the Sun to the Earth ?

Options:
A. $$
S=1. 8 6 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
B. $$
S=1. 9 2 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
C. $$
S=1. 8 4 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
D. $$
S=1. 7 8 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
E. $$
S=2. 5 6 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
F. $$
S=1. 8 8 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
G. $$
S=1. 8 3 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
H. $$
S=2. 0 0 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
I. $$
S=1. 9 5 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
J. $$
S=2. 0 1 \times1 0^{-1 5} \mathrm{W} / \mathrm{M H z}
$$
Answer: A
Given: A thin flat plate measuring $0.2m \times 0.2m$ is placed parallel in a uniform gas flow field created by a wind tunnel. At an airflow velocity of $u_{\infty} = 40m/s$, it is measured with a dynamometer that to keep the plate steady in the airflow, a force of 0.075N must be applied. At this point, the airflow temperature $t_{\circ}=20$ °C and the temperature of both surfaces of the plate $^{f_w}=120$ °C. The gas pressure is $1.013 \times 10^3 Pa$.
Seek: Using analogy theory, determine the convective heat transfer amount on the two surfaces of the plate.

Options:
A. $$225.4W$$
B. $$230.0W$$
C. $$285.8W$$
D. $$240.9W$$
E. $$295.2W$$
F. $$210.3W$$
G. $$300.7W$$
H. $$250.5W$$
I. $$260.1W$$
J. $$275.5W$$
Answer: D
Given: Air with an average temperature of 100°C and pressure of 120 kPa is flowing at a velocity of 1.5 m/s through an electrically heated tube with an inner diameter of 25 mm. Under the uniform heat flux boundary condition, in the fully developed laminar convection heat transfer region inside the tube, the Nusselt number (Nu) is 4.36.
Find: Estimate the convective heat transfer surface coefficient in the fully developed heat transfer region.

Options:
A. $$
6. 2 W / \left( m^{2} \cdot K \right)
$$
B. $$
5. 2 W / \left( m^{2} \cdot K \right)
$$
C. $$
4. 5 W / \left( m^{2} \cdot K \right)
$$
D. $$
4. 9 W / \left( m^{2} \cdot K \right)
$$
E. $$
5. 6 W / \left( m^{2} \cdot K \right)
$$
F. $$
8. 3 W / \left( m^{2} \cdot K \right)
$$
G. $$
6. 4 W / \left( m^{2} \cdot K \right)
$$
H. $$
7. 5 W / \left( m^{2} \cdot K \right)
$$
I. $$
7. 1 W / \left( m^{2} \cdot K \right)
$$
J. $$
7. 8 W / \left( m^{2} \cdot K \right)
$$
Answer: E
The evaporative heating surface tube wall in the furnace of a steam steel boiler is heated by flue gas at a temperature of 1000°C, while the water temperature inside the tube is 200°C. The heat transfer coefficient for the composite heat exchange surface between the flue gas and the outside wall of the heated tube is 100 W/(m²·K), and the heat transfer coefficient for the boiling water with the inner wall is 5000 W/(m²·K). The tube wall is 6 mm thick, with a thermal conductivity (λ) of 42 W/(m·K), and an outer diameter of 52 mm. Calculate the heat load per unit length given the following condition: there is a 2 mm thick layer of scale on the inner surface, with a thermal conductivity (λ) of 1 W/(m·K).

Options:
A. $$
3456.89W
$$
B. $$
7548.27W
$$
C. $$
8123.45W
$$
D. $$
4829.31W
$$
E. $$
5207.06W
$$
F. $$
6921.03W
$$
G. $$
5992.15W
$$
H. $$
4301.17W
$$
I. $$
7210.58W
$$
J. $$
6954.23W
$$
Answer: E
There is a batch of outdoor liquefied petroleum gas storage tanks with a diameter of 2 meters. The tanks maintain an internal temperature of $-40^{\circ} \mathrm{C}$ by having a refrigerant flow through a jacket layer with a fin exterior thickness of 1 cm. Outside the jacket is an insulation layer with a thickness of 30 cm, and the thermal conductivity of the insulation material is $0.1 \, W/(m \cdot K)$. Under harsh summer conditions, the ambient temperature is 40°C, and the composite heat transfer coefficient between the outer surface of the insulation layer and the environment can reach $30 \, W/(m^{2} \cdot K)$. Determine the capacity of the refrigeration equipment necessary to maintain the liquefied gas at $-40^{\circ} \mathrm{C}$ for 10 spherical tanks. The wall thicknesses of the tanks and jacket steel plates can be neglected.

Options:
A. $$
3 7 7 4. 8 0 W
$$
B. $$
4 7 9 9. 9 3 W
$$
C. $$
4 6 5 8. 5 1 W
$$
D. $$
3 0 8 5. 7 2 W
$$
E. $$
4 4 8 1. 6 8 W
$$
F. $$
5 4 1 0. 1 4 W
$$
G. $$
4 3 2 1. 8 6 W
$$
H. $$
3 5 9 2. 4 5 W
$$
I. $$
5 0 2 5. 3 2 W
$$
J. $$
4 0 1 2. 6 9 W
$$
Answer: E
Given: Water at 20°C flows parallel over a flat plate at a velocity of $2 \mathrm{m/s}$, with the velocity distribution within the boundary layer following a cubic polynomial.
Task: Calculate the mass flow rate of fluid within the boundary layer at cross-sections located 10 cm and 20 cm from the leading edge of the plate. (per unit width perpendicular to the flow direction).

Options:
A. $$
1. 6 1 0 \quad k g / m^{2}
$$
B. $$
2. 0 4 8 \quad k g / m^{2}
$$
C. $$
2. 9 4 5 \quad k g / m^{2}
$$
D. $$
1. 5 7 6 \quad k g / m^{2}
$$
E. $$
1. 8 3 4 \quad k g / m^{2}
$$
F. $$
1. 9 5 3 \quad k g / m^{2}
$$
G. $$
3. 1 2 9 \quad k g / m^{2}
$$
H. $$
2. 2 8 7 \quad k g / m^{2}
$$
I. $$
3. 0 5 8 \quad k g / m^{2}
$$
J. $$
2. 3 7 2 \quad k g / m^{2}
$$
Answer: E
Find the $z$-transform of the following sequence, and determine its corresponding zeros, poles, and region of convergence is ().
$x(n) = a^{|n|}, \quad 0 < |a| < 1$

Options:
A. $$\mid z\mid> a$$ Poles: $z= -a$, $z= a$ Zeros: $z= \frac1{a}$, $z= 0$
B. $$0<\mid z\mid<a$$ Poles: $z= a$, $z= 0$ Zeros: $z= \infty$, $z= \frac1{a}$
C. $$\mid z\mid<a$$ Poles: $z= \frac1{a}$, $z= -a$ Zeros: $z= a$, $z=\infty$
D. $$0<\mid a\mid$$ Poles: $z= a$, $z= \infty$ Zeros: $z= 0$, $z= \frac 1a$
E. $$\mid z\mid<\frac1{a}$$ Poles: $z= -a$, $z= 0$ Zeros: $z= \infty$, $z= \frac 1{a}$
F. $$\frac1{a}<\mid z\mid$$ Poles: $z= \infty$, $z= 0$ Zeros: $z= a$, $z= \frac1{a}$
G. $$\mid a\mid>\frac1{\mid z\mid}$$ Poles: $z= a$, $z= \frac 1{a}$ Zeros: $z= -a$, $z= \infty$
H. $$\mid a\mid<\mid z\mid<\frac1{\mid a\mid}$$
Poles: $z= a$, $z= \frac 1a$
Zeros: $z= 0$, $z= \infty$
I. $$\mid a\mid>\mid z\mid$$ Poles: $z= \frac 1{a}$, $z=\infty$ Zeros: $z= 0$, $z= a$
J. $$\mid z\mid=a$$ Poles: $z= \frac 1{a}$, $z= a$ Zeros: $z= \infty$, $z= 0$
Answer: H
Given the following $N$-point DFT $X(k)$, find $x(n) = \mathrm{IDFT} \big[ X(k) \big]$ is ().
$$
X(k) = \begin{cases}
\frac{N}{2} \mathrm{e}^{i \theta}, & k = m \\
\frac{N}{2} \mathrm{e}^{-i \theta}, & k = N-m \\
0, & \text{otherwise}
\end{cases}
$$

