MikaStars39/nano-eval huggingface dataset:
Assume there is a spherical celestial body in the solar system, positioned at a distance from the Sun equal to the distance from the Earth to the Sun, ($R = 1.5 \times 10^{11}$ m). Consider the Sun as a black body equivalent to $( T_c = 6000 K)$, with a radius of $( R_c = 7 \times 10^8 m)$. What is the temperature of the celestial body based on the following assumptions ?
The celestial body selectively absorbs light near the wavelength $( \lambda = 5000 \, \text{Å} )$.

Options:
A. $$
9 2 0 \mathrm{K}
$$
B. $$
8 9 0 \mathrm{K}
$$
C. $$
1 4 6 \mathrm{K}
$$
D. $$
4 4 0 \mathrm{K}
$$
E. $$
3 6 0 \mathrm{K}
$$
F. $$
6 8 0 \mathrm{K}
$$
G. $$
1 0 7 \mathrm{K}
$$
H. $$
7 1 0 \mathrm{K}
$$
I. $$
2 5 0 \mathrm{K}
$$
J. $$
5 2 0 \mathrm{K}
$$
Answer: C
The average temperature of the flame inside a furnace is 1500K, and there is an observation port on the furnace wall. Try to calculate the power radiating outward from the port when it is opened. What is the spectral radiance of the radiation with a wavelength of 2 μm?

Options:
A. $6.39\times 10^{ 10}W/m^3$
B. $1.37\times 10^{ 11}W/m^3$
C. $9.74\times 10^{ 10}W/m^3$
D. $7.68\times 10^{ 10}W/m^3$
E. $8.46\times 10^{ 11}W/m^3$
F. $9.04\times 10^{ 10}W/m^3$
G. $1.05\times 10^{ 11}W/m^3$
H. $1.12\times 10^{ 10}W/m^3$
I. $9.12\times 10^{ 10}W/m^3$
J. $8.29\times 10^{ 10}W/m^3$
Answer: C
Given: To utilize the exhaust from a gas turbine to heat high-pressure water, a type 1-2 finned tube heat exchanger is used. In a comparison test, it was determined that the mass flow rate of the gas is $2 \ \text{kg/s}$, the inlet temperature is $325 \ \text{°C}$, the cooling water mass flow rate is $0.5 \ \text{kg/s}$, the temperatures $r=25 \ \text{°C}$ and $r'=150 \ \text{°C}$, and the heat transfer area based on the diameter of the gas-side base tube is $3.8 \ \text{m}^2$.For the properties of fuel gas, approximate values based on standard flue gas are taken.
Find: The overall heat transfer coefficient under these conditions.

Options:
A. $$
5 1 2 W \left( m^{2} \cdot k \right)
$$
B. $$
3 7 5 W \left( m^{2} \cdot k \right)
$$
C. $$
4 2 6 W \left( m^{2} \cdot k \right)
$$
D. $$
3 5 4 W \left( m^{2} \cdot k \right)
$$
E. $$
5 4 3 W \left( m^{2} \cdot k \right)
$$
F. $$
4 9 0 W \left( m^{2} \cdot k \right)
$$
G. $$
4 1 5 W \left( m^{2} \cdot k \right)
$$
H. $$
6 0 2 W \left( m^{2} \cdot k \right)
$$
I. $$
3 8 9 W \left( m^{2} \cdot k \right)
$$
J. $$
4 7 8 W \left( m^{2} \cdot k \right)
$$
Answer: C
The radiation aperture on the artificial black body is a circle with a diameter of 20 mm, with a radiance of $E_{b} = 3.72 \times 10^{5} \, \text{W/m}^{2}$. A radiometer is placed directly in front of this black body aperture at a distance $l = 0.5 \, \text{m}$, and the area of the radiometer that absorbs heat is $1.6 \times 10^{-5} \, \text{m}^{2}$. What is the radiation received from the black body by this radiometer?

Options:
A. $$
3. 4 9 \times1 0^{-3} \, \mathrm{W}
$$
B. $$
1. 9 6 \times1 0^{-3} \, \mathrm{W}
$$
C. $$
3. 2 5 \times1 0^{-3} \, \mathrm{W}
$$
D. $$
2. 3 8 \times1 0^{-3} \, \mathrm{W}
$$
E. $$
1. 5 4 \times1 0^{-3} \, \mathrm{W}
$$
F. $$
3. 1 8 \times1 0^{-3} \, \mathrm{W}
$$
G. $$
4. 0 4 \times1 0^{-3} \, \mathrm{W}
$$
H. $$
2. 7 3 \times1 0^{-3} \, \mathrm{W}
$$
I. $$
5. 9 1 \times1 0^{-3} \, \mathrm{W}
$$
J. $$
4. 2 7 \times1 0^{-3} \, \mathrm{W}
$$
Answer: D
A crankshaft with approximately 0.5% carbon content is heated to $600^{\circ} \mathrm{C}$ and then tempered in air at $20^{\circ} \mathrm{C}$. Given the mass of the shaft is 7.84 kg, the surface area is $870 \ \mathrm{cm}^{2}$, the specific heat capacity is $418.7 \ J / (kg \cdot K)$, and the density is $7840 \ kg/m^{3}$, it can be referenced at $300^{\circ} \mathrm{C}$. The average surface heat transfer coefficient during the cooling process is taken as $29.1 \ W / (m^{2} \cdot K)$. How long will it take for the crankshaft to cool to a temperature 10° above the air temperature?

Options:
A. $$
4 2 7 8 s
$$
B. $$
5 9 0 1 s
$$
C. $$
4 8 3 2 s
$$
D. $$
6 3 4 9 s
$$
E. $$
5 2 6 7 s
$$
F. $$
6 1 0 5 s
$$
G. $$
5 8 2 3 s
$$
H. $$
5 7 3 6 s
$$
I. $$
6 5 8 0 s
$$
J. $$
4 9 6 4 s
$$
Answer: E
Given: A factory has manufactured a simple shell-and-tube heat exchanger to utilize exhaust gases for heating domestic water. The exhaust gases flow inside a steel pipe with an inner diameter of 30 mm at a speed of 30 m/s, with an inlet temperature of 200°C and an outlet temperature set at 100°C. The cold water flows in the opposite direction of the exhaust gases in the space between the tube bundle and the shell, and it needs to be heated from 20°C at the inlet to 50°C at the outlet. The properties of the exhaust gases can be referenced from the standard values given in the appendix. The surface heat transfer coefficient on the water side is much greater than that on the exhaust gas side, and radiation heat transfer of the exhaust gas can be ignored and not calculated.
Requirement: Estimate the required length of the straight pipe.

Options:
A. $$
1. 4 6 7 m
$$
B. $$
1. 9 2 3 m
$$
C. $$
1. 8 5 2 m
$$
D. $$
1. 6 3 1 m
$$
E. $$
1. 8 0 7 m
$$
F. $$
1. 5 7 9 m
$$
G. $$
1. 7 8 4 m
$$
H. $$
1. 2 8 4 m
$$
I. $$
1. 1 1 2 m
$$
J. $$
1. 3 9 5 m
$$
Answer: G
Let $X(k)$ denote the $N$-point discrete Fourier transform of the $N$-point sequence $x(n)$, where $X(k)$ itself is also an $N$-point sequence. If the discrete Fourier transform of $X(k)$ is computed to obtain a sequence $x_{1}(n)$, express $x_{1}(n)$ using $x(n)$ is ().

