MikaStars39/nano-eval huggingface dataset:
A point moves with simple harmonic motion according to the law $x=a \operatorname{sin} k t$. Given that when $x=x_{1}$, the velocity $\boldsymbol{v}=\boldsymbol{v}_{1}$, and when $x=x_{2}$, the velocity $\upsilon=\upsilon_{2}$, what are the amplitude $a$ and the angular frequency $k$ of the vibration ?

Options:
A. $$ a=\sqrt{\frac{x_{1}^{2} v_{1}^{2}-x_{2}^{2} v_{2}^{2}} {v_{2}^{2}+v_{1}^{2}}}, \quad k=\sqrt{\frac{v_{2}^{2}+v_{1}^{2}} {x_{2}^{2}-x_{1}^{2}}}. $$
B. $$ a=\sqrt{\frac{v_{1}^{2} x_{1}^{2}-v_{2}^{2} x_{2}^{2}} {x_{2}^{2}-x_{1}^{2}}}, \quad k=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}} {x_{2}^{2}+x_{1}^{2}}}. $$
C. $$ a=\sqrt{\frac{x_{2}^{2} v_{1}^{2}-x_{1}^{2} v_{2}^{2}} {x_{1}^{2}-x_{2}^{2}}}, \quad k=\sqrt{\frac{v_{2}^{2}-v_{1}^{2}} {x_{1}^{2}+x_{2}^{2}}}. $$
D. $$ a=\sqrt{\frac{v_{1}^{2} x_{1}^{2}-v_{2}^{2} x_{2}^{2}} {v_{1}^{2}-v_{2}^{2}}}, \quad k=\sqrt{\frac{x_{1}^{2}+x_{2}^{2}} {v_{2}^{2}-v_{1}^{2}}}. $$
E. $$
a=\sqrt{\frac{v_{1}^{2} x_{2}^{2}-v_{2}^{2} x_{1}^{2}} {v_{1}^{2}-v_{2}^{2}}}, \quad k=\sqrt{\frac{v_{1}^{2}-v_{2}^{2}} {x_{2}^{2}-x_{1}^{2}}}.
$$
F. $$ a=\sqrt{\frac{v_{2}^{2} x_{2}^{2}-v_{1}^{2} x_{1}^{2}} {v_{1}^{2}+v_{2}^{2}}}, \quad k=\sqrt{\frac{x_{2}^{2}-x_{1}^{2}} {v_{1}^{2}-v_{2}^{2}}}. $$
G. $$ a=\sqrt{\frac{x_{1}^{2} v_{2}^{2}-x_{2}^{2} v_{1}^{2}} {v_{2}^{2}-v_{1}^{2}}}, \quad k=\sqrt{\frac{x_{1}^{2}-x_{2}^{2}} {v_{2}^{2}-v_{1}^{2}}}. $$
H. $$ a=\sqrt{\frac{v_{2}^{2} x_{1}^{2}-v_{1}^{2} x_{2}^{2}} {v_{1}^{2}+v_{2}^{2}}}, \quad k=\sqrt{\frac{v_{2}^{2}-v_{1}^{2}} {x_{1}^{2}-x_{2}^{2}}}. $$
I. $$ a=\sqrt{\frac{x_{2}^{2} v_{2}^{2}-x_{1}^{2} v_{1}^{2}} {v_{2}^{2}-v_{1}^{2}}}, \quad k=\sqrt{\frac{x_{2}^{2}+x_{1}^{2}} {v_{1}^{2}-v_{2}^{2}}}. $$
J. $$ a=\sqrt{\frac{v_{2}^{2} x_{2}^{2}-v_{1}^{2} x_{1}^{2}} {x_{1}^{2}+x_{2}^{2}}}, \quad k=\sqrt{\frac{v_{2}^{2}+v_{1}^{2}} {x_{1}^{2}-x_{2}^{2}}}. $$
Answer: E
Rod $AB$ has a length of $4 \sqrt{2} \mathrm{m}$. Endpoint $A$ slides downward along the $y$-axis, while endpoint $B$ slides to the right along the $x$-axis. Point $A$ moves according to the rule $y_{A} = (5 - t^{2})$ (with $y_{A}$ in meters). At the same time, point $M$ slides along the rod from $A$ to $B$. It is known that point $M$ moves along an axis coincident with the rod. The motion rule is $s = AM = 2 \sqrt{2} t^{2}$ (with $s$ in meters). What are the magnitude of the absolute velocity and absolute acceleration of point $M$ at $t = 1$ second ?