Options:
A. $$
x ( n )= \frac{1}{N} \sum_{k=0}^{N-1} X(k) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
B. $$
x ( n )= \operatorname{c o s} \! \left( \frac{2 \pi} {N} n \, m+\theta\right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
C. $$
x ( n )= \operatorname{s i n} \! \left( \frac{2 \pi} {N} m \, n-\theta\right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
D. $$
x ( n )= \operatorname{r e} \{ \operatorname{e}^{-i \left( \frac{2 \pi} {N} k \, n + \theta \right)}\} \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
E. $$
x ( n )= \operatorname{s i n} \! \left( \frac{2 \pi} {N} m \, n+\theta\right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
F. $$
x ( n )= \operatorname{c o s} \! \left( \frac{2 \pi} {N} m \, n+\theta\right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
G. $$
x ( n )= \operatorname{r e} \{ \operatorname{e}^{i \left( \frac{2 \pi} {N} k \, n - \theta \right)}\} \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
H. $$
x ( n )= \sum_{k=0}^{N-1} \frac{X(k)}{N} \operatorname{e}^{i \frac{2 \pi}{N} k n} \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
I. $$
x ( n )= \operatorname{c o s} \! \left( \frac{2 \pi} {N} n \, m-\theta\right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
J. $$
x ( n )= \frac{1}{2} \operatorname{r e} \left( \operatorname{e}^{i \left( \frac{2 \pi} {N} k \, n \right)} \right) \!, \quad n=0 \,, 1 \,, 2 \,, \cdots, N-1
$$
Answer: F
The time-domain $1/O$ difference equation of the filter is set as:
$$
y(n) = x(n) + x(n-1) + \frac{1}{3} y(n-1) + \frac{1}{4} y(n-2)
$$
Given a sampling frequency of 10kHz, an input sine wave with an amplitude of 5, and a frequency of 1kHz, find the steady-state output of this filter is ().

Options:
A. $$
y(n) = 11.45 \operatorname{sin}(0.2\pi n - 1.0) $$
B. $$
y(n) = 13.02 \operatorname{sin}(0.25\pi n - 0.5) $$
C. $$
y(n) = 12.67 \operatorname{sin}(0.15\pi n - 1.2) $$
D. $$
y ( n )=1 2. 1 3 \operatorname{s i n} ( 0.2 \pi n-0.9 )
$$
E. $$
y(n) = 11.89 \operatorname{sin}(0.3\pi n + 0.7) $$
F. $$
y(n) = 11.75 \operatorname{sin}(0.2\pi n + 0.1) $$
G. $$
y(n) = 13.01 \operatorname{sin}(0.18\pi n + 0.6) $$
H. $$
y(n) = 12.89 \operatorname{sin}(0.22\pi n + 0.4) $$
I. $$
y(n) = 12.34 \operatorname{sin}(0.2\pi n + 0.3) $$
J. $$
y(n) = 11.23 \operatorname{sin}(0.2\pi n - 0.8) $$
Answer: D
Starting from the system function of a second-order Butterworth prototype filter, design a low-pass digital filter using bilinear transformation. It is known that the 3dB cutoff frequency of the digital low-pass filter is 100 Hz, and the sampling frequency of the digital system is 1 kHz is ().

Options:
A. $$
H ( z )= \frac{0. 0 7 2 \times( 1+2.5 z^{-1}+z^{-2} )} {1-1. 2 5 z^{-1}+0. 4 0 5 z^{-2}}
$$
B. $$
H ( z )= \frac{0. 0 3 9 \times( 1+3 z^{-1}+z^{-2} )} {1-1. 3 5 8 z^{-1}+0. 4 1 9 z^{-2}}
$$
C. $$
H ( z )= \frac{0. 0 9 5 \times( 1+2.2 z^{-1}+z^{-2} )} {1-1. 0 9 5 z^{-1}+0. 3 7 2 z^{-2}}
$$
D. $$
H ( z )= \frac{0. 0 5 7 \times( 1+1.7 z^{-1}+z^{-2} )} {1-1. 3 0 0 z^{-1}+0. 3 8 4 z^{-2}}
$$
E. $$
H ( z )= \frac{0. 0 1 9 \times( 1+1.5 z^{-1}+z^{-2} )} {1-1. 1 7 8 z^{-1}+0. 4 6 6 z^{-2}}
$$
F. $$
H ( z )= \frac{0. 0 4 5 \times( 1+2.3 z^{-1}+z^{-2} )} {1-1. 2 8 4 z^{-1}+0. 4 5 2 z^{-2}}
$$
G. $$
H ( z )= \frac{0. 0 6 0 \times( 1+2.1 z^{-1}+z^{-2} )} {1-1. 2 0 1 z^{-1}+0. 4 2 5 z^{-2}}
$$
H. $$
H ( z )= \frac{0. 0 6 4 \times( 1+2 z^{-1}+z^{-2} )} {1-1. 1 6 8 z^{-1}+0. 4 2 4 z^{-2}}
$$
I. $$
H ( z )= \frac{0. 0 2 8 \times( 1+2.4 z^{-1}+z^{-2} )} {1-1. 1 2 2 z^{-1}+0. 4 8 4 z^{-2}}
$$
J. $$
H ( z )= \frac{0. 0 8 1 \times( 1+1.8 z^{-1}+z^{-2} )} {1-1. 1 4 9 z^{-1}+0. 3 9 0 z^{-2}}
$$
Answer: H
Given $r = a_x x + a_y y + a_z z$, where $A$ is a constant, and $r = \mid r \mid$, find
$\textcircled {1} \nabla \cdot r; \textcircled {2}$ $\nabla \times r; \textcircled {3}$ $\nabla \times \frac{r}{r}; \textcircled {4} \cdot (A r)$ is ().

Options:
A. 1,0,1,1F
B. 0,3,0,4A
C. 2,2,0,0H
D. 2,0,0,3B
E. 1,0,0,2C
F. 3,0,0,3A
G. 1,1,1,0F
H. 3,1,0,1D
I. 2,0,1,2E
J. 2,1,1,2B
Answer: F
Given that the operating frequency $f = 150$ MHz. At $z = 0$. A uniform plane wave propagates in an ideal medium ($\mu=\mu_0, \varepsilon=4\varepsilon_0, \sigma=0$), and the expression for its electric field intensity $E$ is $E=a_{x}10\cos(\omega t - kz + 30^{\circ}) \quad \text{mV/m}$ . What is the moment $t$ when $E_{x}$ first reaches its maximum value?

Options:
A. $$
6. 9 \times1 0^{-5} \quad\mu\mathrm{s}
$$
B. $$
1. 5 \times1 0^{-2} \quad\mu\mathrm{s}
$$
C. $$
5. 7 \times1 0^{-3} \quad\mu\mathrm{s}
$$
D. $$
7. 2 \times1 0^{-4} \quad\mu\mathrm{s}
$$
E. $$
4. 1 \times1 0^{-3} \quad\mu\mathrm{s}
$$
F. $$
2. 5 \times1 0^{-3} \quad\mu\mathrm{s}
$$
G. $$
2. 8 \times1 0^{-3} \quad\mu\mathrm{s}
$$
H. $$
8. 1 \times1 0^{-3} \quad\mu\mathrm{s}
$$
I. $$
3. 0 \times1 0^{-4} \quad\mu\mathrm{s}
$$
J. $$
9. 3 \times1 0^{-3} \quad\mu\mathrm{s}
$$
Answer: G
A waveguide with dimensions $a \times b = 72.14 \text{mm} \times 34.04 \text{mm}$ transmits a $\mathrm{TE}_{10}$ mode with a wavelength of 10 cm. Find the power capacity of this waveguide is ().