Options:
A. $$
x_{1} ( n )=N \cdot\sum_{l=0}^{l} x (-n+N l )=N \cdot x ( (-n ) )_{N} R_{N} ( n )
$$
B. $$
x_{1} ( n )=R_{N} \cdot\sum_{l=0}^{N} x (n-2l )=N \cdot x (-n )
$$
C. $$
x_{1} ( n )=R_{N} \sum_{l=0}^{N} x (-n\cdot l )=N \cdot x ( n ) l_{N} ( n )
$$
D. $$
x_{1} ( n )=N \cdot\sum_{l=0}^{l} X (n+N l )-\sum_{k=0}^{N} \cdot R_{N} ( n )
$$
E. $$
x_{1} ( n )=\sum_{l=0}^{l} x (n-N l )+\sum_{k=0}^{N} \cdot R_{N} ( n )
$$
F. $$
x_{1} ( n )=\sum_{k=0}^{N} X (-k-n )=N \cdot x ( n ) - R_{N} ( n )
$$
G. $$
x_{1} ( n )=N \cdot\sum_{m=0}^{m} x (-n+m N )+\sum_{p=0}^{N} \cdot x ( n )
$$
H. $$
x_{1} ( n )=N \sum_{l=0}^{N} x ( n+l )=N \cdot x ( n ) / R_{N} ( n )
$$
I. $$
x_{1} ( n )=\sum_{l=0}^{l} x (-n\cdot N l )=N \cdot x ( n ) R_{N} ( n )
$$
J. $$
x_{1} ( n )=\sum_{l=0}^{N} x (-n/N l )=N \cdot X ( n ) l_{N} ( n )
$$
Answer: A
The known system function of the analog filter is: $$H_{\mathrm{a}}(s)=\frac{1}{s^{2}+s+1}$$ Try converting it into the system function $H(z)$ of a digital filter using the impulse invariance method. Let the time-domain sampling interval $T=2$s for the digital filter is ().

Options:
A. $$H(z)=\frac{2\sqrt{3}}3\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{3}}{1-2z^{-1}\mathrm{e}^{-1}\cos\sqrt{3}+z^{-2}\mathrm{e}^{-2}}$$
B. $$H(z)=\frac{2\sqrt{2}}3\cdot\frac{z^{-1}\mathrm{e}^{-2}\sin\sqrt{2}}{1-2z^{-1}\mathrm{e}^{-2}\cos\sqrt{2}+z^{-2}\mathrm{e}^{-4}}$$
C. $$H(z)=\frac{3\sqrt{3}}4\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{5}}{1-3z^{-1}\mathrm{e}^{-1}\cos\sqrt{5}+z^{-2}\mathrm{e}^{-2}}$$
D. $$H(z)=\frac{2\sqrt{3}}2\cdot\frac{z^{-1}\mathrm{e}^{-4}\sin\sqrt{3}}{1-2z^{-1}\mathrm{e}^{-4}\cos\sqrt{3}+z^{-2}\mathrm{e}^{-8}}$$
E. $$H(z)=\frac{4\sqrt{3}}3\cdot\frac{z^{-1}\mathrm{e}^{-2}\sin\sqrt{3}}{1-4z^{-1}\mathrm{e}^{-2}\cos\sqrt{3}+z^{-2}\mathrm{e}^{-4}}$$
F. $$H(z)=\frac{\sqrt{3}}2\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{4}}{1-z^{-1}\mathrm{e}^{-1}\cos\sqrt{4}+z^{-2}\mathrm{e}^{-2}}$$
G. $$H(z)=\frac{2\sqrt{3}}5\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{6}}{1-2z^{-1}\mathrm{e}^{-1}\cos\sqrt{6}+z^{-2}\mathrm{e}^{-2}}$$
H. $$H(z)=\frac{2\sqrt{3}}7\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{7}}{1-2z^{-1}\mathrm{e}^{-1}\cos\sqrt{7}+z^{-2}\mathrm{e}^{-2}}$$
I. $$H(z)=\frac{2\sqrt{6}}3\cdot\frac{z^{-1}\mathrm{e}^{-1}\sin\sqrt{2}}{1-2z^{-1}\mathrm{e}^{-1}\cos\sqrt{2}+z^{-2}\mathrm{e}^{-2}}$$
J. $$H(z)=\frac{2\sqrt{5}}3\cdot\frac{z^{-1}\mathrm{e}^{-3}\sin\sqrt{3}}{1-2z^{-1}\mathrm{e}^{-3}\cos\sqrt{3}+z^{-2}\mathrm{e}^{-6}}$$
Answer: A
Design a second-order Butterworth band-stop digital filter with stopband edges of 3dB at frequencies of 40kHz and 20kHz, with a sampling frequency of $f_{1} = 200 kHz$ for the digital system is ().

Options:
A. $$
H ( z )= \frac{0. 6 3 7 9 2 4 ( 1-1. 3 2 1 0 6 7 z^{-1}+z^{-2} )} {1-0. 9 1 5 8 4 9 z^{-1}+0. 5 7 4 3 8 2 z^{-2}}
$$
B. $$
H ( z )= \frac{0. 8 4 5 3 9 2 ( 1-1. 3 7 9 8 5 4 z^{-1}+z^{-2} )} {1-0. 8 5 1 4 2 1 z^{-1}+0. 4 9 5 3 8 2 z^{-2}}
$$
C. $$
H ( z )= \frac{0. 6 5 4 7 1 2 3 ( 1-1. 1 5 8 0 9 8 z^{-1}+z^{-2} )} {1-0. 8 2 9 3 1 5 z^{-1}+0. 6 5 9 3 2 4 z^{-2}}
$$
D. $$
H ( z )= \frac{0. 7 6 4 9 3 8 ( 1-1. 1 0 8 5 7 4 z^{-1}+z^{-2} )} {1-0. 8 9 7 1 5 2 z^{-1}+0. 4 8 5 3 6 2 z^{-2}}
$$
E. $$
H ( z )= \frac{0. 6 3 7 5 4 8 ( 1-1. 2 0 1 4 9 8 z^{-1}+z^{-2} )} {1-0. 8 5 3 7 1 9 z^{-1}+0. 6 2 9 5 8 7 z^{-2}}
$$
F. $$
H ( z )= \frac{0. 7 8 9 4 8 3 ( 1-1. 1 8 4 3 6 9 z^{-1}+z^{-2} )} {1-0. 9 0 5 2 1 4 z^{-1}+0. 5 9 6 4 8 1 z^{-2}}
$$
G. $$
H ( z )= \frac{0. 7 4 3 8 2 7 ( 1-1. 2 5 3 8 4 5 z^{-1}+z^{-2} )} {1-0. 8 6 4 9 2 3 z^{-1}+0. 4 6 9 5 1 7 z^{-2}}
$$
H. $$
H ( z )= \frac{0. 7 8 5 3 9 5 ( 1-1. 0 9 7 6 3 2 z^{-1}+z^{-2} )} {1-0. 9 2 8 7 6 4 z^{-1}+0. 4 1 2 5 8 5 z^{-2}}
$$
I. $$
H ( z )= \frac{0. 6 9 4 7 1 2 ( 1-1. 3 4 2 7 6 3 z^{-1}+z^{-2} )} {1-0. 8 3 7 5 9 8 z^{-1}+0. 5 8 7 2 3 9 z^{-2}}
$$
J. $$
H ( z )= \frac{0. 7 5 4 7 6 2 7 ( 1-1. 2 3 6 0 6 8 z^{-1}+z^{-2} )} {1-0. 9 3 2 9 3 8 1 z^{-1}+0. 5 0 9 5 2 5 5 z^{-2}}
$$
Answer: J
Given the vectors in cylindrical coordinates $A=4 a_{\rho}+3 a_{\phi}+2 a_{z}$ and $B=-3 a_{\rho}+2 a_{\phi}+2 a_{z}$, with starting coordinates at point $P \left( 4 , \frac{\pi} {6} , 2 \right)$ and point $Q \left( 2, {\frac{\pi} {3}} , 2 \right)$ respectively. Find the vector at the starting coordinate $R \left( 1, {\frac{\pi} {4}}, 2 \right)$ such that $\mathbf{C}=\mathbf{A}+\mathbf{B}$ is ().