Options:
A. $$7. 0 5 \ \mathrm{m / s}, 8. 0 6 \ \mathrm{m / s}^{2}$$
B. $$7. 3 5 \ \mathrm{m / s}, 9. 1 0 \ \mathrm{m / s}^{2}$$
C. $$7. 1 0 \ \mathrm{m / s}, 7. 8 8 \ \mathrm{m / s}^{2}$$
D. $$7. 2 3 \ \mathrm{m / s}, 7. 5 9 \ \mathrm{m / s}^{2}$$
E. $$6. 6 7 \ \mathrm{m / s}, 7. 6 8 \ \mathrm{m / s}^{2}$$
F. $$5. 5 5 \ \mathrm{m / s}, 6. 5 4 \ \mathrm{m / s}^{2}$$
G. $$6. 7 5 \ \mathrm{m / s}, 6. 3 7 \ \mathrm{m / s}^{2}$$
H. $$6. 8 9 \ \mathrm{m / s}, 7. 2 4 \ \mathrm{m / s}^{2}$$
I. $$8. 0 4 \ \mathrm{m / s}, 7. 9 2 \ \mathrm{m / s}^{2}$$
J. $$8. 1 5 \ \mathrm{m / s}, 8. 9 3 \ \mathrm{m / s}^{2}$$
Answer: A
A heavy object with a mass of $m = 200$ kg is placed on a rough inclined plane. Both the angle of inclination and the coefficient of sliding friction can be assigned different values. Currently, it is assumed that the inclination angle $\gamma$ and the friction coefficient $f$ are independent random variables following Gaussian distributions, with mathematical expectations of $m_{\gamma} = 0$ and $m_{f} = 0.2$, and mean square errors of $\sigma_{\gamma} = 3^{\circ}$ and $\sigma_{f} = 0.04$, respectively. Find the force level $Q$ needed to make the probability of the object starting to slide down the inclined plane reaching a level of 0.999 . What is the value of $Q$ ?
Hint: The approximate value of $\cos \gamma$ is taken as 1.

Options:
A. $$
720N
$$
B. $$
850N
$$
C. $$
740N
$$
D. $$
800N
$$
E. $$
865N
$$
F. $$
780N
$$
G. $$
810N
$$
H. $$
795N
$$
I. $$
770N
$$
J. $$
690N
$$
Answer: F
There is a large pressure vessel containing an ideal gas. It is known that $p=690\mathbf{kN/m}^2, T=282\mathbf{°C}, \gamma=1.4$, $R=166.6\mathbf{Nm/kgK}$. The gas is expelled into the atmosphere through a converging nozzle. The atmospheric pressure is $p_{a}=101.3\mathbf{kN/m^{2}}$, and the mass flow rate is $m=0.45kg/s$. What is the nozzle exit velocity?

Options:
A. 290.7m/s
B. 342.9m/s
C. 375.1m/s
D. 340.3m/s
E. 328.4m/s
F. 356.8m/s
G. 331.2m/s
H. 315.6m/s
I. 325.0m/s
J. 300.5m/s
Answer: E
A small sphere with a diameter of $d = 12 \mathrm{mm}$ rises uniformly in oil at a speed of $V_0 = 35 \mathrm{mm/s}$. Given the oil density $p = 918 \mathrm{kg/m^3}$ and viscosity $\mu = 0.34 \mathrm{Pas}$, the density of the sphere $\rho_{1}$ is ().

Options:
A. $$
7 7 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
B. $$
8 2 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
C. $$
6 9 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
D. $$
7 5 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
E. $$
8 5 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
F. $$
9 3 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
G. $$
9 0 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
H. $$
8 0 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
I. $$
7 8 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
J. $$
8 8 0 \mathbf{k g} / \mathbf{m}^{\mathbf{3}}
$$
Answer: D
Given that the density of seawater at sea level under $100 \mathrm{kPa}$ is $1025 \mathrm{kg/m^{3}}$, and the average bulk modulus of seawater is $234 \times 10^{7} \mathrm{Pa}$, with the absolute pressure at the seabed being $817 \times 10^{2} \, \mathrm{kPa}$, the density of seawater at the seabed is ().