Options:
A. $$
2 6 \ \mathrm{k V} / \mathrm{c m}
$$
B. $$
3 0 \ \mathrm{k V} / \mathrm{c m}
$$
C. $$
2 7 \ \mathrm{k V} / \mathrm{c m}
$$
D. $$
2 9 \ \mathrm{k V} / \mathrm{c m}
$$
E. $$
3 5 \ \mathrm{k V} / \mathrm{c m}
$$
F. $$
3 2 \ \mathrm{k V} / \mathrm{c m}
$$
G. $$
3 4 \ \mathrm{k V} / \mathrm{c m}
$$
H. $$
2 5 \ \mathrm{k V} / \mathrm{c m}
$$
I. $$
3 1 \ \mathrm{k V} / \mathrm{c m}
$$
J. $$
2 8 \ \mathrm{k V} / \mathrm{c m}
$$
Answer: B
A uniformly magnetized permanent magnet sphere with a radius of $a$ and a magnetization intensity of $M$ rotates with a constant angular velocity $\omega$ around an axis passing through the center of the sphere and perpendicular to $M$. Assume $ωa$$\leq$$c$ (the speed of light in vacuum). Using the sphere's center as the origin and the rotation axis as the polar axis, in spherical coordinates, find its average energy flow density is _____.

Options:
A. $$\bar{\boldsymbol{S}}=\frac{1}{6}\mathrm{Re}\boldsymbol{B}\times\frac{\boldsymbol{E}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{6}M^{2}}{18\boldsymbol{\varepsilon}_{0}c^{3}}\:\frac{\mathrm{sin}^{2}\theta}{r^{2}}\boldsymbol{e}_{r}$$
B. $$\bar{\boldsymbol{S}}=\frac{1}{2}\mathrm{Re}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{6}M^{2}}{18\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{1+\mathrm{cos}^{2}\theta}{r^{2}}\boldsymbol{e}_{r}$$
C. $$\bar{\boldsymbol{S}}=\frac{1}{6}\mathrm{Im}\boldsymbol{E}\cdot\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{5}\boldsymbol{a}^{5}M^{2}}{20\boldsymbol{\varepsilon}_{0}c^{4}}\:\frac{\mathrm{sin}^{2}\theta}{r^{3}}\boldsymbol{e}_{\theta}$$
D. $$\bar{\boldsymbol{S}}=\frac{1}{4}\mathrm{Re}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{3}\boldsymbol{a}^{7}M^{2}}{14\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{\mathrm{sin}^{3}\theta}{r^{2}}\boldsymbol{e}_{r}$$
E. $$\bar{\boldsymbol{S}}=\frac{1}{8}\mathrm{Re}\boldsymbol{E}\cdot\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{6}M^{2}}{25\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{\mathrm{sin}^{2}\theta}{r^{3}}\boldsymbol{e}_{r}$$
F. $$\bar{\boldsymbol{S}}=\frac{3}{5}\mathrm{Im}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{5}\boldsymbol{a}^{4}M^{2}}{12\boldsymbol{\varepsilon}_{0}c^{4}}\:\frac{\mathrm{cos}^{2}\theta}{r^{2}}\boldsymbol{e}_{\phi}$$
G. $$\bar{\boldsymbol{S}}=\frac{1}{2}\mathrm{Im}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{2}\boldsymbol{a}^{6}M^{4}}{18\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{1-\mathrm{cos}^{2}\theta}{r^{2}}\boldsymbol{e}_{\theta}$$
H. $$\bar{\boldsymbol{S}}=\frac{1}{3}\mathrm{Re}\boldsymbol{B}\times\frac{\boldsymbol{E}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{5}M^{2}}{22\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{\mathrm{cos}^{2}\theta}{r^{4}}\boldsymbol{e}_{r}$$
I. $$\bar{\boldsymbol{S}}=\frac{2}{5}\mathrm{Re}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{6}M^{3}}{16\boldsymbol{\varepsilon}_{0}c^{6}}\:\frac{\mathrm{cos}^{}\theta}{r^{2}}\boldsymbol{e}_{r}$$
J. $$\bar{\boldsymbol{S}}=\frac{2}{9}\mathrm{Re}\boldsymbol{E}\times\frac{\boldsymbol{B}^{*}}{\mu_{0}}=\frac{\boldsymbol{\omega}^{4}\boldsymbol{a}^{6}M^{3}}{18\boldsymbol{\varepsilon}_{0}c^{5}}\:\frac{\mathrm{cos}^{3}\theta}{r^{2}}\boldsymbol{e}_{\phi}$$
Answer: B
Inside a cylinder with a vacuum, with length $l$ and a cross-sectional radius of $a$, the potentials at both the base and the top surface are zero, and the potential on the side surface is $U$. Taking the center of the base as the origin, and the axis as the $z$-axis, using a cylindrical coordinate system, find the potential at any point $P(r, \phi, z)$ inside the cylinder is _____.

Options:
A. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{n\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{J}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{J}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
B. $\varphi(r,z)=\frac{2U}{\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{2n\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{I}_{0}\biggl[\frac{2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
C. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=1}^{\infty}\frac{\cos\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
D. $\varphi(r,z)=\frac{8U}{\pi}\sum_{n=0}^{\infty}\frac{\cos\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{J}_{1}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{J}_{1}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
E. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=0}^{\infty}\frac{\cos\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{I}_{1}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{1}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
F. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{2n+2}\frac{\mathrm{J}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{J}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
G. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
H. $\varphi(r,z)=\frac{4U}{\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{2n\pi}{l}z\biggr]}{2n+1}\frac{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
I. $\varphi(r,z)=\frac{4U}{3\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{3n+1}\frac{\mathrm{I}_{1}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{1}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
J. $\varphi(r,z)=\frac{4U}{2\pi}\sum_{n=0}^{\infty}\frac{\sin\biggl[\frac{(2n+1)\pi}{l}z\biggr]}{n+1}\frac{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}r\biggr]}{\mathrm{I}_{0}\biggl[\frac{(2n+1)\pi}{l}a\biggr]}$
Answer: G
At standard atmospheric pressure and 20°C, air steadily flows over a flat plate surface. What is the freestream velocity of the air where the Reynolds number is $6.7 \times 10^{4}$ at a boundary layer thickness of 1.8 mm?

Options:
A. $$
0. 0 5 8 {\mathrm{m}} / {\mathrm{s}}
$$
B. $$
0. 3 2 1 {\mathrm{m}} / {\mathrm{s}}
$$
C. $$
0. 1 1 9 {\mathrm{m}} / {\mathrm{s}}
$$
D. $$
0. 0 0 9 {\mathrm{m}} / {\mathrm{s}}
$$
E. $$
0. 0 8 0 {\mathrm{m}} / {\mathrm{s}}
$$
F. $$
0. 0 1 2 {\mathrm{m}} / {\mathrm{s}}
$$
G. $$
0. 0 7 6 {\mathrm{m}} / {\mathrm{s}}
$$
H. $$
0. 1 4 2 {\mathrm{m}} / {\mathrm{s}}
$$
I. $$
0. 2 0 4 {\mathrm{m}} / {\mathrm{s}}
$$
J. $$
0. 1 3 5 {\mathrm{m}} / {\mathrm{s}}
$$
Answer: F
A Pitot tube is installed at the center of a pipe with an internal diameter of $0.3 \, \text{m}$ to measure the gas flow rate. The correction factor for the Pitot tube is taken as $1.00$. The gas temperature is $40^\circ\text{C}$, the pressure is $101.3\,\text{kPa}$, and the viscosity is $2 \times 10^{-5} \, \text{Pa} \cdot \text{s}$. The average relative molar mass of the gas is 60. The maximum reading measured by the Pitot tube at the same pipe section is $30 \, \text{mm}$ water column. What is the flow rate of the gas in the pipe at this time?