Options:
A. $$
1. 2 2 5 a_{\rho}+3. 0 1 7 a_{\phi}+4 a_{z}
$$
B. $$ 1. 1 4 2 a_{\rho}+0. 8 7 3 a_{\phi}+5 a_{z} $$
C. $$ 1. 3 4 5 a_{\rho}+4. 0 0 7 a_{\phi}+3 a_{z} $$
D. $$ 1. 2 5 1 a_{\rho}+3. 4 1 9 a_{\phi}+5 a_{z} $$
E. $$ 1. 8 2 6 a_{\rho}+0. 5 1 7 a_{\phi}+4 a_{z} $$
F. $$ 1. 7 4 4 a_{\rho}+3. 3 0 2 a_{\phi}+1 a_{z} $$
G. $$ 1. 4 3 3 a_{\rho}+2. 2 1 7 a_{\phi}+3 a_{z} $$
H. $$ 1. 5 5 0 a_{\rho}+1. 9 8 3 a_{\phi}+2 a_{z} $$
I. $$ 1. 0 9 5 a_{\rho}+2. 7 8 4 a_{\phi}+6 a_{z} $$
J. $$ 1. 2 3 3 a_{\rho}+1. 9 2 8 a_{\phi}+2 a_{z} $$
Answer: A
Given that the complex vector of the magnetic field intensity of a uniform plane wave in free space is
$$\dot{H}=(-a_{x}+a_{y}+a_{z}\:\dot{H}_{z0})\:\mathrm{e}^{-\mathrm{j}2\pi(x+y)}\quad\mu\mathrm{A/m}$$
where $\dot{H}_{\mathrm{z 0}}$ is an unknown complex constant. Find the wave vector of this plane wave, the unit vector in the direction of wave propagation, the wavelength, and the frequency of the plane wave is ( ).

Options:
A. $$
2 \pi( a_{x}+a_{z} )
$$
$$
{\frac{1} {3}} ( a_{y}+a_{y} )
$$
$$
\frac{\sqrt{5}} {2} \, \mathrm{m},
$$
$$
3 \, \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
B. $$
2 \pi( a_{z}+a_{z} )
$$
$$
{\frac{\sqrt{2}} {2}} ( a_{x}+a_{y} )
$$
$$
\frac{\sqrt{2}} {2} \, \mathrm{m},
$$
$$
3 \, \sqrt{2} \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
C. $$
2 \pi( a_{y}+a_{z} )
$$
$$
{\frac{3} {2}} ( a_{x}+a_{z} )
$$
$$
\sqrt{2} \, \mathrm{m},
$$
$$
5 \, \sqrt{2} \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
D. $$
2 \pi( a_{y}+a_{z} )
$$
$$
{\frac{2} {3}} ( a_{x}+a_{y} )
$$
$$
\sqrt{5} \, \mathrm{m},
$$
$$
2 \, \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
E. $$
2 \pi( a_{x}+a_{x} )
$$
$$
{\frac{\sqrt{3}} {2}} ( a_{y}+a_{z} )
$$
$$
\frac{2} {\sqrt{2}} \, \mathrm{m},
$$
$$
8 \, \sqrt{2} \times 1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
F. $$
2 \pi( a_{z}+a_{x} )
$$
$$
{\sqrt{2}} ( a_{z}+a_{x} )
$$
$$
\sqrt{3} \, \mathrm{m},
$$
$$
1 \, \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
G. $$
2 \pi( a_{y}+a_{x} )
$$
$$
{\frac{1} {\sqrt{2}}} ( a_{z}+a_{y} )
$$
$$
1 \, \mathrm{m},
$$
$$
2 \, \sqrt{3} \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
H. $$
2 \pi( a_{x}+a_{y} )
$$
$$
{\frac{1} {2}} ( a_{z}+a_{x} )
$$
$$
\frac{\sqrt{3}} {2} \, \mathrm{m},
$$
$$
4 \, \times 1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
I. $$
2 \pi( a_{z}+a_{y} )
$$
$$
{\frac{\sqrt{3}} {2}} ( a_{y}+a_{x} )
$$
$$
\frac{1} {2} \, \mathrm{m},
$$
$$
6 \, \times 10^{\mathrm{8}} \quad\mathrm{H z}
$$
J. $$
2 \pi( a_{y}+a_{y} )
$$
$$
{\frac{2} {\sqrt{2}}} ( a_{x}+a_{y} )
$$
$$
2 \, \mathrm{m},
$$
$$
7 \, \sqrt{2} \times1 0^{\mathrm{8}} \quad\mathrm{H z}
$$
Answer: B
The diameter of the circular waveguide is $5 \mathrm{cm}$ and it is filled with air. When the operating wavelength is $7$ cm, find the waveguide wavelength $\lambda_{\mathbf{s}}$ for the lowest-order mode is ().

Options:
A. $$
0 9. 8 5 \times1 0^{-2} \ \mathrm{m}
$$
B. $$
1 4. 2 0 \times1 0^{-2} \ \mathrm{m}
$$
C. $$
1 5. 3 0 \times1 0^{-2} \ \mathrm{m}
$$
D. $$
1 2. 7 5 \times1 0^{-2} \ \mathrm{m}
$$
E. $$
1 0. 9 5 \times1 0^{-2} \ \mathrm{m}
$$
F. $$
1 1. 1 5 \times1 0^{-2} \ \mathrm{m}
$$
G. $$
1 2. 2 5 \times1 0^{-2} \ \mathrm{m}
$$
H. $$
1 3. 4 5 \times1 0^{-2} \ \mathrm{m}
$$
I. $$
1 6. 0 0 \times1 0^{-2} \ \mathrm{m}
$$
J. $$
1 1. 6 0 \times1 0^{-2} \ \mathrm{m}
$$
Answer: G
A dipole antenna has a length of $l$ and carries a current $I = I_{0}\operatorname{sin}(\omega t)$, where it is known that $\omega l \ll c$ (speed of light in vacuum). Find the radiative field components $H$ and $E$ is_____.

Options:
A. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{4\pi c^{2}} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\phi} .\\&E(r,t)=cB(r,t)\times e_{\theta}=\frac{I_{0}\omega l}{4\pi\varepsilon_{0}c^{3}} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\theta}\end{aligned}$
B. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{8\pi c} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\phi} .\\&E(r,t)=cB(r,t)\times e_{\phi}=\frac{I_{0}\omega l}{8\pi\varepsilon_{0}c^{2}} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\theta}\end{aligned}$
C. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{\pi c} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\theta} .\\&E(r,t)=cB(r,t)\times e_{\phi}=\frac{I_{0}\omega l}{\pi\varepsilon_{0}c^{2}} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\phi}\end{aligned}$
D. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{4\pi c} \frac{\cos(kr+\omega t)}{r}\mathrm{sin}\theta e_{\phi} .\\&E(r,t)=cB(r,t)\times e_{r}=\frac{I_{0}\omega l}{4\pi\varepsilon_{0}c^{2}} \frac{\cos(kr+\omega t)}{r}\mathrm{sin}\theta e_{\theta}\end{aligned}$
E. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{12\pi c} \frac{\sin(kr+\omega t)}{r}\mathrm{cos}\theta e_{r} .\\&E(r,t)=\frac{I_{0}\omega l}{12\pi\varepsilon_{0}c^{3}} \frac{\sin(kr+\omega t)}{r}\mathrm{cos}\theta e_{r}\end{aligned}$
F. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{4\pi c} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\phi} .\\&E(r,t)=\frac{I_{0}\omega l}{4\pi\varepsilon_{0}c^{2}} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\theta}\end{aligned}$
G. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{4\pi c} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\phi} .\\&E(r,t)=cB(r,t)\times e_{r}=\frac{I_{0}\omega l}{4\pi\varepsilon_{0}c^{2}} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\theta}\end{aligned}$
H. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{4\pi c^{2}} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\theta} .\\&E(r,t)=cB(r,t)\times e_{\phi}=\frac{I_{0}\omega l}{4\pi\varepsilon_{0}c^{3}} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{r}\end{aligned}$
I. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{6\pi c} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{r} .\\&E(r,t)=\frac{I_{0}\omega l}{6\pi\varepsilon_{0}c^{3}} \frac{\cos(kr-\omega t)}{r}\mathrm{sin}\theta e_{\phi}\end{aligned}$
J. $\begin{aligned}&H(r,t)=\frac{I_{0}\omega l}{2\pi c} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\phi} .\\&E(r,t)=cB(r,t)\times e_{r}=\frac{I_{0}\omega l}{2\pi\varepsilon_{0}c^{2}} \frac{\sin(kr-\omega t)}{r}\mathrm{cos}\theta e_{\theta}\end{aligned}$
Answer: G
A carriage with a rest length of $l_0$ moves at a constant speed $v$ relative to the ground. Inside the carriage, a small ball starts from the rear wall and moves forward at a constant speed $u_0$ relative to the carriage. The diameter of the ball is much smaller than $l_0$, so it can be neglected. Find the time required for a ground observer to see the ball travel from the rear wall to the front wall is _____.