Options:
A. $$
\rho=1 0 7 5 \mathrm{k g} / \mathrm{m}^{3}
$$
B. $$
\rho=1 1 0 3 \mathrm{k g} / \mathrm{m}^{3}
$$
C. $$
\rho=1 0 2 0 \mathrm{k g} / \mathrm{m}^{3}
$$
D. $$
\rho=1 0 6 1 \mathrm{k g} / \mathrm{m}^{3}
$$
E. $$
\rho=1 0 8 2 \mathrm{k g} / \mathrm{m}^{3}
$$
F. $$
\rho=1 0 4 9 \mathrm{k g} / \mathrm{m}^{3}
$$
G. $$
\rho=1 0 9 5 \mathrm{k g} / \mathrm{m}^{3}
$$
H. $$
\rho=1 0 3 8 \mathrm{k g} / \mathrm{m}^{3}
$$
I. $$
\rho=1 0 5 4 \mathrm{k g} / \mathrm{m}^{3}
$$
J. $$
\rho=1 0 5 0 \mathrm{k g} / \mathrm{m}^{3}
$$
Answer: D
Three charged spheres $A$, $B$, and $C$ are considered, with sphere $A$ carrying a charge of $+q_{1}$, and spheres $B$ and $C$ each carrying a charge of $+q_{2}$. The three spheres can move freely within a circular groove. When the system is in equilibrium, the arc between $B$ and $C$ is 60°. What is the ratio of $q_{1}$ to $q_{2}$?

Options:
A. $8.5$
B. $9.8$
C. $15.0$
D. $14.9$
E. $10.2$
F. $13.7$
G. $12.5$
H. $7.3$
I. $4.6$
J. $11.1$
Answer: G
Some charge is uniformly distributed on the surfaces of two concentric conducting spheres (the density is unknown). Assume that moving a charge of one unit from infinity to the common center of the spheres requires work equal to $W = 1 \times 10^{-6} \, \mathrm{J}$ The radii of the two spheres are $r = 0.05 \, \mathrm{m}$ and $R = 0.1 \, \mathrm{m}$, respectively. Try to find the charges $Q_{1}$ and $Q_{2}$ carried by these two spherical surfaces.

Options:
A. $$
q_{1}=\frac{r^{2} W} {k ( r-R )} \approx6. 5 3 \times1 0^{-1 0} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{2} \, W} {k \, ( \, r-R )} {\approx} 2. \, 5 1 \, \times1 0^{-9} \, \, \, G
$$
B. $$
q_{1}=\frac{r^{3} W} {k R} \approx7. 5 3 \times1 0^{-1 1} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{3} \, W} {k \, r} {\approx} 1. \, 8 1 \, \times1 0^{-8} \, \, \, G
$$
C. $$
q_{1}=\frac{r W} {k R} \approx4. 5 3 \times1 0^{-9} \mathrm{~ G}
$$
$$
q_{2}=\frac{R W} {k r} {\approx} 3. \, 3 1 \, \times1 0^{-8} \, \, \, G
$$
D. $$
q_{1}=\frac{(r^{2} + W)} {k ( R+r )} \approx5. 5 3 \times1 0^{-1 0} \mathrm{~ G}
$$
$$
q_{2}=\frac{(R^{2} + W)} {k \, ( \, R+r )} {\approx} 2. \, 2 1 \, \times1 0^{-9} \, \, \, G
$$
E. $$
q_{1}=\frac{r^{2} W} {k ( R-r )} \approx4. 5 3 \times1 0^{-1 1} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{2} \, W} {k \, ( \, R-r )} {\approx} 2. \, 2 1 \, \times1 0^{-8} \, \, \, G
$$
F. $$
q_{1}=\frac{W r^{2}} {k ( R+r )} \approx6. 5 3 \times1 0^{-1 0} \mathrm{~ G}
$$
$$
q_{2}=\frac{W R^{2} } {k \, ( \, R+r )} {\approx} 1. \, 2 1 \, \times1 0^{-8} \, \, \, G
$$
G. $$
q_{1}=\frac{r^{2} W} {k ( R+r )} \approx5. 5 3 \times1 0^{-1 0} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{2} \, W} {k \, ( \, R+r )} {\approx} 2. \, 2 1 \, \times1 0^{-9} \, \, \, G
$$
H. $$
q_{1}=\frac{r W} {k ( R-r )} \approx5. 5 3 \times1 0^{-9} \mathrm{~ G}
$$
$$
q_{2}=\frac{R \, W} {k \, ( R-r )} {\approx} 2. \, 1 1 \, \times1 0^{-8} \, \, \, G
$$
I. $$
q_{1}=\frac{r^{2} W} {k R} \approx3. 5 3 \times1 0^{-1 1} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{2} \, W} {k \, r} {\approx} 4. \, 1 1 \, \times1 0^{-8} \, \, \, G
$$
J. $$
q_{1}=\frac{r^{2} } {k ( R-r )} \approx5. 5 3 \times1 0^{-1 0} \mathrm{~ G}
$$
$$
q_{2}=\frac{R^{2} } {k \, ( \, R-r )} {\approx} 2. \, 2 1 \, \times1 0^{-9} \, \, \, G
$$
Answer: G
An $RLC$ series circuit is known to have $R = 5.00 \Omega$, $L = 636 \mathrm{mH}$, and $C = 159 \mu\mathrm{F}$. An AC voltage of $U = 311 \mathrm{V},~50.0 \mathrm{Hz}$ is applied across it. What is the voltage on each component in the circuit?