Options:
A. $$
1. 4 0 m^{3} / s
$$
B. $$
0. 7 5 m^{3} / s
$$
C. $$
0. 9 6 m^{3} / s
$$
D. $$
0. 9 0 m^{3} / s
$$
E. $$
0. 8 8 m^{3} / s
$$
F. $$
1. 2 4 m^{3} / s
$$
G. $$
1. 1 0 m^{3} / s
$$
H. $$
1. 3 5 m^{3} / s
$$
I. $$
0. 8 5 m^{3} / s
$$
J. $$
1. 0 2 m^{3} / s
$$
Answer: C
In a heat exchanger, kerosene is cooled using cold water. The water flows inside a steel pipe with a diameter of $\varphi1 9 \mathrm{mm} \times 2 \mathrm{mm}$, and the convective heat transfer coefficient of water is 3490 W/(m²·K), while the convective heat transfer coefficient of kerosene is 458 W/(m²·K). After the heat exchanger has been in use for some time, fouling occurs on both sides of the pipe wall. The fouling thermal resistance on the kerosene side and water side are 0.000176 m²·K/W and 0.00026 m²·K/W, respectively. The thermal conductivity of the pipe wall is 45 W/(m·K). Calculate the overall heat transfer coefficient based on the outer surface area of the pipe is ().

Options:
A. $$
3 2 5. 6 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
B. $$
2 9 7. 8 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
C. $$
4 0 1. 3 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
D. $$
3 4 7. 2 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
E. $$
4 1 2. 5 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
F. $$
2 8 9. 1 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
G. $$
3 5 0. 7 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
H. $$
3 3 8. 9 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
I. $$
3 1 6. 8 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
J. $$
3 6 3. 4 \mathrm{W / ~ ( m^{2} \cdot K )_{o}}
$$
Answer: H
The graduated cylinder with an inner diameter of 30mm contains water, with a water temperature of 25°C. The surrounding air temperature is 30°C, and the pressure is 101.33 kPa. The water vapor content in the air is negligible. The distance from the surface of the water to the top edge of the graduated cylinder is 10mm. Assuming the air in this space is still, and air movement at the mouth of the cylinder can quickly carry away the evaporated water vapor, how much will the water level in the graduated cylinder decrease after 2 days? According to the table, the molecular diffusion coefficient of water in air at 25°C is 0.26 cm²/s.

Options:
A. $$
6.8mm
$$
B. $$
8.4mm
$$
C. $$
5.3mm
$$
D. $$
8.1mm
$$
E. $$
7.7mm
$$
F. $$
9.0mm
$$
G. $$
10.2mm
$$
H. $$
6.1mm
$$
I. $$
4.9mm
$$
J. $$
5.7mm
$$
Answer: E
A falling ball viscometer consists of a steel ball and a glass tube. The liquid to be tested is filled into the glass tube, and the time taken for the ball to fall a certain distance is recorded to calculate the viscosity of the liquid. It is known that the steel ball has a diameter of 10mm and a density of \(7900 \mathrm{kg/m}^3\). The density of the liquid to be measured is \(1300 \mathrm{kg/m}^3\). The steel ball falls 200mm in the liquid, taking 9.02 seconds. Calculate the viscosity of the liquid is ().

Options:
A. $
14.58 Pa·s
$
B. $
15.40 Pa·s
$
C. $
21.67 Pa·s
$
D. $
20.56 Pa·s
$
E. $
13.84 Pa·s
$
F. $
12.95 Pa·s
$
G. $
18.73 Pa·s
$
H. $
16.35 Pa·s
$
I. $
11.29 Pa·s
$
J. $
19.42 Pa·s
$
Answer: H
A certain fluid flows through horizontally connected straight pipe 1 and straight pipe 2. It is known that $d_{1}=d_{2} / 2$, $l_{1}=10 \mathrm{m}$, and $Re_{1}=1760$. It has been measured that the pressure drop of the fluid flowing through pipe 1 is equal to that through pipe 2. If $Re_{1}=3.5 \times 10^{5}$, and the relative roughness of both pipe 1 and pipe 2 is 0.03, with the pressure drop in pipe 1 equal to that in pipe 2, what is the length of pipe 2 in meters at this moment?

Options:
A. 340m
B. 310m
C. 315m
D. 320m
E. 330m
F. 300m
G. 325m
H. 350m
I. 360m
J. 290m
Answer: D
A certain plate-and-frame filter press has 25 filter frames, with each frame measuring $0.65 \, \mathrm{m} \times 0.65 \, \mathrm{m} \times 0.025 \, \mathrm{m}$. It is used to filter a certain type of water suspension. Each cubic meter of the suspension contains $0.022 \, \mathrm{m}^{3}$ of solids, and the filter cake contains 50% water (by mass). Calculate the volume of filtrate obtained $(\mathrm{m}^{3})$ when the filter frames are completely filled with filter cake is ().
Given that the density of the solid particles $\rho_{\mathrm{p}} = 1500 \, \mathrm{kg/m}^{3}$, and the density of water $\rho_{\mathrm{water}} = 1000 \, \mathrm{kg/m}^{3}$.

Options:
A. $3.114m^3$
B. $5.927m^3$
C. $2.789m^3$
D. $6.001m^3$
E. $1.942m^3$
F. $9.485m^3$
G. $2.674m^3$
H. $4.536m^3$
I. $7.852m^3$
J. $8.233m^3$
Answer: H
In an acrylonitrile fluidized bed reactor with an inner diameter of 1.2m, 3.62t of catalyst is loaded, and after fluidization, the bed height is 10m with a pressure drop of 31.4kPa. If the bed porosity remains unchanged, what is the height of the fluidized bed when the pressure drop is 40.5kPa?

Options:
A. 10.9m
B. 11.2m
C. 16.1m
D. 9.5m
E. 10.2m
F. 12.9m
G. 13.5m
H. 14.8m
I. 11.7m
J. 15.3m
Answer: F
To reduce heat loss, an insulation layer is applied to the outer surface of a saturated steam pipe with an outer diameter of $\phi208{\mathrm{mm}}$. The thermal conductivity of the insulation material is known to be $\lambda=0.\,113+0.\,000124t$ (where $t$ is measured in °C), and the outer wall temperature of the steam pipe is $170^{\circ}\mathrm{C}$. The outer wall temperature of the insulation layer must not exceed 40°, and the amount of steam condensation per meter of pipe due to heat loss must be controlled below $1\times10^{-4} \,\mathrm{kg}/$ $(\mathrm{m}\cdot\mathrm{s} )$. If the insulation layer thickness is $60\mathrm{mm}$, what is the amount of steam condensation per meter of pipe due to actual heat loss?

Options:
A. $$
1. \, 8 0 \times1 0^{-4} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
B. $$
2. \, 0 0 \times1 0^{-4} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
C. $$
3. \, 0 0 \times1 0^{-4} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
D. $$
1. \, 0 5 \times1 0^{-5} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
E. $$
5. \, 5 0 \times1 0^{-6} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
F. $$
4. \, 0 0 \times1 0^{-5} \, \mathrm{kg} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
G. $$
1. \, 5 0 \times1 0^{-5} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
H. $$
0. \, 9 0 \times1 0^{-5} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
I. $$
1. \, 1 0 \times1 0^{-4} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
J. $$
2. \, 3 0 \times1 0^{-4} \, \mathrm{k g} / ( \mathrm{m} \! \cdot\! \mathrm{s} )
$$
Answer: I
There is a shell-and-tube heat exchanger equipped with 150 steel tubes, each 2 meters long. The task is to heat air at an atmospheric pressure with a mass flow rate of $4000\mathrm{kg}/\mathrm{h}$ from 32°C to 97°C within the tube side, using 120°C saturated steam condensate for heating in the shell side. The heat transfer coefficient for steam condensation is $12000\mathrm{W/(m^{2}\cdot K)}$. Heat loss, as well as thermal resistance from the tube wall and fouling on both sides, is neglected. The physical properties of air at the average temperature are as follows: specific heat capacity is $1\mathrm{kJ}/(\mathrm{kg}\cdot\mathrm{K})$, thermal conductivity is $0.0285\mathrm{W/(m\cdot K)}$, viscosity is $1.98 \times10^{-5}\,\mathrm{N}\cdot\mathrm{s/m}^{2}$, and the Prandtl number is 0.7. The tube diameter is $\phi\,25\,\mathrm{mm}\times2.5\,\mathrm{mm}$. What is the convection heat transfer coefficient of air inside the tube?