Options:
A. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{u^{2}}{c^{2}}}}{\frac{u_{0}+v}{1-\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1+\frac{v^{2}}{c^{2}}\right)}{u_{0}\sqrt{1+\frac{u_{0}^{2}}{c^{2}}}}$
B. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}{\frac{u_{0}+v}{1+\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1+\frac{u_{0}v}{c^{2}}\right)}{u_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}$
C. $\Delta t=\frac{l}{v}=\frac{l_{0}\sqrt{1+\frac{v^{2}}{c^{2}}}}{\frac{u_{0}-v}{1+\frac{u_{0}v}{c^{2}}}+v}=\frac{l_{0}\left(1+\frac{u_{0}v}{c^{2}}\right)}{v\sqrt{1-\frac{u_{0}^{2}}{c^{2}}}}$
D. $\Delta t=\frac{l}{u+v}=\frac{l_{0}\sqrt{1+\frac{v^{2}}{c^{2}}}}{\frac{u_{0}-v}{1-\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1-\frac{u_{0}v}{c^{2}}\right)}{u_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}$
E. $\Delta t=\frac{l}{u+v}=\frac{l_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}{\frac{u_{0}+v}{1-\frac{u_{0}v}{c^{2}}}+v}=\frac{l_{0}\left(1-\frac{u_{0}v}{c^{2}}\right)}{u_{0}\sqrt{1+\frac{v^{2}}{c^{2}}}}$
F. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}{\frac{u_{0}+v}{1+\frac{u_{0}v}{c^{2}}}-u}=\frac{l_{0}\left(1+\frac{u_{0}v}{c^{2}}\right)}{v\sqrt{1-\frac{u_{0}^{2}}{c^{2}}}}$
G. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{u^{2}}{c^{2}}}}{\frac{u_{0}+v}{1+\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1+\frac{v^{2}}{c^{2}}\right)}{u_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}$
H. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}{\frac{u_{0}+v}{1-\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1-\frac{u_{0}v}{c^{2}}\right)}{u_{0}\sqrt{1+\frac{v^{2}}{c^{2}}}}$
I. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1+\frac{v^{2}}{c^{2}}}}{\frac{u_{0}-v}{1+\frac{u_{0}v}{c^{2}}}-v}=\frac{l_{0}\left(1+\frac{u_{0}v}{c^{2}}\right)}{u_{0}\sqrt{1-v^{2}}}$
J. $\Delta t=\frac{l}{u-v}=\frac{l_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}}{\frac{u_{0}+u}{1+\frac{uv_{0}}{c^{2}}}-v}=\frac{l_{0}\left(1+\frac{v^{2}}{c^{2}}\right)}{u_{0}\sqrt{1-u^{2}}}$
Answer: B
In a wastewater treatment plant, the sewage is pumped from the equalization tank to the sedimentation tank. The maximum water surface level difference between the two tanks is $10 \mathrm{m}$, the pipeline friction loss is $4 \mathrm{J} / \mathrm{kg}$, and the flow rate is $34 \mathrm{m}^{3} / \mathrm{h}$. Calculate the power required to pump the water is (). Assume the water temperature is $25^{\circ} C$.

Options:
A. $$
1 0 5 0. 2 W
$$
B. $$
1 0 9 8. 9 W
$$
C. $$
8 5 0. 7 W
$$
D. $$
1 2 0 3. 6 W
$$
E. $$
1 1 1 1. 4 W
$$
F. $$
7 2 5. 8 W
$$
G. $$
9 0 4. 1 W
$$
H. $$
9 5 0. 8 W
$$
I. $$
9 6 4. 3 W
$$
J. $$
8 0 0. 5 W
$$
Answer: I
The thermal conductivity of a certain flat wall material is $\lambda=\lambda_{0} \left( 1+a T \right)$ (with T in °C). If the heat flux through the flat wall is known to be $\mathrm{q \cdot W / m^{2}}$, the temperature on the inner surface of the wall is $\mathbf{T}_{1}$, and the wall thickness is $\mathbf{b}_{0}$, find the temperature distribution within the flat wall is ().

Options:
A. $$
b_{0} \cdot q \cdot T
$$
B. $$
a \cdot b_{0} \cdot q
$$
C. $$
T_{1} \cdot \lambda_{0} \cdot T
$$
D. $$
0
$$
E. $$
T/q \cdot b_{0}
$$
F. $$
q - b_{0} \cdot T_{1}
$$
G. $$
T_{1} \cdot a \cdot \lambda_{0}
$$
H. $$
\lambda_{0} \cdot T_{1}/a
$$
I. $$
\lambda_{0} / T
$$
J. $$
q \cdot b_{0} \cdot T_{1}
$$
Answer: D
In a shell-and-tube heat exchanger, cold water is used to cool hot water from 100°C to 50°C, with the hot water having a mass flow rate of 3500 kg/h. The cooling water flows inside a pipe with a diameter of $\varphi1 8 0 \mathrm{mm} \times 1 0 \mathrm{mm}$, with its temperature rising from 20°C to 30°C. Given that the overall heat transfer coefficient based on the outside surface of the pipe is $2320 \mathrm{W / ~ ( m^{2} \cdot K )}$, and assuming negligible heat loss and that the specific heat capacities of both cold and hot water are approximately equal at 4.18 kJ/(kg·K), determine the required pipe length for both parallel and counterflow operations of the two fluids is ().

Options:
A. $$
4.50m
$$
$$
3.90m
$$
B. $$
4.20m
$$
$$
3.60m
$$
C. $$
3.20m
$$
$$
2.90m
$$
D. $$
2.70m
$$
$$
3.10m
$$
E. $$
3.00m
$$
$$
2.80m
$$
F. $$
5.30m
$$
$$
4.40m
$$
G. $$
5.00m
$$
$$
4.10m
$$
H. $$
3.58m
$$
$$
3.28m
$$
I. $$
3.80m
$$
$$
4.00m
$$
J. $$
2.50m
$$
$$
3.50m
$$
Answer: H
Under the conditions of a total pressure of $2.026 \times 10^{5} \mathrm{Pa}$ and a temperature of 298K, components A and $\mathbf{B}$ undergo equimolar counter-diffusion. When the partial pressures of component A at the two endpoints are $\mathrm{P}_{\mathrm{A1}} = 0.40 \mathrm{atm}$ and $\mathrm{P}_{\mathrm{A2}} = 0.1 \mathrm{atm}$, respectively, the experimentally measured value of $\mathrm{k_{0}}$ is $1.26 \times 10^{-8} \mathrm{kmol} / ( \mathrm{m^2 \!-\! s \!-\! Pa} )$. Try to estimate, under the same conditions, the mass transfer coefficient $\mathrm{k_{G}}$ for component A through the stagnant component B and the mass transfer flux $\mathrm{N_{A}}$ is ().

