MikaStars39/nano-eval huggingface dataset:
A free rotor is a quantum "rigid body" with the Hamiltonian $H=\frac{J_{z}^{2}}{2I_z}$, and has a moment of inertia $I_z$. It rotates freely in the $xy$ plane, where $\varphi$ is the angle of rotation. At time $t=0$, the rotor is described by the wave packet $\psi(0) = A \operatorname{sin}^{2} \varphi$. Find $\psi(t)$ for $t > 0$ is().

Options:
A. $$
\psi( t )=A \operatorname{cos}^{2} \varphi -\mathrm{e}^{-i \hbar t / I_z}
$$
B. $$
\psi( t )=\frac{A} {2}-\frac{A} {2} \mathrm{e}^{-2 i \hbar t / I_z} \operatorname{c o s} 2 \varphi
$$
C. $$
\psi( t )=\frac{A} {2}+\frac{A} {2} \mathrm{e}^{+2 i \hbar t / I_z} \operatorname{c o s} 2 \varphi
$$
D. $$
\psi( t )=A \operatorname{c o s} \varphi \mathrm{e}^{-2 i \hbar t / I_z}
$$
E. $$
\psi( t )=\mathrm{e}^{-2 i \hbar t / I_z} \operatorname{sin}^{2} \varphi A
$$
F. $$
\psi( t )=\frac{A}{2} -\frac{A}{2}\mathrm{e}^{-i \hbar t / I_z} \operatorname{sin}2 \varphi
$$
G. $$
\psi( t )=A\mathrm{e}^{-i \hbar t / I_z} \operatorname{sin}^{2} \varphi
$$
H. $$
\psi( t )=A\operatorname{sin}^{2} \varphi \mathrm{e}^{2 i \hbar t / I_z}
$$
I. $$
\psi( t )=\frac{A} {2}\mathrm{e}^{-2 i \hbar t / I_z} +\frac{A} {2} \operatorname{c o s} 2 \varphi
$$
J. $$
\psi( t )=\frac{A} {2}+\frac{A} {2} \mathrm{e}^{-i \hbar t / I_z} \operatorname{c o s} 2 \varphi
$$
Answer: B
A particle with a mass of $m$ is in a one-dimensional short-range potential $V(x) = -V_{0} \delta(x)$. Determine the binding energy.

Options:
A. $$
\frac{\hbar^{2} 2 V_{0}} {m}
$$
B. $$
- \frac{m \hbar^{2}} {2 V_{0}^{2}}
$$
C. $$
- \frac{m V_{0}^{2}} {2 \hbar^{2}}
$$
D. $$
- \frac{2 m V_{0}} {\hbar^{2}}
$$
E. $$
\frac{m V_{0}^{2}} {\hbar^{2} 2}
$$
F. $$
\frac{m \hbar^{2}} {2 V_{0}^{2}}
$$
G. $$
- \frac{\hbar^{2} V_{0}^{2}} {2 m}
$$
H. $$
- \frac{V_{0}^{2} \hbar^{2}} {2 m}
$$
I. $$
\frac{2 \hbar^{2} V_{0}} {m}
$$
J. $$
\frac{V_{0}^{2}} {2 m \hbar^{2}}
$$
Answer: C
An electron is confined in the ground state of a one-dimensional harmonic oscillator, making
$$
\sqrt{\left( [ x-\left< x \right> ] \right)^{2}}=1 0^{-1 0} \mathrm{m}
$$
Find the energy required to excite this electron to its first excited state (expressed in $\mathrm{eV}$) is().

Options:
A. $$
\approx7. 6 \mathrm{e V}
$$
B. $$
\approx2. 5 \mathrm{e V}
$$
C. $$
\approx1. 7 \mathrm{e V}
$$
D. $$
\approx9. 1 \mathrm{e V}
$$
E. $$
\approx5. 3 \mathrm{e V}
$$
F. $$
\approx8. 4 \mathrm{e V}
$$
G. $$
\approx4. 9 \mathrm{e V}
$$
H. $$
\approx0. 9 \mathrm{e V}
$$
I. $$
\approx3. 8 \mathrm{e V}
$$
J. $$
\approx6. 2 \mathrm{e V}
$$
Answer: I
A non-relativistic particle with mass $m$ and charge $q$ moves in an electromagnetic field $B = \nabla \times A$. Define the mechanical momentum operator:
$$
L = \frac{1}{2} \left( \boldsymbol{r} \times m \boldsymbol{v} - m \boldsymbol{v} \times \boldsymbol{r} \right)
$$
with $\boldsymbol{v}$ as the (mechanical) velocity operator. Find $\frac{\mathrm{d} L}{\mathrm{d} t}$.

Options:
A. $$
\frac{1}{2} \left[ \boldsymbol{a} \times\boldsymbol{v}-\boldsymbol{v} \times\boldsymbol{a} \right]
$$
B. $$
\frac{1}{2} \left[ \boldsymbol{r} \times\boldsymbol{B}-\boldsymbol{B} \times\boldsymbol{r} \right]
$$
C. $$
\frac{1}{2} \left[ \boldsymbol{p} \times\boldsymbol{F}-\boldsymbol{F} \times\boldsymbol{p} \right]
$$
D. $$
\frac{1}{2} \left[ \boldsymbol{r} \times\boldsymbol{p}-\boldsymbol{p} \times\boldsymbol{r} \right]
$$
E. $$
\frac{1}{2} \left[ \boldsymbol{a} \times\boldsymbol{p}-\boldsymbol{p} \times\boldsymbol{a} \right]
$$
F. $$
\frac{1}{2} \left[ \boldsymbol{v} \times\boldsymbol{F}-\boldsymbol{F} \times\boldsymbol{v} \right]
$$
G. $$
\frac{1}{2} \left[ m\boldsymbol{v} \times\boldsymbol{F}-\boldsymbol{F} \times m\boldsymbol{v} \right]
$$
H. $$
\frac{1}{2} \left[ m\boldsymbol{a} \times\boldsymbol{B}-\boldsymbol{B} \times m\boldsymbol{a} \right]
$$
I. $$
\frac{1}{2} \left[ \boldsymbol{r} \times m\boldsymbol{a} - m\boldsymbol{a} \times \boldsymbol{r} \right]
$$
J. $$
\frac{1} {2} \left[ \boldsymbol{r} \times\boldsymbol{F}-\boldsymbol{F} \times\boldsymbol{r} \right]
$$
Answer: J
The magnetic moment operator of the electron can be expressed as $\mu = -\frac{e}{2mc} (L + 2s)$, and the observed value of the magnetic moment is defined as
$$
\mu = \langle l j m_{j} | \mu_{z} | l j m_{j} \rangle|_{m_{j} = j} = \langle l j j | \mu_{z} | l j j \rangle
$$
where $| l j m_{j} \rangle$ is the common eigenstate of $(L^{2}, s^{2}, j_{z})$. Calculate $\mu$.