Options:
A. $$
9 8. 1 \mathrm{W / ( m^{2} \cdot K )}
$$
B. $$
9 5. 2 \mathrm{W / ( m^{2} \cdot K )}
$$
C. $$
8 9. 4 \mathrm{W / ( m^{2} \cdot K )}
$$
D. $$
7 8. 3 \mathrm{W / ( m^{2} \cdot K )}
$$
E. $$
8 5. 6 \mathrm{W / ( m^{2} \cdot K )}
$$
F. $$
1 0 7. 5 \mathrm{W / ( m^{2} \cdot K )}
$$
G. $$
1 0 2. 7 \mathrm{W / ( m^{2} \cdot K )}
$$
H. $$
8 7. 9 \mathrm{W / ( m^{2} \cdot K )}
$$
I. $$
1 1 0. 4 \mathrm{W / ( m^{2} \cdot K )}
$$
J. $$
9 0. 1 \mathrm{W / ( m^{2} \cdot K )}
$$
Answer: J
A certain single-pass shell-and-tube heat exchanger with a heat transfer area of $25 \mathrm{m}^2$ is used for cooling hot oil with counterflow water in the tube side. Under the original operating conditions, the water flow rate is $2 \mathrm{kg/s}$, with a specific heat capacity of 4.18 kJ/(kg·K), and the inlet and outlet temperatures are $20\mathrm{°C}$ and $40\mathrm{°C}$, respectively. The inlet and outlet temperatures of the hot oil are 50°C and 100°C, respectively, and the heat transfer coefficient of the hot oil is $500 \mathrm{W/(m^2 \cdot K)}$. The current water flow rate is reduced to $1.2 \mathrm{kg/s}$, and some tubes are blocked due to tube leaks, reducing the number of tubes to 0.8 times the original. It is known that $Re > 10^4$ for the water inside the tubes, and changes in physical properties, as well as the thermal resistance of the tube wall and fouling layer, can be ignored. Calculate the outlet temperature of the hot fluid under the new operating conditions is ().

Options:
A. 58.7°C
B. 65.3°C
C. 59.9°C
D. 63.5°C
E. 66.8°C
F. 61.4°C
G. 62.2°C
H. 67.2°C
I. 64.7°C
J. 60.1°C
Answer: G
There is a set of tubular heat exchangers, with the hot fluid flowing in the annular space at an inlet temperature of 80°C and a flow rate of 1000kg/h, while the cold fluid flows inside the tube at an inlet temperature of 10°C and a flow rate of 1500kg/h. It is known that the average specific heat capacity of the hot and cold fluids is equal. What is the maximum outlet temperature $t_{2}$ of the cold fluid that can be achieved in counterflow and parallel flow conditions?

Options:
A. 53°C
B. 48°C
C. 52°C
D. 55°C
E. 57°C
F. 54°C
G. 50°C
H. 49°C
I. 58°C
J. 60°C
Answer: E
On the asphalt road, there is a 2mm layer of standing water with a temperature of 20°C, above which lies a 0.2mm thick layer of still air. The water diffuses through this air layer into the atmosphere. The partial pressure of water vapor in the atmosphere is 1.33 kPa. How much time will it take for the water on the road surface to be evaporated and dried?

Options:
A. 0.58h
B. 0.88h
C. 1.15h
D. 0.63h
E. 0.92h
F. 0.45h
G. 1.00h
H. 1.20h
I. 0.75h
J. 1.10h
Answer: A
The main diseases that need to be differentiated during the absorption stage of lobar pneumonia are ().

Options:
A. Asthma
B. COPD
C. Pneumothorax
D. Chronic Bronchitis
E. Bronchitis
F. Acute Bronchitis
G. Tuberculosis
H. Cystic Fibrosis
I. Emphysema
J. Pleural Effusion
Answer: G
A 30-year-old woman has not conceived in the five years since her marriage. She had tuberculosis pleurisy in her childhood, which has been cured. Her menstrual cycle is regular, and no abnormalities were found in gynecological examinations. Endometrial biopsy before menstruation showed a secretory endometrium, with no signs of tuberculosis. A transvaginal ultrasound showed that the fallopian tube fluid passage is unobstructed, and her husband's semen analysis falls within the normal range. What should be considered as the first choice for further examination?

Options:
A. Hysterosalpingogram
B. MRI of Pelvis
C. Ovarian Reserve Testing
D. Hormonal Profiling
E. Genetic Screening
F. Endometrial Scratch Biopsy
G. Cervical Smear Analysis
H. Thyroid Function Test
I. Laparoscopic Surgery
J. Post-Coital Test
Answer: J
A woman, two years post-marriage, experienced a 50-day amenorrhea after missing her birth control pills for three days. Pregnancy test was positive, followed by one week of vaginal bleeding, slightly less than her menstrual flow, accompanied by abdominal pain. Which measure should be chosen as the best option?

Options:
A. Serial Beta-hCG Testing
B. Pelvic Exam and Monitoring
C. Dietary Modifications
D. Pelvic Rest Period
E. Endometrial Ablation
F. Uterine Aspiration
G. Hormonal Therapy
H. Hormonal Suppression
I. Ultrasound Monitoring
J. Expectant Management Now
Answer: F
A 32-year-old woman, married for 8 years, has not conceived. She usually has menstrual periods lasting 6 to 7 days every 30 days. She has missed her period for 60 days and has experienced irregular vaginal bleeding accompanied by dull pain in the lower left abdomen for 15 days. Yesterday morning, she expelled a fleshy mass from the vagina, approximately 3 cm by 2 cm in size. Gynecological examination reveals a closed cervical os, a slightly enlarged and softened uterus, and an irregular mass of 6 cm by 5 cm by 4 cm in the left adnexal region, which is tender and somewhat movable. The most likely diagnosis for this case is ().

Options:
A. Ovarian Cyst Rupture with Hemorrhage
B. Cervical Polyp with Necrosis Symptoms
C. Uterine Fibroid Degeneration Event
D. Uterine Prolapse with Expulsion Episode
E. Pelvic Inflammatory Abscess Condition
F. Miscarriage with Retained Tissue Mass
G. Endometrial Polyp Expulsion Incident
H. Ectopic Pregnancy in the Fallopian Tube
I. Endometriosis with Adhesion Formation
J. Molar Pregnancy with Vaginal Discharge
Answer: H
A 39-year-old woman has experienced increased vaginal discharge for 3 years and irregular vaginal bleeding for the past 2 months. Gynecological examination reveals severe cervical erosion, hard texture, and bleeding upon contact. The anterior vaginal fornix is absent and locally hardened. The uterus is of normal size, and both adnexa are normal. Three-way diagnosis: Both the cardinal ligaments and the uterosacral ligaments are elastic and soft. Preoperative examination reveals a prominent pulmonary artery segment (chest X-ray) and an ECG shows a right axis deviation with severe clockwise rotation and paroxysmal supraventricular tachycardia. Further questioning of her medical history reveals chronic bronchitis. Cervical biopsy pathology indicates squamous cell carcinoma of the cervix, moderately differentiated. The first choice of treatment for this patient should be ().