Options:
A. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=6. 4 4 \times1 0^{-6} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=1. 3 3 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
B. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=2. 5 1 \times1 0^{-5} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 2 2 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
C. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=5. 9 9 \times1 0^{-5} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=1. 0 5 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
D. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=3. 8 8 \times1 0^{-5} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 6 0 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
E. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=1. 4 4 \times1 0^{-5} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 4 4 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
F. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=1. 2 0 \times1 0^{-6} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 2 8 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
G. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=2. 3 3 \times1 0^{-6} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 7 0 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
H. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=2. 7 7 \times1 0^{-7} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 8 7 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
I. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=3. 1 1 \times1 0^{-8} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=0. 9 9 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
J. $$
k_{G}^{0} {\frac{P} {P_{B, n}}}=4. 5 7 \times1 0^{-4} {\mathrm{m o l}} / \ ( {\mathrm{m}}^{2} {\mathrm{e x p a}} )
$$
$$
k_{G} \left( p_{A, 1}-p_{A, 2} \right)=1. 1 1 \, \mathrm{m o l} / \left( \mathrm{m}^{2} \cdot\mathrm{s} \right)
$$
Answer: E
Using a plate and frame filter press for constant-pressure filtration of a certain suspension, the filtration equation is
$$
V^{2} + V = 6 \times 10^{-5} A^{2} t
$$
where the unit of \( t \) is seconds. If 5 \( \mathrm{m}^{3} \) of filtrate is obtained within 30 minutes, how many filter frames with an area of 0.4 \( \mathrm{m}^{2} \) are needed?

Options:
A. $$
\approx2 5
$$
B. $$
\approx4 2
$$
C. $$
\approx6 3
$$
D. $$
\approx9 9
$$
E. $$
\approx3 6
$$
F. $$
\approx3 4
$$
G. $$
\approx2 8
$$
H. $$
\approx5 9
$$
I. $$
\approx7 1
$$
J. $$
\approx5 8
$$
Answer: B
A pipe with an inner diameter of $D = 50mm$ is used to measure water flow with an orifice flow meter. The orifice flow coefficient is $C_0 = 0.62$, and the orifice diameter is $d_0 = 30mm$. The U-tube manometer uses mercury as the indicating liquid. When the U-tube manometer reading is $R = 180mm$, with a known maximum reading of $R_{\mathrm{max}} = 250mm$, and if the maximum water flow rate to be measured is $q_V{\mathrm{max}} = 15\mathrm{m}^{3}/\mathrm{h}$, what should the orifice diameter be?

Options:
A. 34mm
B. 35mm
C. 36mm
D. 29mm
E. 32mm
F. 37mm
G. 30mm
H. 33mm
I. 28mm
J. 31mm
Answer: H
Under a constant pressure, a certain leaf filter is used to filter a suspension, resulting in 80 m³ of filtrate after 4 hours. Ignoring the resistance of the filter medium, try to calculate how much filtrate (in m³) can be obtained after 4 hours if the filtration area is doubled under the same operating conditions?

Options:
A. $120m^3$
B. $200m^3$
C. $160m^3$
D. $90m^3$
E. $80m^3$
F. $40m^3$
G. $50m^3$
H. $60m^3$
I. $100m^3$
J. $140m^3$
Answer: C
Using a settling chamber to remove dust particles from the dust-laden gas, with particle density $\rho_{\mathrm{p}} = 3500\, \mathrm{kg}/\mathrm{m}^{3}$, the chamber is 5 m long, 11 m wide, and 1 m high. The dust-laden gas has a viscosity $\mu = 2.82 \times 10^{-5} \, \mathrm{Pa \cdot s}$ and a density $\rho = 0.617\, \mathrm{kg}/\mathrm{m}^{3}$, with a volumetric flow rate of $1.2 \times 10^{4}\,\mathrm{m}^{3}/\mathrm{h}$. What percentage of particles with a diameter of $15\, \mu\mathrm{m}$ can be removed?

Options:
A. 26.8%
B. 22.3%
C. 12.4%
D. 18.7%
E. 15.3%
F. 25.2%
G. 11.1%
H. 34.6%
I. 40.9%
J. 30.5%
Answer: F
Under atmospheric pressure, a shell-and-tube heat exchanger is used to cool hot air, with the hot air flowing parallel to the tube bundle within the outer shell at a flow rate of $4 \operatorname{kg} / \mathrm{s}$. The inner diameter of the heat exchanger's shell is 300 mm, containing 52 steel tubes of $\phi\,25\,\mathrm{mm}\times2.5\,\mathrm{mm}$. Determine the heat transfer coefficient of the air to the tube wall is (). Given that for air, $\rho=0.815\mathrm{kg/m^{3}}$, $\mu=2.45\times10^{-5}\,\mathrm{Pa}\,\cdot\,\mathrm{s}$, $Pr\approx0.7$, and $\lambda=0.0364\mathrm{W/(m\cdot K)}$.

Options:
A. $$
2 9 0 \mathrm{W / ( m^{2} \cdot K )}
$$
B. $$
1 9 8 \mathrm{W / ( m^{2} \cdot K )}
$$
C. $$
2 3 5 \mathrm{W / ( m^{2} \cdot K )}
$$
D. $$
2 4 0 \mathrm{W / ( m^{2} \cdot K )}
$$
E. $$
2 7 0 \mathrm{W / ( m^{2} \cdot K )}
$$
F. $$
3 0 0 \mathrm{W / ( m^{2} \cdot K )}
$$
G. $$
2 6 5 \mathrm{W / ( m^{2} \cdot K )}
$$
H. $$
2 6 0 \mathrm{W / ( m^{2} \cdot K )}
$$
I. $$
3 5 2 \mathrm{W / ( m^{2} \cdot K )}
$$
J. $$
2 5 8 \mathrm{W / ( m^{2} \cdot K )}
$$
Answer: J
A single-shell, single-tube pass shell-and-tube heat exchanger is composed of a bundle of steel tubes each measuring $\phi\, 25 \, \mathrm{mm} \times 2.5 \, \mathrm{mm}$. An organic solution flows through the tube side with a velocity of $0.5 \, \mathrm{m/s}$, a flow rate of $15 \, \mathrm{t/h}$, a specific heat capacity of $1.76 \, \mathrm{kJ/(kg \cdot K)}$, and a density of $878 \, \mathrm{kg/m}^{3}$. The temperature is heated from 20°C to 50°C. The shell side involves the condensation of saturated steam at 130°C. The heat transfer coefficients for the tube side and shell side are $700 \, \mathrm{W/(m^{2} \cdot K)}$ and $10000 \, \mathrm{W/(m^{2} \cdot K)}$, respectively. The thermal resistances of fouling and tube wall are negligible. Determine the length of the tube in meters is().

Options:
A. 0.49m
B. 6.15m
C. 1.81m
D. 8.20m
E. 3.64m
F. 5.32m
G. 4.76m
H. 9.58m
I. 2.90m
J. 0.37m
Answer: C
There is a heat exchanger operating in parallel flow, with the inlet and outlet temperatures of the cold fluid being 25°C and 70°C, respectively, and the inlet and outlet temperatures of the hot fluid being 150°C and 100°C, respectively. If, under the condition that the flow rates and inlet temperatures of both fluids remain unchanged, the operation is changed from parallel flow to counterflow, what will be the outlet temperature of the cold fluid? (Assume $c_{p}$ and $K$ are constants.)

Options:
A. 65.27°C
B. 74.51°C
C. 68.90°C
D. 60.12°C
E. 81.45°C
F. 77.39°C
G. 72.34°C
H. 80.25°C
I. 55.67°C
J. 78.83°C
Answer: B
A molten salt bath contains molten salt at a temperature of 780°C. An electric heater is immersed in the molten salt. At the start of the power supply, the temperature of the heater is the same as that of the molten salt. During the heating process, the temperature of the molten salt remains constant. Given that the electric heating power is 1.0 kW, the surface area of the heater is 0.05 $m^{2}$, and the heat capacity of the heater is equivalent to that of $1 \mathrm{kg}$ of water, where the specific heat capacity of water is $4.183 \mathrm{kJ / (kg \cdot^{\circ} C)}$. The heat transfer coefficient between the molten salt and the surface of the heater is 1.5 $\mathrm{kW / (m^{2} \cdot^{\circ} C)}$. Assuming the heat transfer coefficient remains constant during heating and the heater's temperature stays uniform, find the heater's wall temperature after 1 minute of power supply is ().