Options:
A. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+3 / 2 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{2} {2}}} \\ {{}} & {{} {{}-j ( j+1 ) \mu_{\mathrm{B}} / ( 2 j+2 ),}} & {{}} & {{} {{} j=l-\frac{3} {2}, l \neq1}} \\ \end{aligned} \right.
$$
B. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+2 / 2 ) \mu_{\mathrm{C}},}} & {{}} & {{} {{} j=l+\frac{1} {3}}} \\ {{}} & {{} {{}-j ( 2 j+3 ) \mu_{\mathrm{B}} / ( 2 j+4 ),}} & {{}} & {{} {{} j=l-\frac{1} {3}, l \neq0}} \\ \end{aligned} \right.
$$
C. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}+( j+1 / 3 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{3} {2}}} \\ {{}} & {{} {{}-j ( 2 j+1 ) \mu_{\mathrm{B}} / ( 3 j+2 ),}} & {{}} & {{} {{} j=l-\frac{2} {3}, l \neq0}} \\ \end{aligned} \right.
$$
D. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}+( j+1 / 4 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{1} {2}}} \\ {{}} & {{} {{}-j ( 2 j+1 ) \lambda_{\mathrm{B}} / ( 2 j+2 ),}} & {{}} & {{} {{} j=l-\frac{1} {2}, l \neq0}} \\ \end{aligned} \right.
$$
E. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}+( j+1 / 6 ) \delta_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{3} {2}}} \\ {{}} & {{} {{}-j ( 2 j+2 ) \mu_{\mathrm{B}} / ( 4 j+1 ),}} & {{}} & {{} {{} j=l-\frac{1} {2}, l \neq2}} \\ \end{aligned} \right.
$$
F. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}+( j+1 / 3 ) \beta_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{1} {2}}} \\ {{}} & {{} {{}-j ( 2 j+2 ) \mu_{\mathrm{B}} / ( 2 j+2 ),}} & {{}} & {{} {{} j=l+\frac{1} {2}, l \neq0}} \\ \end{aligned} \right.
$$
G. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+1 / 2 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{1} {2}}} \\ {{}} & {{} {{}-j ( 2 j+1 ) \mu_{\mathrm{B}} / ( 2 j+2 ),}} & {{}} & {{} {{} j=l-\frac{1} {2}, l \neq0}} \\ \end{aligned} \right.
$$
H. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+2 / 2 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{1} {4}}} \\ {{}} & {{} {{}-j ( 3 j+1 ) \mu_{\mathrm{B}} / ( 2 j+3 ),}} & {{}} & {{} {{} j=l-\frac{1} {2}, l \neq1}} \\ \end{aligned} \right.
$$
I. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+1 / 2 ) \gamma_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{2} {3}}} \\ {{}} & {{} {{}-j ( 3 j+1 ) \mu_{\mathrm{B}} / ( 3 j+1 ),}} & {{}} & {{} {{} j=l-\frac{1} {2}, l \neq0}} \\ \end{aligned} \right.
$$
J. $$
\mu=\left\{\begin{aligned} {{}} & {{} {{}-( j+1 / 5 ) \mu_{\mathrm{B}},}} & {{}} & {{} {{} j=l+\frac{2} {5}}} \\ {{}} & {{} {{}+j ( 2 j+1 ) \mu_{\mathrm{B}} / ( 2 j+3 ),}} & {{}} & {{} {{} j=l-\frac{1} {5}, l \neq0}} \\ \end{aligned} \right.
$$
Answer: G
A vacuum container with adiabatic walls is connected to the atmosphere via a valve. Open the valve to let the atmosphere in, and when the pressure reaches the external atmospheric pressure $p_{0}$, close the valve. If the gas is an ideal gas, find its temperature and volume after entering the container.

Options:
A. $$
\iota_{0} V_{0},~\kappa_{0} p_{0}
$$
B. $$
\eta_{0} p_{0},~\theta_{0} T_{0}
$$
C. $$
\delta_{0} p_{0},~\epsilon_{0} V_{0}
$$
D. $$
\rho_{0} p_{0},~\sigma_{0} T_{0}
$$
E. $$
\nu_{0} V_{0},~\xi_{0} p_{0}
$$
F. $$
\omicron_{0} T_{0},~\pi_{0} V_{0}
$$
G. $$
\gamma_{0} p_{0}V_{0},~\gamma_{0} p_{0}T_{0}
$$
H. $$
\lambda_{0} T_{0},~\mu_{0} p_{0}V_{0}
$$
I. $$
\alpha_{0} p_{0}V_{0},~\beta_{0} T_{0}
$$
J. $$
\gamma_{0} V_{0},~\gamma_{0} T_{0}
$$
Answer: J
Make reasonable assumptions to estimate the surface temperature of Neptune is____. Disregard any potential internal heat sources. Known data: the average distance from the Sun to Earth is $1.5 \times 10^8 \mathrm{km}$; the average distance from the Sun to Neptune is $4.5 \times 10^9 \mathrm{km}$; the solar radiation flux to Earth, $J_{\text{Earth}}$, is 1.4 kW/m²; the Stefan-Boltzmann constant is 5.7 × $10^{-8} \mathrm{W}/m^{2}\cdot\mathrm{K}^4$.

Options:
A. 90K
B. 80K
C. 60K
D. 65K
E. 35K
F. 75K
G. 47K
H. 52K
I. 70K
J. 100K
Answer: H
The universe is filled with blackbody radiation photons at $T = 3 \mathbf{K}$, which can be regarded as a remnant of the Big Bang. Approximately calculate the photon number density $\mathbf{n}$ when $T = 3 \mathbf{K}$.

Options:
A. $$
n \! \sim\! 4 0 0 / \operatorname{c m}^{3}
$$
B. $$
n \! \sim\! 3 8 0 / \operatorname{c m}^{3}
$$
C. $$
n \! \sim\! 5 0 0 / \operatorname{c m}^{3}
$$
D. $$
n \! \sim\! 6 0 0 / \operatorname{c m}^{3}
$$
E. $$
n \! \sim\! 2 0 0 / \operatorname{c m}^{3}
$$
F. $$
n \! \sim\! 3 0 0 / \operatorname{c m}^{3}
$$
G. $$
n \! \sim\! 2 9 0 / \operatorname{c m}^{3}
$$
H. $$
n \! \sim\! 1 5 0 0 / \operatorname{c m}^{3}
$$
I. $$
n \! \sim\! 1 0 0 0 / \operatorname{c m}^{3}
$$
J. $$
n \! \sim\! 4 7 0 / \operatorname{c m}^{3}
$$
Answer: I
Assume a neutron star is a highly degenerate, non-relativistic neutron gas with a spherically symmetric equilibrium structure. They are held together by the gravitational attraction of a massive object located at its center, with mass $M$ and radius $r_{o}$. Ignore all interactions between neutrons. For $r > r_{o}$, calculate the neutron density distribution of this star as a function of $r$ .

Options:
A. $$
\left[ {\frac{M G} {5 a}} \cdot{\frac{1} {r}} \right]^{2 / 3}
$$
B. $$
\left[ {\frac{5 M G} {2 a}} \cdot{\frac{1} {r}} \right]^{3 / 2}
$$
C. $$
\left[ {\frac{2 M G} {6 a}} \cdot{\frac{1} {r}} \right]^{3 / 2}
$$
D. $$
\left[ {\frac{4 M G} {5 a}} \cdot{\frac{1} {r}} \right]^{1 / 3}
$$
E. $$
\left[ {\frac{M G} {2 a}} \cdot{\frac{1} {r}} \right]^{3 / 2}
$$
F. $$
\left[ {\frac{3 M G} {5 a}} \cdot{\frac{1} {r}} \right]^{2 / 3}
$$
G. $$
\left[ {\frac{3 M G} {5 a}} \cdot{\frac{1} {r}} \right]^{3 / 4}
$$
H. $$
\left[ {\frac{2 M G} {4 a}} \cdot{\frac{1} {r}} \right]^{5 / 2}
$$
I. $$
\left[ {\frac{2 M G} {5 a}} \cdot{\frac{1} {r}} \right]^{3 / 2}
$$
J. $$
\left[ {\frac{2 M G} {5 a}} \cdot{\frac{1} {r}} \right]^{1 / 4}
$$
Answer: I
Water flows through the pipeline at a rate of 130 ft³/sec into the treatment plant. The suction section has a diameter of 5 ft and a length of 3000 ft, while the drainage section has a diameter of 3 ft and a length of 1500 ft. The pump imparts energy of $40 \, \text{ft} \cdot \text{lbf/lbf}$ to the water, with a total head loss of 56 ft. Assuming the water pressure at the pipeline inlet is 50 psi and the outlet is 15 ft higher than the inlet, what is the water pressure at the outlet?