Options:
A. Surgical resection
B. Oral antibiotics
C. Physical therapy
D. Immunotherapy
E. Hormone therapy
F. Lifestyle change
G. Hysterectomy
H. Chemotherapy
I. Radiotherapy
J. Antiviral treatment
Answer: I
Let the population $x$ follow a Poisson distribution with parameter λ. $X_1, X_2$ are simple random samples of $x$, and $\bar{X}, S^2$ are the sample mean and sample variance respectively. Then $P(X_{1}=1|\bar{X}=1)=().$

Options:
A. $\frac{2}{5}$
B. $\frac{3}{7}$
C. $\frac{5}{6}$
D. $\frac{3}{8}$
E. $\frac{4}{9}$
F. $\frac{1}{2}$
G. $\frac{1}{4}$
H. $\frac{7}{10}$
I. $\frac{1}{3}$
J. $\frac{6}{11}$
Answer: F
Randomly select two numbers from [0,1] and find the probability that their sum is less than $\frac{6}{5}$ is ().

Options:
A. $\frac{19}{25}$
B. $\frac{21}{25}$
C. $\frac{12}{25}$
D. $\frac{18}{25}$
E. $\frac{17}{25}$
F. $\frac{16}{25}$
G. $\frac{22}{25}$
H. $\frac{23}{25}$
I. $\frac{20}{25}$
J. $\frac{14}{25}$
Answer: E
Let $X_1 \sim P(\lambda_1), X_2 \sim P(\lambda_2)$. Under the condition $X_1 + X_2$ = $n(n = 1, 2, \cdots)$, the conditional distribution of $X_1$ is ().

Options:
A. $b\left(n,\frac{\lambda_i}{\lambda_2+\lambda_2}\right).$
B. $P\left(n,\frac{\lambda_1}{\lambda_2+\lambda_2}\right).$
C. $b\left(n,\frac{\lambda_1}{\lambda_1+\lambda_1}\right).$
D. $g\left(n,\frac{\lambda_2}{\lambda_1+\lambda_2}\right).$
E. $h\left(n,\frac{\lambda_2}{\lambda_1+\lambda_1}\right).$
F. $b\left(n,\frac{\lambda_i}{\lambda_1+\lambda_2}\right).$
G. $b\left(n,\frac{\lambda_1}{\lambda_2+\lambda_1}\right).$
H. $g\left(n,\frac{\lambda_1}{\lambda_1+\lambda_2}\right).$
I. $b\left(n,\frac{\lambda_2}{\lambda_2+\lambda_1}\right).$
J. $b\left(n,\frac{\lambda_2}{\lambda_1+\lambda_1}\right).$
Answer: F
The population $X$ follows a uniform distribution on $[0, \theta]$, where $\theta > 0$ is an unknown parameter. $(X_1, \cdots, X_n)$ is a sample drawn from $X$. Try to derive a $1-\alpha$ confidence interval for $\theta$ using $\frac{X_{(n)}}{\theta}$ is ().

Options:
A. $\left(X_{(n)},\frac{2X_{(n)}}{\alpha^{1/n}}\right)$
B. $\left(X_{(n)},\frac{X_{(n-1)}}{\alpha^{1/n}}\right)$
C. $\left(X_{(n+1)},\frac{X_{(n)}}{\alpha}\right)$
D. $\left(X_{(1)},\frac{X_{(n)}}{\sqrt{n\alpha}}\right)$
E. $\left(X_{(n)},\frac{5X_{(n)}}{\alpha^2}\right)$
F. $\left(X_{(n)},\frac{X_{(n)}}{\sqrt[n]{\alpha}}\right)$
G. $\left(X_{(n)},\frac{X_{(2)}}{\sqrt[n]{2\alpha}}\right)$
H. $\left(X_{(2)},\frac{4X_{(n)}}{\sqrt[n]{\alpha/2}}\right)$
I. $\left(X_{(n-1)},\frac{X_{(n)}}{\alpha^{2/n}}\right)$
J. $\left(X_{(n)},\frac{3X_{(n+1)}}{\alpha^{1/n}}\right)$
Answer: F
In a spring-loaded piston-cylinder system, the cylinder contains 1.5 kg of air at 27°C and 160 kPa. It is heated using a heat source at 900 K, causing the temperature of the gas inside the cylinder to gradually rise to 900 K. At this point, the volume of the cylinder is twice its initial volume. During the process, the pressure and volume of the gas follow a linear relationship, $p = A + B V$. Friction is negligible during the process, and the specific heat capacity of air is constant, $c_{V} = 718 \, \mathrm{J/(kg \cdot K)}$. Calculate the work done, heat transfer, and entropy generation during the process.

Options:
A. $$155.61 kJ$$
$$
805.70kJ
$$
$$
0.540 \mathrm{~ k J / K}
$$
B. $$150.88 kJ$$
$$
800.80kJ
$$
$$
0.520 \mathrm{~ k J / K}
$$
C. $$180.56 kJ$$
$$
820.30kJ
$$
$$
0.600 \mathrm{~ k J / K}
$$
D. $$158.45 kJ$$
$$
797.30kJ
$$
$$
0.550 \mathrm{~ k J / K}
$$
E. $$165.74 kJ$$
$$
812.20kJ
$$
$$
0.590 \mathrm{~ k J / K}
$$
F. $$170.32 kJ$$
$$
815.90kJ
$$
$$
0.600 \mathrm{~ k J / K}
$$
G. $$160.10 kJ$$
$$
799.99kJ
$$
$$
0.560 \mathrm{~ k J / K}
$$
H. $$161. 44 kJ$$
$$
807.64kJ
$$
$$
0. 5 8 4 \mathrm{~ k J / K}
$$
I. $$175.00 kJ$$
$$
810.50kJ
$$
$$
0.620 \mathrm{~ k J / K}
$$
J. $$140.72 kJ$$
$$
790.00kJ
$$
$$
0.500 \mathrm{~ k J / K}
$$
Answer: H
In a pneumatic pistol, before shooting, there is 1 MPa of compressed air at 27 °C within the barrel, and 1 cm³ is held by the trigger. A 15g bullet acts as a piston, sealing the air. After pulling the trigger, the compressed air expands to propel the bullet. Assuming the expansion process is isothermal, calculate the bullet's velocity at the moment it exits the barrel, when the pressure inside is 0.1 MPa.

Options:
A. 15.02 m/s
B. 12.54 m/s
C. 13.50 m/s
D. 14.35 m/s
E. 13.80 m/s
F. 13.66 m/s
G. 14.12 m/s
H. 13.21 m/s
I. 14.78 m/s
J. 12.98 m/s
Answer: F
In the compressed gas refrigeration cycle, the state of the air as it enters the compressor is $p_{1}=0.1 \ \mathrm{M Pa}$, $t_{1}=-20 \ \mathrm{^\circ C}$. In the compressor, it is isentropically compressed to $p_{2}=0.5 \ \mathrm{M Pa}$, and then enters the cooler. When the air exits the cooler, its temperature is $t_{3}=20 \ \mathrm{^\circ C}$. Given that $t_{\mathrm{c}}=-20 \ \mathrm{^\circ C}$, $t_{0}=20$ °C, and treating the air as an ideal gas with constant specific heat, $\kappa=1.4$, calculate the refrigeration coefficient $\varepsilon$ and the cooling capacity $q_{c}$ for 1 kg of air.