Options:
A. $$
U_{R}=8. 5~\mathrm{V}
,\
U_{L}=3 5 0~\mathrm{V}
,\
U_{C}=3 0. 6~\mathrm{V}
$$
B. $$
U_{R}=8. 9~\mathrm{V}
,\
U_{L}=3 4 8~\mathrm{V}
,\
U_{C}=3 3. 6~\mathrm{V}
$$
C. $$
U_{R}=8. 7~\mathrm{V}
,\
U_{L}=3 4 6~\mathrm{V}
,\
U_{C}=3 4. 6~\mathrm{V}
$$
D. $$
U_{R}=8. 2~\mathrm{V}
,\
U_{L}=3 4 4~\mathrm{V}
,\
U_{C}=3 7. 6~\mathrm{V}
$$
E. $$
U_{R}=9. 0~\mathrm{V}
,\
U_{L}=3 4 0~\mathrm{V}
,\
U_{C}=3 9. 6~\mathrm{V}
$$
F. $$
U_{R}=8. 6~\mathrm{V}
,\
U_{L}=3 4 2~\mathrm{V}
,\
U_{C}=3 5. 6~\mathrm{V}
$$
G. $$
U_{R}=9. 1~\mathrm{V}
,\
U_{L}=3 5 4~\mathrm{V}
,\
U_{C}=3 1. 6~\mathrm{V}
$$
H. $$
U_{R}=8. 3~\mathrm{V}
,\
U_{L}=3 4 2~\mathrm{V}
,\
U_{C}=3 8. 6~\mathrm{V}
$$
I. $$
U_{R}=8. 1~\mathrm{V}
,\
U_{L}=3 5 2~\mathrm{V}
,\
U_{C}=3 5. 6~\mathrm{V}
$$
J. $$
U_{R}=8. 4~\mathrm{V}
,\
U_{L}=3 5 6~\mathrm{V}
,\
U_{C}=3 6. 6~\mathrm{V}
$$
Answer: C
Two parallel long straight power lines, belonging to the same circuit, have currents flowing in opposite directions. Their radii are $a$ and $b$, respectively, and the distance between their axes is $d$. The currents are uniformly distributed across their respective cross-sections. What is the value of the self-inductance per unit length when $a \!=\! b \!=\! 10 \text{ mm}$ and $d \!=\! 20 \text{ cm}$?