Options:
A. $$
3 4. 6 \mathrm{p s i}
$$
B. $$
3 5. 7 \mathrm{p s i}
$$
C. $$
2 9. 1 \mathrm{p s i}
$$
D. $$
3 9. 5 \mathrm{p s i}
$$
E. $$
3 1. 4 \mathrm{p s i}
$$
F. $$
2 7. 8 \mathrm{p s i}
$$
G. $$
3 7. 3 \mathrm{p s i}
$$
H. $$
4 3. 2 \mathrm{p s i}
$$
I. $$
4 0. 9 \mathrm{p s i}
$$
J. $$
2 8. 6 \mathrm{p s i}
$$
Answer: A
At sea level, wind at a temperature of $-20^\circ C$ blows at a speed of 15 m/s across a telephone wire with a diameter of 2 mm. What is the frequency generated?

Options:
A. $$
1 5 7 5 \mathrm{H z}
$$
B. $$
1 2 0 0 \mathrm{H z}
$$
C. $$
2 5 0 0 \mathrm{H z}
$$
D. $$
1 4 8 9 \mathrm{H z}
$$
E. $$
1 6 8 0 \mathrm{H z}
$$
F. $$
2 2 0 0 \mathrm{H z}
$$
G. $$
1 9 2 0 \mathrm{H z}
$$
H. $$
1 7 9 9 \mathrm{H z}
$$
I. $$
1 3 5 0 \mathrm{H z}
$$
J. $$
3 0 0 1 \mathrm{H z}
$$
Answer: D
An indium antimonide sample has a hole concentration at room temperature that is 9 times the electron concentration. Calculate the value of the Hall coefficient $R$ and indicate the type of conductivity of the sample. Assume at room temperature $b = \mu_{n} / \mu_{p} = 100$, and $n_{i} = 1.1 \times 10^{16} \mathrm{cm}^{-3}$. What is $R$?

Options:
A. $$
4. 0 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
B. $$
- 3. 6 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
C. $$
- 2. 2 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
D. $$
7. 2 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
E. $$
1. 4 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
F. $$
- 5. 5 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
G. $$
- 1. 3 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
H. $$
6. 3 \times1 0^{2} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
I. $$
- 9. 8 \times1 0^{2} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
J. $$
2. 5 \times1 0^{3} ( \mathrm{{\, c m}}^{3} / \mathrm{C} )
$$
Answer: G
A pn junction diode is used as a voltage-controlled capacitor (varactor). When the reverse bias voltage is 2V, its variable capacitance is 200pF. Assuming the contact potential is 0.85V. What reverse bias voltage is needed to reduce its capacitance to 100pF?

Options:
A. $$
0. 7 8 ( \mathrm{V} )
$$
B. $$
1 5. 2 ( \mathrm{V} )
$$
C. $$
2 5. 7 ( \mathrm{V} )
$$
D. $$
2 0. 3 ( \mathrm{V} )
$$
E. $$
7. 1 4 ( \mathrm{V} )
$$
F. $$
4. 0 0 ( \mathrm{V} )
$$
G. $$
1 0. 6 ( \mathrm{V} )
$$
H. $$
1. 9 0 ( \mathrm{V} )
$$
I. $$
9. 3 1 ( \mathrm{V} )
$$
J. $$
3 8. 5 ( \mathrm{V} )
$$
Answer: G
In certain localized regions of some semiconductor devices, there exists an extremely strong electric field, causing the electron temperature $T$ to differ from the lattice temperature $T_{\mathrm{L}}$ (magnetic field effect). Let $\mu_{\mathrm{n}}$ and $\mathrm{n}_{\mathrm{e}}$ be the electron mobility and energy relaxation time, respectively. Suppose $\tau_{\mathrm{e}} = 10^{-11} \, \mathrm{s}$, $\mu_{\mathrm{n}} = 10^{3} \, \mathrm{cm}^{2} / \mathrm{V} \cdot\, \mathrm{s}$, and $\mathcal{E} = 10^{3} \, \mathrm{V} / \mathrm{cm}$; what is the difference $\Delta T$ between the electron temperature $T_{\mathrm{e}}$ and the lattice temperature?

Options:
A. $$
6 6. 1 \mathrm{K}
$$
B. $$
4 3. 7 \mathrm{K}
$$
C. $$
7 0. 0 \mathrm{K}
$$
D. $$
8 1. 6 \mathrm{K}
$$
E. $$
7 7. 3 \mathrm{K}
$$
F. $$
9 8. 5 \mathrm{K}
$$
G. $$
9 9. 0 \mathrm{K}
$$
H. $$
8 8. 2 \mathrm{K}
$$
I. $$
6 4. 4 \mathrm{K}
$$
J. $$
5 5. 9 \mathrm{K}
$$
Answer: E
End of the optical plate of a Grike plate $L = 30 \, \text{cm}$, thickness $d = 1 \, \text{cm}$, refractive index $n = 1.52$. What is the resolving power for the hydrogen atomic spectral line $H_{\beta}$ ?
It is known that $\lambda = 4861 \, \text{Å}$, $\frac{\mathrm{d} n}{\mathrm{d} \lambda} = 9.6 \times 10^{-6} \, \text{Å}^{-1}$.

Options:
A. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-1 )-(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=8. 4 5 \times1 0^{5}
$$
B. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-1 )+(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=9. 7 6 \times1 0^{5}
$$
C. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-1 )+(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=2. 2 4 \times1 0^{6}
$$
D. $$
A=\frac{L} {\lambda} \Big[ ( n^{2} + 1 )+(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=6. 3 0 \times1 0^{5}
$$
E. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}+2 )-(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=7. 2 9 \times1 0^{5}
$$
F. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-3 )+(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=4. 5 8 \times1 0^{5}
$$
G. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-2 )-(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=5. 8 4 \times1 0^{5}
$$
H. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}+1 )-(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=1. 2 1 \times1 0^{6}
$$
I. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}-1 )-(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=4. 3 3 \times1 0^{5}
$$
J. $$
A=\frac{L} {\lambda} \Big[ ( n^{2}+3 )+(n \lambda)\frac{\mathrm{d} n} {(\mathrm{d} \lambda)} \Big]=3. 5 9 \times1 0^{5}
$$
Answer: A
Given: A dual-side enhanced tube for refrigerant condensation heat transfer is made from base tubes with diameters of 19 mm and 16.4 mm and is 1.0 m long. In a test, the inlet and outlet temperatures of the cooling water were measured to be 24.6°C and 29.2°C, respectively, with an average water velocity of 0.91 m/s. The average internal surface heat transfer coefficient based on the base tube dimensions is calculated to be 1.82×10³ W/(m²*K), and the external condensation heat transfer surface coefficient is 1.25×10⁴ W/(m²*K). The tube material is copper.
Find: The overall heat transfer coefficient based on the external surface of the base tube is ().

Options:
A. $6985.0w/(m^{2}*k)$
B. $6720.6w/(m^{2}*k)$
C. $6521.3w/(m^{2}*k)$
D. $6821.7w/(m^{2}*k)$
E. $6650.2w/(m^{2}*k)$
F. $6883.4w/(m^{2}*k)$
G. $7002.5w/(m^{2}*k)$
H. $6759.8w/(m^{2}*k)$
I. $6904.9w/(m^{2}*k)$
J. $6794.1w/(m^{2}*k)$
Answer: J
Saturated steam of pure water at a temperature of 50°C condenses on the outside of a vertical tube bundle with an outer diameter of 25.4 mm. The temperature difference between the steam and the tube wall is 11°C, with each tube being 1.5 m long and a total of 50 tubes. Calculate the heat load of this condenser tube bundle.

Options:
A. $435.6kW$
B. $157.8kW$
C. $112.9kW$
D. $489.3kW$
E. $292.4kW$
F. $326.2kW$
G. $368.1kW$
H. $413.8kW$
I. $200.5kW$
J. $256.7kW$
Answer: F
Assuming the sun's surface is a black body at $\mathrm{T=5800 K}$, determine the percentage of the radiation emitted by the sun that is in the visible light range.