Options:
A. $$
2. 3 2
$$
$$
6 5. 5 5 \mathrm{~ k J / k g}
$$
B. $$
1. 9 0
$$
$$
6 3. 0 0 \mathrm{~ k J / k g}
$$
C. $$
1. 8 5
$$
$$
6 9. 5 0 \mathrm{~ k J / k g}
$$
D. $$
2. 1 0
$$
$$
6 6. 8 0 \mathrm{~ k J / k g}
$$
E. $$
1. 6 5
$$
$$
7 1. 0 5 \mathrm{~ k J / k g}
$$
F. $$
1. 9 9
$$
$$
6 7. 1 5 \mathrm{~ k J / k g}
$$
G. $$
1. 5 0
$$
$$
7 2. 8 0 \mathrm{~ k J / k g}
$$
H. $$
1. 7 1
$$
$$
6 8. 4 8 \mathrm{~ k J / k g}
$$
I. $$
1. 8 0
$$
$$
7 5. 2 0 \mathrm{~ k J / k g}
$$
J. $$
2. 0 3
$$
$$
7 0. 2 0 \mathrm{~ k J / k g}
$$
Answer: H
An automobile air conditioning system uses R134a as the refrigerant and inputs a power of 1.5 kW to the compressor, compressing the refrigerant from 201.7 kPa to 1,200 kPa. The air conditioner cools external air from 30°C to 10°C and blows it into the passenger compartment. Assuming the refrigeration cycle is an ideal cycle, determine the air volume flow rate into the passenger compartment. The pressure inside the passenger compartment is 100 kPa.

Options:
A. $$
0. 4 0 3 \ \mathrm{m}^{3} / \mathrm{s}
$$
B. $$
0. 3 1 5 \ \mathrm{m}^{3} / \mathrm{s}
$$
C. $$
0. 1 9 8 \ \mathrm{m}^{3} / \mathrm{s}
$$
D. $$
0. 4 5 2 \ \mathrm{m}^{3} / \mathrm{s}
$$
E. $$
0. 3 8 1 \ \mathrm{m}^{3} / \mathrm{s}
$$
F. $$
0. 3 5 8 \ \mathrm{m}^{3} / \mathrm{s}
$$
G. $$
0. 1 8 9 \ \mathrm{m}^{3} / \mathrm{s}
$$
H. $$
0. 2 9 4 \ \mathrm{m}^{3} / \mathrm{s}
$$
I. $$
0. 2 6 7 \ \mathrm{m}^{3} / \mathrm{s}
$$
J. $$
0. 2 1 1 \ \mathrm{m}^{3} / \mathrm{s}
$$
Answer: J
When $CO_{2}$ gas enters an adiabatic converging nozzle, its flow speed is $100 \ \mathrm{m/s}$, with a pressure of 0.5 MPa and a temperature of 473 K. The nozzle back pressure $p_{\mathrm{b}}$ is 0.28 MPa, and the mass flow rate $q_{m}$ is 2 kg/s. Assuming the gas can be treated as an ideal gas with specific heat at constant pressure, $c_{p} = 855 \ \mathrm{J/(kg \cdot K)}$, and specific gas constant $R_{g} = 189 \ \mathrm{J/(kg \cdot K)}$. Determine the nozzle exit cross-sectional area and the flow speed of the gas at the exit.

Options:
A. $$
1. 1 1 0 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 5 5. \ 5 \ \mathrm{m/s}
$$
B. $$
1. 7 1 3 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 1 9. \ 1 \ \mathrm{m / s}
$$
C. $$
1. 5 7 3 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 5 7. \ 9 \ \mathrm{m/s}
$$
D. $$
1. 8 2 0 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 2 5. \ 3 \ \mathrm{m/s}
$$
E. $$
1. 9 1 0 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
2 7 0. \ 4 \ \mathrm{m/s}
$$
F. $$
1. 6 5 0 {\times} 1 0^{-4} \mathrm{~ m}^{2}
$$
$$
2 9 8. \ 2 \ \mathrm{m/s}
$$
G. $$
1. 4 3 3 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 4 0. \ 6 \ \mathrm{m/s}
$$
H. $$
1. 7 9 2 {\times} 1 0^{-4} \mathrm{~ m}^{2}
$$
$$
3 2 0. \ 1 \ \mathrm{m/s}
$$
I. $$
1. 3 8 5 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
2 6 8. \ 7 \ \mathrm{m/s}
$$
J. $$
1. 2 4 0 {\times} 1 0^{-3} \mathrm{~ m}^{2}
$$
$$
3 3 3. \ 8 \ \mathrm{m/s}
$$
Answer: B
A compressed air tank with a volume of $V = 0.6 \; \mathrm{m}^{3}$ contains compressed air at a gauge pressure of $p_{\mathrm{e l}} = 9.9 \; \mathrm{MPa}$ and a temperature of $t_{1} = 27 \; \mathrm{°C}$. The valve on the air tank is opened to start the diesel engine. How much air is used when the pressure in the tank drops to $p_{2} = 7 \; \mathrm{MPa}$?

Options:
A. 18.3kg
B. 20.1kg
C. 15.7kg
D. 25.9kg
E. 16.8kg
F. 19.5kg
G. 10.2kg
H. 14.4kg
I. 21.7kg
J. 12.5kg
Answer: C
Methyl methacrylate undergoes polymerization at 50°C, with chain termination occurring through both bimolecular coupling and bimolecular disproportionation (each comprising a certain proportion). Experimental measurements determine that the ratio of initiator fragment number to macromolecule number is 1.25. What are the respective percentages of bimolecular disproportionation and bimolecular coupling in this polymerization reaction?

Options:
A. $$
4 2 \ \%,\ 5 8 \ \%
$$
B. $$
3 5 \ \%,\ 6 5 \ \%
$$
C. $$
6 0 \ \%,\ 4 0 \ \%
$$
D. $$
3 8 \ \%,\ 6 2 \ \%
$$
E. $$
5 5 \ \%,\ 4 5 \ \%
$$
F. $$
5 0 \ \%,\ 5 0 \ \%
$$
G. $$
4 5 \ \%,\ 5 5 \ \%
$$
H. $$
4 4 \ \%,\ 5 6 \ \%
$$
I. $$
6 2 \ \%,\ 3 8 \ \%
$$
J. $$
3 0 \ \%,\ 7 0 \ \%
$$
Answer: C
Styrene is polymerized at 60°C using benzoyl peroxide as an initiator: monomer concentration $[\mathrm{M}] = 8.35 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$, initiator concentration $[\mathrm{I}] = 0.01 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$, initiator efficiency $f = 0.66$, initiator decomposition rate constant $k_{\mathrm{d}} = 2.25 \times 10^{-6} \ \mathrm{s}^{-1}$, chain propagation rate constant $k_{p} = 176 \ \mathrm{L \cdot mol}^{-1} \cdot \mathrm{s}^{-1}$, chain termination rate constant $k_{t} = 3.6 \times 10^{7} \ \mathrm{L \cdot mol}^{-1} \cdot \mathrm{s}^{-1}$. Without considering chain transfer, what are the radical lifetime $(\tau)$, kinetic chain length $(\nu)$, and the average relative molecular weight of polymers $({\overline{{M_{n}}}})$ ?

Options:
A. $$
0. 7 3 ( \mathrm{s} ),\ 1.03 {\times} 1 0^{3},\ 2.18 {\times} 1 0^{5}
$$
B. $$
0. 6 8 ( \mathrm{s} ),\ 9.95 {\times} 1 0^{2},\ 1.90 {\times} 1 0^{5}
$$
C. $$
0. 6 9 ( \mathrm{s} ),\ 1.01 {\times} 1 0^{3},\ 2.10 {\times} 1 0^{5}
$$
D. $$
0. 8 1 ( \mathrm{s} ),\ 1.10 {\times} 1 0^{3},\ 2.30 {\times} 1 0^{5}
$$
E. $$
0. 7 2 ( \mathrm{s} ),\ 9.85 {\times} 1 0^{2},\ 1.95 {\times} 1 0^{5}
$$
F. $$
0. 7 5 ( \mathrm{s} ),\ 1.05 {\times} 1 0^{3},\ 2.20 {\times} 1 0^{5}
$$
G. $$
0. 6 0 ( \mathrm{s} ),\ 1.02 {\times} 1 0^{3},\ 2.15 {\times} 1 0^{5}
$$
H. $$
0. 7 0 ( \mathrm{s} ),\ 1.15 {\times} 1 0^{3},\ 2.25 {\times} 1 0^{5}
$$
I. $$
0. 6 7 ( \mathrm{s} ),\ 1.00 {\times} 1 0^{3},\ 2.05 {\times} 1 0^{5}
$$
J. $$
0. 5 9 ( \mathrm{s} ),\ 0.95 {\times} 1 0^{3},\ 1.85 {\times} 1 0^{5}
$$
Answer: C
Vinyl chloride undergoes suspension polymerization at 50°C using AIBN as an initiator. At this temperature, the initiator has a half-life of $t_{1/2} = 74$ hours, with an initiator concentration of $0.01 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$ and an initiation efficiency $f = 0.75$. Theoretically, what is the degree of polymerization of the initially formed polyvinyl chloride?