Options:
A. 783.9°C
B. 791.6°C
C. 790.2°C
D. 789.3°C
E. 784.8°C
F. 792.5°C
G. 788.8°C
H. 785.7°C
I. 786.4°C
J. 787.2°C
Answer: G
In a certain packed absorption tower, pure water is used to absorb the soluble component A from a gas mixture in a countercurrent flow. The overall gas phase mass transfer unit height, $H_{\mathrm{O G}}$, is $0.3 \, \text{m}$. The content of component A in the incoming gas is 0.06 (mole fraction, same below), and the process requires a recovery rate of 95% for component A. The liquid-to-gas ratio used is 1.4 times the minimum liquid-to-gas ratio. It is known that within the operating range, the phase equilibrium relationship is $y = 1.2x$. Find out what the effective height of the packed tower should be is ().

Options:
A. 2.11m
B. 1.60m
C. 2.50m
D. 2.30m
E. 1.75m
F. 3.00m
G. 1.95m
H. 2.45m
I. 1.90m
J. 2.70m
Answer: A
MRI imaging, hepatic lesion target sign refers to().

Options:
A. T2-weighted image, medium signal lesion with no obvious central shadow
B. T2-weighted image, with areas of high signal showing even higher signal intensity.
C. DWI images show low signal edges in areas of restricted diffusion.
D. T1-weighted image shows a low signal area with a central necrotic zone.
E. T2-weighted image shows a hyperintense lesion with an even higher signal intensity within.
F. STIR image shows low signal shadow surrounding the high signal lesion.
G. T1-weighted image, shows a ring of no signal in the necrotic area after enhancement.
H. On the T2-weighted image, there is nodular enhancement within the low signal area.
I. T1-weighted image, showing a significant shadow in the central cavity after infusion.
J. FLAIR image shows a high signal lesion with a surrounding area of diffuse low signal margin.
Answer: B
Which of the following statements about fetal blood circulation is correct?

Options:
A. The blood from the left ventricle flows into the arterial duct.
B. The temperature of blood in fetal veins is higher than that in pulmonary arteries.
C. The blood flow in fetal systemic circulation is greater than in the umbilical vein.
D. The carbon dioxide concentration in pulmonary artery blood is lower than that in umbilical vein blood.
E. The velocity of blood in umbilical artery is higher than that in pulmonary vein blood.
F. The oxygen saturation in fetal renal arteries is higher than that in umbilical vein blood.
G. The oxygen concentration in fetal capillary blood is higher than that in umbilical vein blood.
H. The oxygen gradient between fetal lungs and heart is greater than that in the umbilical cord.
I. The pressure in left atrium is higher than that in umbilical vein blood.
J. The oxygen concentration in umbilical artery blood is higher than that in pulmonary artery blood.
Answer: J
Amenorrhea for 50 days, with early pregnancy symptoms, positive urine pregnancy test, began to have slight vaginal bleeding 2 days ago, this morning the bleeding increased, and abdominal pain intensified, subsequently passed a piece of tissue, after which the bleeding decreased. Gynecological examination: slight blood in the vagina, cervical os closed, uterus anteverted, slightly enlarged, both adnexa normal. The management plan should first choose ().

Options:
A. Immediate referral to surgical team.
B. Administer intravenous fluids urgently.
C. Surgical intervention immediately required.
D. Schedule an ultrasound for next week.
E. Begin antibiotics for suspected infection.
F. Observation, no special treatment.
G. Prescribe painkillers to manage discomfort.
H. Hospital admission for constant monitoring.
I. Perform dilation and curettage procedure.
J. Initiate hormonal therapy at once.
Answer: F
A 32-year-old pregnant woman, 2 months into pregnancy, experiences chest tightness, shortness of breath, and palpitations after doing housework. Over the past week, she often wakes up at night due to chest tightness. Physical examination: heart rate 116/min, respiratory rate 22/min, heart border expanded to the left, a grade III systolic murmur heard at the apex, moist rales at the lung bases, and edema in the lower limbs (+). The management should be ().

Options:
A. Labor Induction with Inotropic Support
B. Surgical Valve Replacement within First Trimester
C. Antenatal Vitamins with Low-Sodium Diet
D. Oxygen Therapy with Diuretic Administration
E. Echocardiogram Monitoring and Iron Supplementation
F. Abortion Procedure Following Heart Failure Control
G. Low-Dose Aspirin and Regular Rest Periods
H. Mild Exercise and Dietary Modifications
I. Antihypertensive Therapy and Bed Rest Only
J. Emergency Cesarean Section Immediately Recommended
Answer: F
The patient experienced a 3-month absence of menstruation, followed by 20 days of vaginal bleeding after which dilation and curettage was performed twice. Post-surgery, the patient had intermittent vaginal bleeding for over 20 days and suddenly experienced severe lower abdominal pain, anemia, a drop in blood pressure, and a rapid pulse. Percussion of the abdomen revealed shifting dullness, the uterus had unclear boundaries, and there were fist-sized cystic masses on both sides. A chest X-ray showed multiple small patchy shadows in both lungs. Which of the following is more likely?

Options:
A. Severe Adenomyosis Flare-Up
B. Cervical Polyp Rupture Incident
C. Endometrial Cancer Progression
D. Ovarian Cyst Rupture Syndrome
E. Hyperplasia Uterine Bleeding Disorder
F. Acute Endometritis Complications
G. Pelvic Inflammatory Disease Crisis
H. Uterine Fibroid Degeneration Event
I. Ectopic Pregnancy Complications
J. Invasive Mole Uterine Perforation
Answer: J
Let A and B be two random events, with known values $(A)=0.45$ and
$P(A|B)$=$P$($\overline{A}$|$\overline{B}$)=$0.6$. Then $P(B)$=().

Options:
A. 0.55
B. 0.45
C. 0.25
D. 0.30
E. 0.15
F. 0.50
G. 0.70
H. 0.35
I. 0.65
J. 0.40
Answer: C
Toss a coin twice independently, and introduce the events: $A_1=\{$heads appear on the first toss$\},A_2=\{$heads appear on the second toss$\},A_3=\langle$heads and tails each appear once$\rangle,A_4=\langle$heads appear twice$\rangle$. The events are ().

Options:
A. $A_1$, $A_3$, $A_4$ are mutually exclusive.
B. $A_1$, $A_3$, $A_4$ are equally likely.
C. $A_1$, $A_2$, $A_3$ are mutually exclusive.
D. $A_1$, $A_2$, $A_4$ are dependent events.
E. $A_1$, $A_3$, $A_4$ are pairwise independent.
F. $A_2$, $A_3$, $A_4$ are pairwise independent.
G. $A_1$, $A_2$, $A_3$ are pairwise independent.
H. $A_2$, $A_3$, $A_4$ are collectively exhaustive.
I. $A_1$, $A_2$, $A_4$ are statistically irrelevant.
J. $A_2$, $A_3$, $A_4$ are statistically dependent.
Answer: G
Let $X_1, X_2, X_3, X_4$ be a simple random sample from the normal population $N(0, 2^2)$,
$$X=a(X_1-2X_2)^2+b(3X_3-4X_4)^2,$$
then, when $a=()$, $b=()$, the statistic $X$ follows a $\chi^2$ distribution with () degrees of freedom.

Options:
A. $\frac1{20},\frac1{100},2$
B. $\frac1{30},\frac1{90},3$
C. $\frac1{40},\frac1{80},4$
D. $\frac1{15},\frac1{60},3$
E. $\frac1{45},\frac1{85},3$
F. $\frac1{55},\frac1{70},4$
G. $\frac1{25},\frac1{75},1$
H. $\frac1{50},\frac1{100},2$
I. $\frac1{10},\frac1{50},1$
J. $\frac1{35},\frac1{95},2$
Answer: A
Given a population $X \sim \mathcal{N}(\mu, 9)$, where $\mu$ is an unknown parameter, and $(X_1, \cdots, X_{22})$ is a sample from $X$, the hypothesis testing problem is as follows:
$H_0: \mu = \mu_0 \rightarrow H_1: \mu \neq \mu_0,$
with the rejection region defined as $C = \{(x_1, \cdots, x_{25}) \mid |\overline{x} - \mu_0| \geqslant \epsilon\}$. Determine the constant $c$ so that the significance level of this test is 0.05. The answer is ().