Options:
A. $$
50.12\%
$$
B. $$
35.91\%
$$
C. $$
60.05\%
$$
D. $$
32.14\%
$$
E. $$
35.98\%
$$
F. $$
47.29\%
$$
G. $$
28.34\%
$$
H. $$
44.87\%
$$
I. $$
49.67\%
$$
J. $$
39.76\%
$$
Answer: H
A container for storing liquid ammonia is approximately viewed as a sphere with an internal diameter of 300mm. The sphere is covered with a 30mm thick multi-layered insulation material. The thermal conductivity in the radial direction of the insulation is $1.8 \times 10^{-4} W / (m \cdot K)$. The temperature of the liquid helium inside the sphere is -195.6°C, and the room temperature is 25°C. The latent heat of evaporation of liquid helium is $199.6 \mathrm{kJ / kg}$. Estimate the daily evaporation rate of liquid ammonia under the above conditions.

Options:
A. $$
0. 9 2 4 4 K g
$$
B. $$
0. 0 8 5 4 K g
$$
C. $$
0. 2 4 1 8 K g
$$
D. $$
0. 3 5 6 2 K g
$$
E. $$
0. 5 7 3 9 K g
$$
F. $$
0. 1 9 6 3 K g
$$
G. $$
0. 6 6 7 0 K g
$$
H. $$
0. 7 3 8 5 K g
$$
I. $$
0. 4 1 2 9 K g
$$
J. $$
0. 8 4 7 3 K g
$$
Answer: D
Plasma spraying is a high-tech process used to enhance the surface properties of materials, such as corrosion resistance and wear resistance. Ceramics are a common material used in this spraying process. The basic procedure is as follows: ceramic powder is injected into a plasma gas stream with a temperature reaching up to 10,000 K. Before reaching the surface to be coated, the ceramic powder absorbs the heat from the plasma gas stream, quickly rising to its melting point and fully melting into droplets. These droplets are then propelled onto the surface to be coated, where they quickly solidify to form a coating.
Suppose the diameter of the aluminum oxide (Al₂O₃) powder is $D_p = 50 \, \mu m$, with a density $\rho = 3970 \, kg/m^3$, thermal conductivity $\lambda = 11 \, W/(m \cdot K)$, specific heat capacity $c = 1560 \, J/(kg \cdot K)$, and the surface heat transfer coefficient between the powder particles and the airflow is $10000 \, W/(m^2 \cdot K)$. The melting point of the powder particles is 2300 K, and the latent heat of fusion is $3580 \, \text{J/g}$. Calculate the time required for the particles to reach the melting point and fully melt into liquid droplets from an initial temperature of $t_0 = 3000 \, K$, neglecting the radiation heat loss of the particles.

Options:
A. $$
1. 7 0 \times1 0^{-3} s
$$
B. $$
1. 5 5 \times1 0^{-3} s
$$
C. $$
1. 6 8 \times1 0^{-3} s
$$
D. $$
2. 0 5 \times1 0^{-3} s
$$
E. $$
2. 4 7 \times1 0^{-3} s
$$
F. $$
2. 6 3 \times1 0^{-3} s
$$
G. $$
1. 3 4 \times1 0^{-3} s
$$
H. $$
1. 8 8 \times1 0^{-3} s
$$
I. $$
1. 2 2 \times1 0^{-3} s
$$
J. $$
3. 0 9 \times1 0^{-3} s
$$
Answer: B
Based on the $N$ point discrete samples of the Fourier transform of the following discrete-time signal, determine each corresponding discrete-time domain signal is ().
$X(k) = \cos\left(\frac{\pi k}{N}\right) + j\sin\left(\frac{2\pi k}{N}\right),\quad -\pi \leq \frac{2\pi}{N}k \leq \pi$

Options:
A. $$
x(n)= \frac{(-1 )^{n}} {4 \pi\Big( n^{2}-\frac{1} {6} \Big)}+\frac{1} {2} \delta( n-1 )-\frac{1} {4} \delta( n+2 )
$$
B. $$
x(n)= \frac{(-1 )^{n}} {3 \pi\Big( n^{2}-\frac{1} {4} \Big)}+\frac{1} {4} \delta( n+1 )-\frac{1} {3} \delta( n-1 )
$$
C. $$
x(n)= \frac{(-1 )^{n}} {2 \pi\Big( n^{2}-\frac{1} {3} \Big)}+\frac{1} {3} \delta( n+1 )-\frac{1} {3} \delta( n-1 )
$$
D. $$
x(n)= \frac{-(-1 )^{n}} {2 \pi\Big( n^{2}-\frac{1} {4} \Big)}+\frac{1} {2} \delta( n+1 )-\frac{1} {2} \delta( n-1 )
$$
E. $$
x(n)= \frac{-(-1 )^{n}} {3 \pi\Big( n^{2}-\frac{1} {2} \Big)}+\frac{1} {3} \delta( n+1 )-\frac{1} {2} \delta( n-1 )
$$
F. $$
x(n)= \frac{-(-1 )^{n}} {4 \pi\Big( n^{2}-\frac{1} {4} \Big)}+\frac{1} {2} \delta( n+2 )-\frac{1} {2} \delta( n+1 )
$$
G. $$
x(n)= \frac{(-1 )^{n}} {2 \pi\Big( n^{2}+\frac{1} {4} \Big)}+\frac{1} {2} \delta( n+2 )-\frac{1} {2} \delta( n-2 )
$$
H. $$
x(n)= \frac{-(-1 )^{n}} {2 \pi\Big( n^{3}-\frac{1} {4} \Big)}+\frac{1} {2} \delta( n+1 )-\frac{1} {3} \delta( n-1 )
$$
I. $$
x(n)= \frac{-(-1 )^{n}} {3 \pi\Big( n^{2}-\frac{1} {5} \Big)}+\frac{1} {2} \delta( n+1 )-\frac{1} {3} \delta( n-2 )
$$
J. $$
x(n)= \frac{-(-1 )^{n}} {2 \pi\Big( n^{2}-\frac{1} {4} \Big)}+\frac{1} {3} \delta( n+1 )-\frac{1} {2} \delta( n+2 )
$$
Answer: D
Design a band-pass digital filter with a passband range from 0.25π rad to 0.45π rad, with a maximum passband gain attenuation of 3dB. The stopband is below 0.15π rad and above 0.55π rad, with a minimum stopband gain attenuation of 15dB. Try using a Butterworth filter to implement it.

Options:
A. $$H(z)=\frac{0.02-0.056z^{-2}+0.056z^{-4}-0.02z^{-6}}{1-1.492z^{-1}+2.892z^{-2}-3.607z^{-3}+3.516z^{-4}-2.072z^{-5}+0.406z^{-6}}$$
B. $$H(z)=\frac{0.02-0.052z^{-2}+0.052z^{-4}-0.02z^{-6}}{1-1.485z^{-1}+2.888z^{-2}-3.604z^{-3}+3.513z^{-4}-2.067z^{-5}+0.403z^{-6}}$$
C. $$H(z)=\frac{0.01-0.045z^{-2}+0.045z^{-4}-0.01z^{-6}}{1-1.400z^{-1}+2.800z^{-2}-3.500z^{-3}+3.400z^{-4}-2.000z^{-5}+0.400z^{-6}}$$
D. $$H(z)=\frac{0.06-0.059z^{-2}+0.059z^{-4}-0.06z^{-6}}{1-1.494z^{-1}+2.891z^{-2}-3.609z^{-3}+3.519z^{-4}-2.073z^{-5}+0.407z^{-6}}$$
E. $$H(z)=\frac{0.04-0.050z^{-2}+0.050z^{-4}-0.04z^{-6}}{1-1.470z^{-1}+2.880z^{-2}-3.600z^{-3}+3.510z^{-4}-2.060z^{-5}+0.420z^{-6}}$$
F. $$H(z)=\frac{0.02-0.055z^{-2}+0.055z^{-4}-0.02z^{-6}}{1-1.490z^{-1}+2.900z^{-2}-3.610z^{-3}+3.520z^{-4}-2.070z^{-5}+0.410z^{-6}}$$
G. $$H(z)=\frac{0.02-0.053z^{-2}+0.053z^{-4}-0.02z^{-6}}{1-1.486z^{-1}+2.889z^{-2}-3.605z^{-3}+3.514z^{-4}-2.068z^{-5}+0.404z^{-6}}$$
H. $$H(z)=\frac{0.05-0.054z^{-2}+0.054z^{-4}-0.05z^{-6}}{1-1.480z^{-1}+2.886z^{-2}-3.608z^{-3}+3.518z^{-4}-2.065z^{-5}+0.408z^{-6}}$$
I. $$H(z)=\frac{0.02-0.051z^{-2}+0.051z^{-4}-0.02z^{-6}}{1-1.487z^{-1}+2.885z^{-2}-3.602z^{-3}+3.512z^{-4}-2.066z^{-5}+0.405z^{-6}}$$
J. $$H(z)=\frac{0.03-0.060z^{-2}+0.060z^{-4}-0.03z^{-6}}{1-1.500z^{-1}+3.000z^{-2}-3.700z^{-3}+3.600z^{-4}-2.100z^{-5}+0.500z^{-6}}$$
Answer: G
Design a linear phase low-pass FIR filter using a rectangular window function. The approximation of the filter's transfer function is:
$$
H_{d}(\mathrm{e}^{\mathrm{j\omega}})=\begin{cases}\mathrm{e}^{-\mathrm{j\omega}a},&0\leqslant\mid\omega\mid\leqslant\omega_{\epsilon}\\\\0,&\omega_{\epsilon}<\mid\omega\mid\leqslant\pi\end{cases}
$$
Determine the unit sample impulse response $h_{d}(n)$ corresponding to the ideal low-pass filter is ().