Options:
A. $95\%$
B. $78\%$
C. $680$
D. $68\%$
E. $102\%$
F. $81\%$
G. $83\%$
H. $74\%$
I. $89\%$
J. $87\%$
Answer: C
Add 0.242 g of benzoyl peroxide to 1000 mL of methyl methacrylate and polymerize at 60°C. After 1.5 hours of reaction, 30 g of polymer is obtained, with a number average molecular weight measured at 831,500. It is known that the half-life of benzoyl peroxide at 60°C is 48 hours, with an initiation efficiency $f = 0.8$, $C_{\mathrm{I}} = 0.02$, and $C_{\mathrm{M}} = 0.1 \times 10^{-4}$. The density of methyl methacrylate is $0.93 \ \mathrm{g \cdot cm}^{-3}$. The relative molecular weight of benzoyl peroxide is 242. What is the proportion of disproportionation termination and coupling termination?

Options:
A. $15.0\%,84.5\%$
B. $14.7\%,85.3\%$
C. $12.7\%,87.3\%$
D. $85.9\%,14.1\%$
E. $18.3\%,81.7\%$
F. $11.9\%,88.1\%$
G. $10.8\%,89.2\%$
H. $16.2\%,83.8\%$
I. $17.5\%,82.5\%$
J. $13.5\%,86.0\%$
Answer: D
Using AIBN as the initiator (concentration of $0.1 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$), the polymerization of styrene was conducted at 40°C in a dilatometer. DPPH (1,1-diphenyl-2-picrylhydrazyl) was used as the inhibitor, and the experimental results showed a linear relationship between the amount of inhibitor used and the induction period. When the amounts of DPPH were $0$ and $8 \times 10^{-5} \ \mathrm{mol} \cdot \mathrm{L}^{-1}$, the induction periods were 0 minutes and 15 minutes, respectively. It is known that the half-life of AIBN at 40°C $(t_{1/2})$ is 350 hours. What is the initiation efficiency $(f)$ of AIBN?

Options:
A. $$
0. 4 8
$$
B. $$
0. 9 2
$$
C. $$
0. 8 1
$$
D. $$
0. 6 9
$$
E. $$
0. 7 3
$$
F. $$
1. 2 3
$$
G. $$
0. 5 4
$$
H. $$
1. 1 5
$$
I. $$
0. 2 7
$$
J. $$
1. 0 1
$$
Answer: C
Methyl methacrylate $( r_{1}=0.444 )$ and 2,5-dichlorostyrene $( r_{2}=2.25 )$ are copolymerized at 60°C. If it is required that the molar fraction of methyl methacrylate in the initial copolymer be around 16%, what is the value of $f_1$ ?

Options:
A. $0.3$
B. $0.12$
C. $0.23$
D. $0.67$
E. $0.7$
F. $0.45$
G. $0.9$
H. $0.5$
I. $0.54$
J. $0.18$
Answer: A
The known reactivity ratios of acrylonitrile ($M_1$) and vinylidene chloride ($M_2$) during copolymerization are $r_1 = 0.91$ and $r_2 = 0.37$. What is the mass fraction of acrylonitrile ($M_1$) in the copolymer at the initial stage of the reaction when the mass ratio of the raw materials is $M_1 : M_2 = 20 : 80$?

Options:
A. $0.28$
B. $0.33$
C. $0.61$
D. $0.45$
E. $0.25$
F. $0.52$
G. $0.19$
H. $0.30$
I. $0.42$
J. $0.36$
Answer: B
(Vinyl chloride $\mathbf{M}_{1}$, $r_{1}=1.68;$ vinyl acetate $\mathrm{M}_{2}$, $r_{2}=0.23$). A benzene solution containing 1.5 mol·L$^{-1}$ vinyl chloride and 3.5 mol·L$^{-1}$ vinyl acetate is initiated with 0.1 mol·L$^{-1}$ azobisisobutyronitrile and undergo copolymerization at 60°C. What is the probability of having a vinyl acetate sequence length of 8?

Options:
A. $$
9. 0 0 {\times} 1 0^{-1}
$$
B. $$
3. 8 9 {\times} 1 0^{-3}
$$
C. $$
8. 5 4 {\times} 1 0^{-9}
$$
D. $$
0. 5 5 {\times} 1 0^{-0}
$$
E. $$
2. 3 4 {\times} 1 0^{-6}
$$
F. $$
1. 9 8 {\times} 1 0^{-8}
$$
G. $$
6. 2 1 {\times} 1 0^{-7}
$$
H. $$
4. 1 2 {\times} 1 0^{-4}
$$
I. $$
7. 0 1 {\times} 1 0^{-2}
$$
J. $$
5. 7 6 {\times} 1 0^{-5}
$$
Answer: H
Dissolve 1.0 × 10^-3 mol of sodium naphthalenide in tetrahydrofuran, then quickly add 2.0 mol of styrene. The total volume of the solution is 1L. Assuming the monomers are instantly and uniformly mixed, and half of the monomers have polymerized after 2000 seconds. How much time is needed to reach a polymerization degree of 3000?

Options:
A. $$
t {=} 4 5 0 0 \mathrm{~ s}
$$
B. $$
t {=} 3 8 0 0 \mathrm{~ s}
$$
C. $$
t {=} 4 1 0 0 \mathrm{~ s}
$$
D. $$
t {=} 5 2 0 0 \mathrm{~ s}
$$
E. $$
t {=} 5 0 0 0 \mathrm{~ s}
$$
F. $$
t {=} 3 9 0 0 \mathrm{~ s}
$$
G. $$
t {=} 3 5 0 0 \mathrm{~ s}
$$
H. $$
t {=} 4 2 0 0 \mathrm{~ s}
$$
I. $$
t {=} 4 0 0 0 \mathrm{~ s}
$$
J. $$
t {=} 4 6 0 0 \mathrm{~ s}
$$
Answer: I
Polycondense equimolar amounts of dicarboxylic acid and diol, adding 1% (molar fraction) acetic acid. When the degree of hydroxyl reaction is 0.9, what are the degree of polymerization of the polyester and the maximum degree of polymerization of the polyester?

Options:
A. $7,\ 97$
B. $9,\ 99$
C. $6,\ 94$
D. $8,\ 96$
E. $10,\ 100$
F. $7,\ 100$
G. $10,\ 97$
H. $12,\ 98$
I. $11,\ 95$
J. $8,\ 98$
Answer: B
A polystyrene sample with a relative molecular mass of $4.3 \times 10^{5}$ was measured in a benzene solution at 30°C using the viscosity method to yield an intrinsic viscosity $\left[ \begin{array} {c} {{{\eta}}} \\ \end{array} \right]=147 \mathrm{\ mL \cdot g^{-1}}$. Determine its mean square end-to-end distance $\overline{{{h^{2}}}}$ using $\left[ \eta\right]=\varphi\, \frac{( \overline{{{{h^{2}}}}} )^{3 / 2}} {M}$, where $\varphi=2.1 \times 10^{28} \mathrm{mol}^{-1}$. What is its mean square end-to-end distance $\overline{{{h^{2}}}}$?

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