Options:
A. 1.282
B. 1.645
C. 2.326
D. 1.500
E. 0.975
F. 1.176
G. 2.054
H. 2.576
I. 1.960
J. 0.842
Answer: F
A certain heat exchanger uses 4,500 kg/h of cold water to cool hot oil, with the water inlet temperature at 20°C. The 2,250 kg of hot oil has an inlet temperature of 150°C and an exit temperature of 65°C, with an average specific heat $c_{p} = 2.51 \ \mathrm{kJ} / (\mathrm{kg} \cdot \mathrm{K})$. Assuming the heat loss and pressure drop of the heat exchanger can be ignored, calculate the entropy generation of the heat exchange process.

Options:
A. $$
2 9 8. 7 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
B. $$
3 1 0. 8 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
C. $$
3 2 5. 1 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
D. $$
3 1 5. 2 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
E. $$
3 0 5. 4 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
F. $$
2 8 9. 9 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
G. $$
3 0 8. 3 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
H. $$
2 9 3. 4 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
I. $$
3 2 0. 0 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
J. $$
2 9 5. 6 \mathrm{~ k J / ( \, K \cdot\, h \, )}
$$
Answer: E
Stored in a spherical steel tank with a volume of $3.0 \times 10^{-2} \mathrm{m}^{3}$ is 0.5 kg of methane (CH₄). If the methane's temperature rises from 25°C to 33°C, use the R-K equation to calculate the change in pressure.

Options:
A. $$
0. 3 4 2 \mathrm{~ M P a}
$$
B. $$
0. 2 5 0 \mathrm{~ M P a}
$$
C. $$
0. 9 8 3 \mathrm{~ M P a}
$$
D. $$
1. 9 3 7 \mathrm{~ M P a}
$$
E. $$
3. 7 8 6 \mathrm{~ M P a}
$$
F. $$
1. 5 2 8 \mathrm{~ M P a}
$$
G. $$
1. 1 0 5 \mathrm{~ M P a}
$$
H. $$
0. 0 7 1 \mathrm{~ M P a}
$$
I. $$
0. 0 1 9 \mathrm{~ M P a}
$$
J. $$
2. 4 5 1 \mathrm{~ M P a}
$$
Answer: H
A counterflow heater heats 2 MPa saturated steam into 2 MPa, 450°C superheated steam. The heating fluid is air, with an inlet temperature of 1200 K. The air outlet temperature is 20°C higher than the steam inlet temperature. If the steam flow rate is 2.5 kg/s, determine the minimum air flow rate.

Options:
A. $$
1. 5 0 \ \mathrm{k g / s}
$$
B. $$
2. 2 0 \ \mathrm{k g / s}
$$
C. $$
1. 8 0 \ \mathrm{k g / s}
$$
D. $$
1. 9 0 \ \mathrm{k g / s}
$$
E. $$
3. 0 0 \ \mathrm{k g / s}
$$
F. $$
2. 5 0 \ \mathrm{k g / s}
$$
G. $$
2. 6 0 \ \mathrm{k g / s}
$$
H. $$
2. 0 0 \ \mathrm{k g / s}
$$
I. $$
2. 1 0 \ \mathrm{k g / s}
$$
J. $$
2. 3 0 \ \mathrm{k g / s}
$$
Answer: H
The normal boiling point of helium $\mathrm{He}^{4}$ is 4.2 $\mathrm{K}$ (at $p_{0}=760 \,\mathrm{mmHg}$), but at a pressure of 1 mmHg, the boiling point becomes 1.2 K. Estimate the average latent heat of vaporization of liquid helium within this temperature range. The gas constant for helium $R_{\mathrm{g}}=$ 2077.1 J/(kg·K).

Options:
A. $$
2 2 \ 8 9 2. 7 \ \mathrm{J} / \mathrm{k g}
$$
B. $$
2 0 \ 7 3 5. 6 \ \mathrm{J} / \mathrm{k g}
$$
C. $$
1 8 \ 3 6 9. 5 \ \mathrm{J} / \mathrm{k g}
$$
D. $$
2 3 \ 9 5 1. 3 \ \mathrm{J} / \mathrm{k g}
$$
E. $$
2 5 \ 0 2 4. 8 \ \mathrm{J} / \mathrm{k g}
$$
F. $$
2 4 \ 6 8 3. 1 \ \mathrm{J} / \mathrm{k g}
$$
G. $$
1 9 \ 5 7 8. 4 \ \mathrm{J} / \mathrm{k g}
$$
H. $$
2 1 \ 2 6 0. 9 \ \mathrm{J} / \mathrm{k g}
$$
I. $$
2 1 \ 5 4 6. 9 \ \mathrm{J} / \mathrm{k g}
$$
J. $$
2 3 \ 1 4 7. 2 \ \mathrm{J} / \mathrm{k g}
$$
Answer: J
A piston compressor produces 0.5 kg of compressed air with a pressure of 0.35 MPa with each piston stroke. The temperature of the air entering the compressor is 17°C, and the pressure is 0.098 MPa. If the compression process follows a polytropic process with n = 1.35, and the clearance volume ratio is 0.05, calculate the mass of the air inside the cylinder during the compression process.

Options:
A. $$0.4753kg$$
B. $$0.4937kg$$
C. $$0.5284kg$$
D. $$0.5870kg$$
E. $$0.5799kg$$
F. $$0.6128kg$$
G. $$0.5902kg$$
H. $$0.5695kg$$
I. $$0.5011kg$$
J. $$0.5561kg$$
Answer: H
The new steam pressure of a certain Rankine cycle is $3 MPa$, with a temperature of 600°C. The condenser is maintained at 45°C. Given that the relative internal efficiency of the turbine is 0.85 and ignoring the pump work, calculate the cycle thermal efficiency.

Options:
A. 0.318
B. 0.334
C. 0.297
D. 0.302
E. 0.289
F. 0.328
G. 0.321
H. 0.295
I. 0.306
J. 0.311
Answer: A
For free radical polymerization terminated by bimolecular interaction, if each macromolecule contains 1.3 initiator residues, assuming no chain transfer reaction occurs, what are the relative quantities of coupling termination and disproportionation termination ?

Options:
A. $$
5 0 \ \%,\ 5 0 \ \%
$$
B. $$
3 5 \ \%,\ 6 5 \ \%
$$
C. $$
6 0 \ \%,\ 4 0 \ \%
$$
D. $$
4 6 \ \%,\ 5 4 \ \%
$$
E. $$
5 8 \ \%,\ 4 2 \ \%
$$
F. $$
4 4 \ \%,\ 5 6 \ \%
$$
G. $$
4 8 \ \%,\ 5 2 \ \%
$$
H. $$
5 5 \ \%,\ 4 5 \ \%
$$
I. $$
3 0 \ \%,\ 7 0 \ \%
$$
J. $$
4 0 \ \%,\ 6 0 \ \%
$$
Answer: D
Using BPO as the initiator, styrene polymerizes in benzene at 60°C. The known concentration of styrene is 400 mol·L⁻¹, and the concentration of BPO is 5 × 10⁻⁴ mol·L⁻¹. The rate constants are: $k_p = 1.76 \times 10^2$ L·mol⁻¹·s⁻¹, $k_d = 3.24 \times 10^{-6}$ s⁻¹, $k_t = 3.58 \times 10^7$ L·mol⁻¹·s⁻¹, with an efficiency factor $f = 0.70$. What is the kinetic chain length?