Options:
A. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{-\pi}^{\pi}} H_{d} ( \mathrm{e}^{\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega b} \mathrm{d} \omega=\frac{\operatorname{c o s} [ \omega_{d} ( n-\beta) ]} {\pi( n-\beta)}
$$
B. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{-\pi}^{\pi}} H_{d} ( \mathrm{e}^{\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{c} ( n) ]} {\pi( n-\alpha)}
$$
C. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{-\pi}^{\omega_{\epsilon}}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{b} ( n-\alpha) ]} {2\pi( n-\beta)}
$$
D. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{0}^{\pi}} H_{d} ( \mathrm{e}^{\mathrm{j}\omega} ) \mathrm{e}^{-\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{b} ( n+\beta) ]} {\pi( n-\alpha)}
$$
E. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{0}^{\omega_{\epsilon}}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega b} \mathrm{d} \omega=\frac{\operatorname{c o s} [ \omega_{d} ( n+\beta) ]} {2\pi( n-\beta)}
$$
F. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{-\pi}^{\pi}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{c} ( n-\alpha) ]} {\pi( n-\alpha)}
$$
G. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{0}^{\pi}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{-\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{a} ( n+\alpha) ]} {\pi( n+\alpha)}
$$
H. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{0}^{\omega_{\epsilon}}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega b} \mathrm{d} \omega=\frac{\operatorname{s i n} [ \omega_{d} ( n+\alpha) ]} {2\pi( n-\alpha)}
$$
I. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{-\pi}^{\pi}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{c o s} [ \omega_{a} ( n-\beta) ]} {\pi( n-\beta)}
$$
J. $$
h_{d} ( n )=\frac{1} {2 \pi} {\int_{\omega_{\epsilon}}^{\pi}} H_{d} ( \mathrm{e}^{-\mathrm{j}\omega} ) \mathrm{e}^{\mathrm{j} \omega a} \mathrm{d} \omega=\frac{\operatorname{c o s} [ \omega_{c} ( n-\alpha) ]} {\pi( n+\alpha)}
$$
Answer: F
A uniform plane wave propagates in an ideal medium ($\mu=\mu_0, \varepsilon=4\varepsilon_0, \sigma=0$), with its electric field intensity $E$ expressed as: [$E$ = $a_{x}E_{x}$= $a_{x}10\cos ( \omega t- kz+ 30^{\circ }) \quad \text{mV/m}$] . Given that its operating frequency $f = 150$ MHz, find the average power flow density vector $S_{\mathrm{av}}$ at $t=0$ and $\boldsymbol{z}=1.5$.

Options:
A. $$
0. 3 4 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
B. $$
0. 3 0 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
C. $$
0. 1 1 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
D. $$
0. 7 8 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
E. $$
0. 4 6 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
F. $$
0. 2 9 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
G. $$
0. 1 5 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
H. $$
0. 5 1 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
I. $$
0. 6 2 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
J. $$
0. 2 7 a_{x} \quad\mathbf{W} / \mathbf{m}^{2}
$$
Answer: J
A rectangular waveguide with dimensions $a mm \times b mm$, filled with air, transmits the $\text{TE}_{10}$ mode. When the operating frequency $f_{0} = 9.375 \text{GHz}$, the waveguide wavelength $\lambda_{1} = 4.5 \text{cm}$. Determine the waveguide wavelength $\lambda_{8}^{\prime}$ when the operating frequency is $f_{0}^{\prime} = 10 \text{GHz}$ is().

Options:
A. 4.25cm
B. 3.50cm
C. 3.99cm
D. 4.80cm
E. 4.50cm
F. 3.70cm
G. 4.00cm
H. 4.10cm
I. 5.00cm
J. 3.80cm
Answer: C
Assume there are two rulers that are parallel to each other, each having a length of $l_0$ in their respective rest frames. They are moving at the same speed v relative to a certain reference frame but in opposite directions and parallel to the rulers. The length of one ruler as measured by an observer standing on the other ruler is _____.

Options:
A. $$l=l_{0}\frac{1-\frac{\nu}{c}}{1+\frac{\nu}{c}}$$
B. $$l=l_{0}\frac{1-\frac{\nu^{2}}{c^{2}}}{1+\frac{\nu^{2}}{c^{2}}}$$
C. $$l=l_{0}\left(1+\frac{\nu^{2}}{c^{2}}\right)$$
D. $$l=l_{0}\frac{1+\frac{\nu^{2}}{c^{2}}}{1-\frac{\nu^{2}}{c^{2}}}$$
E. $$l=l_{0}\left(1-\frac{\nu^{2}}{c^{2}}\right)$$
F. $$l=l_{0}\frac{1+\frac{\nu}{c}}{1-\frac{\nu}{c}}$$
G. $$l=l_{0}\frac{1}{\sqrt{1-\frac{\nu^{2}}{c^{2}}}}$$
H. $$l=l_{0}\left(\nu^{2}-c^{2}\right)$$
I. $$l=l_{0}\left(\frac{\nu^{2}}{c^{2}}\right)$$
J. $$l=l_{0}\sqrt{1-\frac{\nu^{2}}{c^{2}}}$$
Answer: B
A nuclear reactor has a total power output of 1000 MW, with 2/3 of the energy carried away by the cooling water, disregarding other energy losses. The cooling water comes from a local river, with a flow rate of 100 m³/s and a water temperature of 20°C. If the heated water is returned to the river, by how many degrees Celsius will the river's water temperature increase?

Options:
A. $$
1. 4 7 \mathrm°C
$$
B. $$
1. 9 0 \mathrm°C
$$
C. $$
1. 1 2 \mathrm°C
$$
D. $$
1. 5 9 \mathrm°C
$$
E. $$
1. 8 8 \mathrm°C
$$
F. $$
1. 6 4 \mathrm°C
$$
G. $$
1. 2 0 \mathrm°C
$$
H. $$
1. 3 0 \mathrm°C
$$
I. $$
1. 7 5 \mathrm°C
$$
J. $$
1. 4 3 \mathrm°C
$$
Answer: D
Water flows under laminar flow conditions through a pipe with an inner diameter of $13 \text{ mm}$ and a length of $3 \text{ m}$ at $20^\circ \text{C}$. Given that the pressure drop across this section of the pipe is $21 \text{ N/m}^{2}$, find the pressure drop when the central velocity of the pipe is $0.1 \text{ m/s}$ is ().

Options:
A. $$
3 0. 5 8 {\mathrm{N}} / {\mathrm{m}}
$$
B. $$
1 5. 7 5 {\mathrm{N}} / {\mathrm{m}}
$$
C. $$
2 4. 1 7 {\mathrm{N}} / {\mathrm{m}}
$$
D. $$
2 8. 3 8 {\mathrm{N}} / {\mathrm{m}}
$$
E. $$
3 3. 0 8 {\mathrm{N}} / {\mathrm{m}}
$$
F. $$
3 2. 6 7 {\mathrm{N}} / {\mathrm{m}}
$$
G. $$
3 5. 9 1 {\mathrm{N}} / {\mathrm{m}}
$$
H. $$
4 0. 1 2 {\mathrm{N}} / {\mathrm{m}}
$$
I. $$
2 9. 5 0 {\mathrm{N}} / {\mathrm{m}}
$$
J. $$
2 7. 9 9 {\mathrm{N}} / {\mathrm{m}}
$$
Answer: D
Water flows at a speed of $\mathrm{l m/s}$ in a $3 \mathrm{m}$-long $\varphi25 \mathrm{mm} \times 25 \mathrm{mm}$ pipe and is heated from 20°C to 40°C. Calculate the convective heat transfer coefficient between the water and the pipe wall.

Options:
A. $$
3. 9 8 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
B. $$
4. 5 9 \times1 0^{3} W / ( m^{2} \cdot K )
$$
C. $$
3. 7 5 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
D. $$
4. 3 1 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
E. $$
4. 0 4 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
F. $$
4. 8 3 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
G. $$
5. 8 6 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
H. $$
5. 5 1 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
I. $$
3. 6 9 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
J. $$
5. 2 7 \times 1 0^{3} W / ( m^{2} \cdot K )
$$
Answer: B
In a narrow tube, water at the bottom evaporates into dry air at a constant temperature of 298 K. The pressure of the dry air is 0.1 MPa, and its temperature is also 298 K. The diffusion distance of the water vapor within the tube (from the liquid surface to the top of the tube) is Δx = 20 cm. At 0.1 MPa and 298 K, the diffusion coefficient of water vapor in air is D_AB = 2.50 × 10^-5 m²/s. Calculate the concentration distribution of the water vapor under steady-state diffusion is ().

Options:
A. $$
\mathrm{y}_{\mathrm{A}}=1-1. 0 9 6 3^{( 1-5 z )}
$$
B. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 6 8 3^{( 1-5 z )}
$$
C. $$
\mathrm{y}_{\mathrm{A}}=1-0. 8 8 3 3^{( 1-5 z )}
$$
D. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 5 0 0^{( 1-5 z )}
$$
E. $$
\mathrm{y}_{\mathrm{A}}=1+0. 9 6 8 3^{( 1-5 z )}
$$
F. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 6 8 2^{( 1-5 z )}
$$
G. $$
\mathrm{y}_{\mathrm{A}}=0. 5-0. 9 6 8 3^{( 1-5 z )}
$$
H. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 6 8 3^{( 5-1 z )}
$$
I. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 6 8 3^{( 1+5 z )}
$$
J. $$
\mathrm{y}_{\mathrm{A}}=1-0. 9 6 8 3^{( 1-4 z )}
$$
Answer: B
Assuming the particle settlement follows Stokes' Law and the initial velocity of the particle is zero, derive the relationship between the particle's settling velocity and the settling time. Given that the particle density is $1600 \mathrm{kg/m}^{3}$ and it is a small sphere with a diameter of 0.18 mm, freely settling in water at 20°C, calculate the time required for the sphere to accelerate to 99% of its settling velocity (given that the density of water is $998.2 \mathrm{kg/m}^{3}$ and the viscosity is $1.005 \times 10^{-3} \mathrm{Pa \cdot s}$) is ().

Options:
A. $$
6. 1 7 \times1 0^{-2} \mathrm{s}
$$
B. $$
5. 2 3 \times1 0^{-2} \mathrm{s}
$$
C. $$
8. 0 7 \times1 0^{-2} \mathrm{s}
$$
D. $$
9. 9 4 \times1 0^{-2} \mathrm{s}
$$
E. $$
1. 5 5 \times1 0^{-2} \mathrm{s}
$$
F. $$
4. 6 8 \times1 0^{-2} \mathrm{s}
$$
G. $$
7. 0 3 \times1 0^{-2} \mathrm{s}
$$
H. $$
1. 3 2 \times1 0^{-2} \mathrm{s}
$$
I. $$
3. 4 5 \times1 0^{-2} \mathrm{s}
$$
J. $$
2. 1 9 \times1 0^{-2} \mathrm{s}
$$
Answer: H
The oil, with a density of 800 kg/m³ and a viscosity of 30 cP, flows through a horizontal pipeline with dimensions of φ108 mm × 4 mm at a mass flow rate of 16,000 kg³/h. At point A on the pipeline, the static fluid pressure is 25 kPa. If the local resistance of the pipeline can be ignored and the oil's viscosity increases to 45 cP due to a drop in temperature (assuming density remains unchanged), what will the mass flow rate of the oil be in kilograms per hour if the pressure drop caused by flow resistance between the two ends of the pipeline, Δp, remains constant?

Options:
A. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.42\times800=2.62 \mathrm{kg/s=9432kg/h}$$
B. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.55\times800=3.46 \mathrm{kg/s=12456kg/h}$$
C. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.60\times800=3.77 \mathrm{kg/s=13572kg/h}$$
D. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.47\times750=2.76 \mathrm{kg/s=9954kg/h}$$
E. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.35\times800=2.19 \mathrm{kg/s=7896kg/h}$$
F. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.65\times800=4.06 \mathrm{kg/s=14616kg/h}$$
G. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.53\times800=3.31 \mathrm{kg/s=11916kg/h}$$
H. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.47\times800=2.95 \mathrm{kg/s=10626kg/h}$$
I. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.50\times800=3.14 \mathrm{kg/s=11304kg/h}$$
J. $$q_m=\frac{\pi}{4}d_{inner}^2u_2\rho=0.785\times0.1^2\times0.49\times800=3.05 \mathrm{kg/s=10980kg/h}$$
Answer: H
For constant pressure filtration of the suspension, the filtration constant $K$ is measured to be $4 \times 10^{-5} \mathrm{m^{2} / s}$ at an operating pressure differential of $46 \, \mathrm{kPa}$. What is the filtration constant $K$ in $\mathrm{m^2 / s}$ when the pressure differential is $100 \mathrm{kPa}$? (The filter cake is incompressible.)

Options:
A. $$
10.0 \times 10^{-5}
$$
B. $$
7.2 \times 10^{-5}
$$
C. $$
9.3 \times 10^{-5}
$$
D. $$
8. 7 \times1 0^{-5}
$$
E. $$
6.1 \times 10^{-5}
$$
F. $$
5.5 \times 10^{-5}
$$
G. $$
3.9 \times 10^{-5}
$$
H. $$
5.0 \times 10^{-5}
$$
I. $$
4.8 \times 10^{-5}
$$
J. $$
7.8 \times 10^{-5}
$$
Answer: D
What is the free settling velocity in air for spherical particles with a density of $2650\mathrm{kg}/\mathrm{m}^{3}$ and a diameter of $50\mu\mathrm{m}$ at $20^{\circ}{C}$ (with air density $\rho=1.205\operatorname{g}/\operatorname{cm}^{3}$ and dynamic viscosity $\mu=1.81\times10^{-5}\,\mathrm{Pa} \cdot\mathrm{s}$) in meters per second?

Options:
A. 0.098
B. 0.220
C. 0.110
D. 0.076
E. 0.189
F. 0.262
G. 0.041
H. 0.321
I. 0.150
J. 0.199
Answer: J
To purify atmospheric pressure air at 20°C with a flow rate of $2500 \mathrm{m}^3/\mathrm{h}$ in a dust-settling chamber, ensuring the purified air contains no particles larger than $10 \mu\mathrm{m}$ in diameter, it is known that the required settling area is 128.6 $m^2$. If the base of the dust-settling chamber is $2\mathrm{m} \times 5\mathrm{m}$, how many wooden boards should be added?