Options:
A. $$
3. 6 2 {\times} 1 0^{6}
$$
B. $$
8. 7 6 {\times} 1 0^{4}
$$
C. $$
9. 1 2 {\times} 1 0^{7}
$$
D. $$
4. 4 9 {\times} 1 0^{3}
$$
E. $$
2. 5 8 {\times} 1 0^{5}
$$
F. $$
5. 3 7 {\times} 1 0^{5}
$$
G. $$
6. 2 1 {\times} 1 0^{2}
$$
H. $$
7. 5 8 {\times} 1 0^{4}
$$
I. $$
1. 7 4 {\times} 1 0^{5}
$$
J. $$
1. 2 0 {\times} 1 0^{4}
$$
Answer: I
In a benzene solution, using azobisisobutyronitrile to initiate the polymerization of styrene at a concentration of $1 \ \mathrm{mol \cdot L^{-1}}$, the initial rate of initiation was measured to be $4.0 \times 10^{-11} \ \mathrm{mol \cdot L^{-1} \cdot s^{-1}}$, and the polymerization rate was $1.5 \times 10^{-7} \ \mathrm{mol \cdot L^{-1} \cdot s^{-1}}$. If the termination is entirely by coupling, from a practical standpoint, the resulting polystyrene has a relatively high molecular weight. To reduce the number average molecular weight to 83,200, what concentration of n-butyl mercaptan $(C_{\mathrm{S}}=21)$ should be added as a chain transfer agent?

Options:
A. $$
4. 8 \times1 0^{-6} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
B. $$
5. 3 \times1 0^{-5} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
C. $$
7. 1 \times1 0^{-9} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
D. $$
1. 7 \times1 0^{-8} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
E. $$
3. 5 \times1 0^{-3} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
F. $$
2. 9 \times1 0^{-7} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
G. $$
9. 2 \times1 0^{-6} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
H. $$
2. 3 \times1 0^{-5} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
I. $$
6. 5 \times1 0^{-4} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
J. $$
8. 4 \times1 0^{-7} \mathrm{~ m o l ~ \cdot~ L^{-1} ~}
$$
Answer: B
In benzene, a solution of methyl methacrylate (MMA) with a concentration of 2.5 mol·L⁻¹ and benzoyl peroxide with a concentration of 0.01 mol·L⁻¹ is prepared. It is heated to 70°C, and the initial rate of initiation of the polymerization reaction is measured as 9.4 × 10⁻¹⁰ mol·L⁻¹·s⁻¹. The polymerization reaction rate is 3.15 × 10⁻⁶ mol·L⁻¹·s⁻¹. The relative molecular mass of methyl methacrylate is 100. Assuming no chain transfer reactions and all terminations are by disproportionation, what are the values of $k_{\mathrm{p}} / k_{1}^{1/2}$ and the number-average relative molecular mass ?

Options:
A. $$
8. 6 4 \times1 0^{-3},\ 670000
$$
B. $$
3. 5 4 \times1 0^{-2},\ 600000
$$
C. $$
4. 9 7 \times1 0^{-2},\ 450000
$$
D. $$
5. 1 9 \times1 0^{-2},\ 710000
$$
E. $$
5. 8 1 \times1 0^{-2},\ 670000
$$
F. $$
2. 7 6 \times1 0^{-2},\ 650000
$$
G. $$
5. 3 3 \times1 0^{-2},\ 780000
$$
H. $$
9. 4 5 \times1 0^{-2},\ 690000
$$
I. $$
6. 2 3 \times1 0^{-3},\ 700000
$$
J. $$
7. 8 1 \times1 0^{-2},\ 520000
$$
Answer: E
Given: At 60°C, $k_{\mathrm{p}} = 176 \, \mathrm{L \cdot mol}^{-1} \cdot \mathrm{s}^{-1}$, $[ \mathrm{M} ] = 5.0 \, \mathrm{mol \cdot L}^{-1}$, $\mathrm{N} = 3.2 \times 10^{14}$ molecules·$\mathrm{mL}^{-1}$, $\rho = 1.1 \times 10^{12}$ molecules·$\mathrm{mL}^{-1} \cdot \mathrm{s}^{-1}$. What are the polymerization rate and degree of polymerization for styrene emulsion polymerization?

Options:
A. $$
2.31 \times1 0^{-4},\ 2. 20 \times1 0^{5}
$$
B. $$
2.10 \times1 0^{-4},\ 3. 12 \times1 0^{5}
$$
C. $$
2.15 \times1 0^{-4},\ 2. 16 \times1 0^{5}
$$
D. $$
1.85 \times1 0^{-4},\ 2. 48 \times1 0^{5}
$$
E. $$
1.94 \times1 0^{-4},\ 2. 70 \times1 0^{5}
$$
F. $$
2.60 \times1 0^{-4},\ 1. 99 \times1 0^{5}
$$
G. $$
2.49 \times1 0^{-4},\ 1. 75 \times1 0^{5}
$$
H. $$
2. 45 \times1 0^{-4},\ 3. 01 \times1 0^{5}
$$
I. $$
1.78 \times1 0^{-4},\ 3. 40 \times1 0^{5}
$$
J. $$
2. 34 \times1 0^{-4},\ 2. 5 6 \times1 0^{5}
$$
Answer: J
If two monomers copolymerize with reactivity ratios of $r_{1} = 0.40$ and $r_{2} = 0.60$, and it is required that the ratio of the two structural units in the resulting copolymer be $F_{1} = 0.50$, try to design a reasonable feed ratio for the two monomers. If the feed concentration of monomer 1 is $2 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$, what is the feed concentration of monomer 2?

Options:
A. $$
1. 8 0 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
B. $$
1. 5 9 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
C. $$
1. 6 4 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
D. $$
2. 7 1 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
E. $$
2. 3 5 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
F. $$
2. 1 0 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
G. $$
1. 4 7 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
H. $$
1. 7 2 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
I. $$
1. 3 8 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
J. $$
1. 9 8 {\mathrm{~ m o l ~}} \cdot\mathrm{L}^{-1}
$$
Answer: C
Ethylene $( \mathrm{M}_{1} )$ - Tetrafluoroethylene $( \mathrm{M}_{2} )$, $r_{1}=0.38$, $r_{2}=0.1$; Vinyl Acetate $( \mathrm{M}_{1} )$ - Vinyl Chloride $( \mathrm{M}_{2} )$, $r_{1}=0.23$, $r_{2}=0.68$.
What is the copolymer composition $F_{1}$ at the azeotropic copolymerization point, and what is the molar ratio of the two monomers at this point $\left[ \mathbf{M}_{1} \right]_{\mathfrak{m}} / \left[ \mathbf{M}_{2} \right]_{\mathfrak{m}}$?

Options:
A. $0.26,\ 0.55$
B. $0.29,\ 0.41$
C. $0.34,\ 0.49$
D. $0.25,\ 0.53$
E. $0.35,\ 0.50$
F. $0.31,\ 0.45$
G. $0.27,\ 0.60$
H. $0.30,\ 0.46$
I. $0.28,\ 0.52$
J. $0.32,\ 0.57$
Answer: B
Given that for butadiene $e_{1}=-1.05, Q_{1}=2.39$ and for styrene $e_{2}=-0.80, Q_{2}=1.00$, what are the reactivity ratios $r_{1}$ and $r_{2}$ when they copolymerize?

Options:
A. $1.92,\ 0.60$
B. $1.83,\ 0.58$
C. $1.84,\ 0.51$
D. $2.10,\ 0.47$
E. $1.70,\ 0.55$
F. $1.76,\ 0.63$
G. $1.88,\ 0.52$
H. $1.95,\ 0.45$
I. $2.05,\ 0.54$
J. $2.00,\ 0.49$
Answer: C
Using sodium naphthalene to initiate the anionic polymerization of MMA in tetrahydrofuran, at the beginning of the reaction, the concentration of sodium naphthalene is 2.0 × 10⁻³ mol·L⁻¹, and the monomer concentration is 3.0 mol·L⁻¹. It is known that 80% of the monomer has been converted into polymer after 200 seconds. What is the number-average degree of polymerization of the polymer. When the polymerization proceeds to 300 seconds, what is the number-average degree of polymerization of the resulting polymer (assuming the concentration of anions remains unchanged during the polymerization process)?

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