Options:
A. 15
B. 8
C. 5
D. 6
E. 10
F. 12
G. 18
H. 22
I. 20
J. 25
Answer: F
There is a tubular heat exchanger with an inner tube made of steel, measuring $\phi180\mathrm{mm}\times10\mathrm{mm}$. Water is used to cool crude oil, employing a countercurrent operation. The water flows inside the tube, entering at a temperature of 15°C and exiting at 55°C. The crude oil flows through the annular space at a flow rate of $500\mathrm{kg}/\mathrm{h}$, with an average specific heat capacity of $3.35\mathrm{kJ}/(\mathrm{kg}\cdot\mathrm{°C})$, and it needs to be cooled from 90°C to 40°C. It is known that the convective heat transfer coefficient on the water side is $1000\mathrm{W/(m^{2}\cdot\mathrm°C)}$ and on the oil side is $299\mathrm{W/(m^{2}\cdot\mathrm°C)}$. The thermal resistance of the tube wall and fouling are negligible, as is any heat loss. Find the required amount of cooling water and the effective length of this tubular heat exchanger is (). It is known that the average specific heat capacity of water is $4.18\mathrm{kJ}/(\mathrm{kg}\cdot\mathrm{°C})$.

Options:
A. 9.8m
B. 6.2m
C. 10.5m
D. 23.9m
E. 18.4m
F. 15.6m
G. 12.5m
H. 78.4m
I. 11.3m
J. 7.1m
Answer: B
A certain shell-and-tube heat exchanger consists of 38 seamless steel tubes with specifications of $\phi\, 25 \, \mathrm{mm} \times 2.5 \, \mathrm{mm}$ and a tube length of 4 meters. Saturated steam at $110^{\circ} \mathrm{C}$ flows through the shell side, heating toluene from 30°C to 72°C, with a toluene flow rate of $7 \mathrm{kg/s}$. The heat transfer coefficient for condensation on the steam side is $10^{4} \, \mathrm{W/(m^{2} \cdot K)}$. The thermal resistance of the tube wall and the fouling resistance on the steam side are considered negligible. The specific heat capacity of toluene is 1.84 kJ/(kg·K). What is the convective heat transfer coefficient on the toluene side?

Options:
A. $$
1 1 2 3 \mathrm{W / ( m^{2} \cdot K )}
$$
B. $$
5 7 8 \mathrm{W / ( m^{2} \cdot K )}
$$
C. $$
2 0 1 4 \mathrm{W / ( m^{2} \cdot K )}
$$
D. $$
1 0 9 2 \mathrm{W / ( m^{2} \cdot K )}
$$
E. $$
1 5 0 0 \mathrm{W / ( m^{2} \cdot K )}
$$
F. $$
3 2 7 4 \mathrm{W / ( m^{2} \cdot K )}
$$
G. $$
6 5 7 \mathrm{W / ( m^{2} \cdot K )}
$$
H. $$
4 4 4 5 \mathrm{W / ( m^{2} \cdot K )}
$$
I. $$
9 8 6 \mathrm{W / ( m^{2} \cdot K )}
$$
J. $$
8 3 9 \mathrm{W / ( m^{2} \cdot K )}
$$
Answer: D
A certain atmospheric pressure gas with a mass flow rate of $7200 \, \mathrm{kg/h}$ flows through 250 steel tubes with dimensions of $\phi 25 \, \mathrm{mm} \times 2.5 \, \mathrm{mm}$. It is heated from $25^{\circ} \mathrm{C}$ to $85^{\circ} \mathrm{C}$ as it passes through the tubes. The gas is heated in the shell side using saturated steam at $198 \, \mathrm{kPa}$. If the heat transfer coefficient for steam condensation is $\alpha_{2}=1 \times 10^{4} \, \mathrm{W/(m^{2} \cdot K)}$, and the thermal resistance of the fouling on the inner wall of the tube is $0.0004 \, (m^{2} \cdot \mathrm{K})/\mathrm{W}$, and the resistances of the tube wall, outside of the tube, and heat losses are neglected. Given the physical properties of the gas at the average temperature are: $c_{p}=1 \, \mathrm{kJ/(kg \cdot K)}$, $\lambda=2.85 \times 10^{-2} \, \mathrm{W/(m \cdot K)}$, $\mu=1.98 \times 10^{-2} \, \mathrm{mPa \cdot s}$. Try to calculate the consumption of saturated steam is ().

Options:
A. 196.00kg/h
B. 172.10kg/h
C. 305.20kg/h
D. 354.15kg/h
E. 490.30kg/h
F. 697.85kg/h
G. 612.90kg/h
H. 256.60kg/h
I. 485.75kg/h
J. 789.40kg/h
Answer: A
A certain counterflow heat exchanger uses hot air to heat cold water, with hot air flowing inside the tubes and cold water flowing through the annular space. The heat transfer resistance is controlled on the hot air side. The inlet and outlet temperatures of the cold fluid are 35°C and 50°C, respectively, while the inlet and outlet temperatures of the hot air are 110°C and 80°C, respectively. Question: When the hot air flow rate is doubled, what will be the outlet temperature of the cold fluid (°C)? Assume that the fouling thermal resistance on both sides of the tube wall, the thermal resistance of the tube wall, and heat loss can be neglected.

Options:
A. 50°C
B. 65°C
C. 80°C
D. 85°C
E. 75°C
F. 45°C
G. 40°C
H. 70°C
I. 60°C
J. 55°C
Answer: I
Given that the height of the packing layer in a certain factory's absorption tower is $4 \mathrm{m}$, it uses clean water to countercurrently absorb the pollutant component A from the tail gas. The inlet and outlet gas phase concentrations are $y_{\text{in}}=0.02$ and $y_{\text{out}}=0.004$, respectively, while the outlet liquid phase concentration is $x_{\text{out}}=0.008$. The equilibrium relation is $y=1.5x$. Find the height of the gas phase mass transfer unit is ().

Options:
A. 1.35m
B. 1.70m
C. 1.20m
D. 1.60m
E. 1.75m
F. 1.50m
G. 1.56m
H. 1.25m
I. 1.30m
J. 1.44m
Answer: J
Which of the following is correct regarding the development of the nutritive layer?

Options:
A. The nourishing layer's central unit consists of basal fibers aiding in muscle repair.
B. The nourishing layer consists of basal enzymes that specialize in energy storage.
C. The key component is the basal receptor, functioning as a hormonal response guide.
D. The basal core's function is to secrete nutrients essential for cardiovascular growth.
E. The nourishing layer is formed by the basal membrane facilitating neural synapses.
F. The nourishing layer's inner layer is the basal gland, which has a placental barrier function.
G. The basal gland's outer area serves primarily as a protective epidermal shield.
H. The nourishing layer's framework is the basal stalk, which has a digestive secretion task.
I. The basal cell matrix constructs an external lining for cellular temperature control.
J. The basal gland is the vital layer's nucleus, acting as an immune system regulator.
Answer: F
A 30-year-old primipara with regular menstruation visited the clinic due to vaginal bleeding for 3 days after 43 days of amenorrhea. Gynecological examination showed a small amount of blood in the vagina, a closed cervix, a uterus the size of a 40-day pregnancy, and a positive pregnancy test. The primary approach for managing this patient should be ().

Options:
A. Hospital Admission
B. Calm and Rest
C. Laparoscopic Surgery
D. Emergency Dilation
E. Hormonal Treatment
F. Endometrial Biopsy
G. Surgical Intervention
H. Medical Induction
I. Immediate Ultrasound
J. Intravenous Medication
Answer: B
21 years old, missed period for 2 months, self-induced abortion 2 days ago, body temperature 38.8°C, pulse 130/min, normal blood pressure, white blood cell count 10x10⁹/L, neutrophils 0.90, uterus size equivalent to 2 months pregnant, soft, tender, infection not controlled with anti-inflammatory treatment, suddenly experiencing heavy vaginal bleeding, which of the following treatments is advisable?

Options:
A. The cervix is slowly dilated using a series of metallic rods, and extensive bed rest is recommended afterwards.
B. The embryonic tissue is reintroduced with sterile gloves, and patient observation is emphasized during recovery.
C. The pelvic region is carefully compressed with both hands, and anti-coagulant therapy is introduced rapidly.
D. The amniotic fluid is incrementally reduced by aspiration, with hydration therapy becoming a primary focus subsequently.
E. The embryo is gently extracted with an oval forceps, and antibiotics are administered postoperatively.
F. The uterine lining is scraped delicately with a firm instrument, while regular saline irrigation is maintained.
G. The placenta is positioned precisely within the cavity, and overall fluid levels are monitored closely.
H. The uterus undergoes careful retraction through tension, and pain management involves light sedatives continuously.
I. The embryo is manually returned with care, and antiseptics are applied externally thereafter.
J. The uterine wall is pressed gently to expel contents, as dietary adjustments are initially prioritized during follow-up.
Answer: E
The first-time woman was 24 years old, 40 weeks of intrauterine pregnancy, and paroxysmal abdominal pain for 10 hours. The blood pressure was normal, the extrapelvic measurement was normal, the official height was 34cm, the fetal heart rate was 132/min, the contractions were 25~30s/5~6min, the intensity was medium and weak, the head presented first, the uterine opening was 3cm, S=-1, the amniotic sac was bulging, the fetal weight was estimated to be 3400g, and there was no obvious progress in the 2-hour labor process. What is the current diagnosis?

Options:
A. Prolonged latent phase
B. Primary uterine inertia
C. Premature rupture of membranes
D. Secondary uterine inertia
E. Complete placenta previa
F. Macrosomia with dystocia
G. Fetal distress syndrome
H. Posterior occiput position
I. Preterm premature labor
J. Cephalopelvic disproportion
Answer: D
Tourists enjoy tossing coins at a particular attraction in the scenic area. Assuming the tourists independently toss 10,000 times, with a hit rate of 0.1, let $X$ represent the number of successful hits, then $X$ follows a ( ) distribution.

Options:
A. $U(1000,0.1)$
B. $G(1000,0.1)$
C. $B(100,0.1)$
D. $B(10000,0.1)$
E. $B(1000,0.1)$
F. $B(1000,0.15)$
G. $B(5000,0.2)$
H. $N(1000,0.1)$
I. $B(1000,0.05)$
J. $P(1000,0.1)$
Answer: E
To understand the spending habits of students in two universities in a certain city, a random survey of 100 people from each university was conducted. The survey results showed that the average monthly expenditure of students from University A was 2,583 yuan, with a sample variance of 882,669, while the average monthly expenditure of students from University B was 2,439 yuan, with a sample variance of 678,976. Assume that the average monthly expenditure of students from University A is $X\sim N(\mu_1,\sigma_1^2)$ and from University B is $Y\sim N(\mu_2, \sigma_2^2)$, where $\mu_1, \mu_2, \sigma_1^2, \sigma_2^2$ are unknown, and the two samples are independent. At a significance level of 0.05, assume $H_0:\sigma_1^2=\sigma_2^2, H_1:\sigma_1^2\neq\sigma_2^2$, and calculate the corresponding p-value is().

Options:
A. 0.5
B. 0.01
C. 0.4
D. 0.2
E. 0.7
F. 0.3
G. 0.35
H. 0.15
I. 0.12
J. 0.6
Answer: D
A shuttle bus at the airport carries 25 passengers and passes through 9 stops. Each passenger is equally likely to get off at any one of these 9 stops, unaffected by whether other passengers get off. The shuttle bus only stops if there are passengers getting off. Let the random variable $Y$ represent the number of passengers getting off at the $i$-th stop, where $i = 1, 2, \ldots,X_{i}$ takes the value of 1 if passengers get off at that stop, otherwise it takes the value of 0. What is the variance of the number of stops $X$ the shuttle bus makes?

Options:
A. $$9\times\left(\frac{6}{9}\right)^{25}+73\times\left(\frac{8}{9}\right)^{25}-81\times\left(\frac{6}{9}\right)^{50}$$
B. $$7\times\left(\frac{7}{9}\right)^{25}+72\times\left(\frac{7}{9}\right)^{25}-80\times\left(\frac{8}{9}\right)^{50}$$
C. $$9\times\left(\frac{8}{9}\right)^{25}+73\times\left(\frac{7}{9}\right)^{25}-80\times\left(\frac{8}{9}\right)^{50}$$
D. $$9\times\left(\frac{6}{9}\right)^{25}+72\times\left(\frac{7}{9}\right)^{25}-80\times\left(\frac{8}{9}\right)^{50}$$
E. $$9\times\left(\frac{8}{9}\right)^{25}+72\times\left(\frac{7}{9}\right)^{25}-81\times\left(\frac{8}{9}\right)^{50}$$
F. $$8\times\left(\frac{8}{9}\right)^{25}+71\times\left(\frac{6}{9}\right)^{25}-81\times\left(\frac{8}{9}\right)^{50}$$
G. $$8\times\left(\frac{8}{9}\right)^{25}+70\times\left(\frac{7}{9}\right)^{25}-81\times\left(\frac{8}{9}\right)^{50}$$
H. $$9\times\left(\frac{7}{9}\right)^{25}+72\times\left(\frac{6}{9}\right)^{25}-81\times\left(\frac{7}{9}\right)^{50}$$
I. $$8\times\left(\frac{7}{9}\right)^{25}+73\times\left(\frac{6}{9}\right)^{25}-81\times\left(\frac{7}{9}\right)^{50}$$
J. $$8\times\left(\frac{6}{9}\right)^{25}+72\times\left(\frac{8}{9}\right)^{25}-81\times\left(\frac{7}{9}\right)^{50}$$
Answer: E
Suppose $(X_1, \cdots, X_{16})$ is a sample drawn from the population $X \sim N(1, \sigma^2)$, where $X$ is the sample mean. Given that $Y = aX + b \sim N(0, 1)$, then we have ().

Options:
A. $$a=\frac2\sigma,b=-\frac2\sigma $$
B. $$a=-\frac4\sigma,b=\frac4\sigma $$
C. $$a=-\frac8\sigma,b=\frac8\sigma $$
D. $$a=\frac5\sigma,b=-\frac5\sigma $$
E. $$a=\frac6\sigma,b=-\frac6\sigma $$
F. $$a=-\frac2\sigma,b=\frac2\sigma $$
G. $$a=\frac3\sigma,b=-\frac3\sigma $$
H. $$a=-\frac7\sigma,b=\frac7\sigma $$
I. $$a=-\frac1\sigma,b=\frac5\sigma $$
J. $$a=\frac4\sigma,b=-\frac5\sigma $$
Answer: B
An adiabatic container is filled with helium gas at $10 \, \mathrm{K}$ (above the critical temperature), which slowly leaks through fine cracks until the pressure inside the container reaches 1 atm and the temperature is 4.2 K (the normal boiling point of helium). Assuming the gas behaves as an ideal gas, and at the end of the process, the helium inside the container is completely liquefied, find the initial pressure of the container. Given that the latent heat of vaporization of He at 4.2 K is $\gamma = 20.92 \, \mathrm{kJ/kg}$, the specific heat capacity of helium $c_{\nu} = 3.116 \, \mathrm{kJ/(kg \cdot K)}$, and $c_{p} = 5.193 \, \mathrm{kJ/(kg \cdot K)}$.

Options:
A. $120atm$
B. $152atm$
C. $140atm$
D. $85atm$
E. $100atm$
F. $72atm$
G. $96atm$
H. $65atm$
I. $110atm$
J. $128atm$
Answer: G