Options:
A. $$
4. 3~\mu\mathrm{H} / \mathrm{m}
$$
B. $$
1. 1~\mu\mathrm{H} / \mathrm{m}
$$
C. $$
0. 5~\mu\mathrm{H} / \mathrm{m}
$$
D. $$
0. 7~\mu\mathrm{H} / \mathrm{m}
$$
E. $$
2. 3~\mu\mathrm{H} / \mathrm{m}
$$
F. $$
2. 7~\mu\mathrm{H} / \mathrm{m}
$$
G. $$
3. 1~\mu\mathrm{H} / \mathrm{m}
$$
H. $$
1. 9~\mu\mathrm{H} / \mathrm{m}
$$
I. $$
1. 3~\mu\mathrm{H} / \mathrm{m}
$$
J. $$
2. 5~\mu\mathrm{H} / \mathrm{m}
$$
Answer: I
A copper wire carries a current $I$, which is uniformly distributed across its cross-section. It is known that the radius of the wire's cross-section is $R$, and the density of free electrons participating in conduction in the copper is $n$, with the charge of an electron being $e$. When $R=5.0 \ \mathrm{mm}, \ I=50 \ \mathrm{A}, \ n=8.4 \times 10^{22} \ /\mathrm{cm}^{3}, \ e=-1.6 \times 10^{-19} \ \mathrm{C}$, what is the value of $U$?

Options:
A. $$
- 3. 3 \times1 0^{-1 0}~\mathrm{V}
$$
B. $$
- 2. 9 \times1 0^{-1 0}~\mathrm{V}
$$
C. $$
- 2. 4 \times1 0^{-1 0}~\mathrm{V}
$$
D. $$
- 2. 7 \times1 0^{-1 0}~\mathrm{V}
$$
E. $$
- 2. 1 \times1 0^{-1 0}~\mathrm{V}
$$
F. $$
- 4. 2 \times1 0^{-1 0}~\mathrm{V}
$$
G. $$
- 3. 6 \times1 0^{-1 0}~\mathrm{V}
$$
H. $$
- 1. 8 \times1 0^{-1 0}~\mathrm{V}
$$
I. $$
- 3. 0 \times1 0^{-1 0}~\mathrm{V}
$$
J. $$
- 1. 5 \times1 0^{-1 0}~\mathrm{V}
$$
Answer: C
On a cylindrical surface with a radius of $R$, a current $I\,$ is carried, flowing parallel to the axis of the cylindrical surface and uniformly distributed over it. What is the magnetic induction (i.e., the magnetic induction at the location of the surface current) at any point on this cylindrical surface?

Options:
A. $$
B=\frac{4} {5} \mu_{0} k \times n
$$
B. $$
B=\frac{1} {3} \mu_{0} k \times n
$$
C. $$
B=\frac{1} {2} \mu_{0} R \times I
$$
D. $$
B=\frac{2} {3} \mu_{0} R \times I
$$
E. $$
B=\mu_{0} I / 3 \pi R
$$
F. $$
B=\mu_{0} I / 4 \pi R
$$
G. $$
B=\frac{3} {4} \mu_{0} k \times n
$$
H. $$
B=\frac{1} {2} \mu_{0} k \times n
$$
I. $$
B=\mu_{0} k \times n / 4
$$
J. $$
B=\mu_{0} I / 2 \pi R
$$
Answer: H
Connect the two capacitors, $C_{1}=2.0 \mu\mathrm{F}$ and $C_{2}=8.0 \mathrm{\mu F}$, in series and apply a 300 V DC voltage across them. Disconnect the power source, and separate $C_{1}$ and $C_{2}$ from each other. Then connect the positively charged plates together and the negatively charged plates together. What is the voltage across each capacitor?

Options:
A. $150~\mathrm{V},~150~\mathrm{V}$
B. $96~\mathrm{V},~96~\mathrm{V}$
C. $50~\mathrm{V},~50~\mathrm{V}$
D. $12~\mathrm{V},~12~\mathrm{V}$
E. $75~\mathrm{V},~75~\mathrm{V}$
F. $48~\mathrm{V},~48~\mathrm{V}$
G. $18~\mathrm{V},~18~\mathrm{V}$
H. $200~\mathrm{V},~200~\mathrm{V}$
I. $100~\mathrm{V},~100~\mathrm{V}$
J. $120~\mathrm{V},~120~\mathrm{V}$
Answer: B
Production of sodium phosphate dodecahydrate $({Na_{2}PO_{4}} \cdot12{H}_{2}O)$ crystals using a cooling crystallizer. The feed solution is a 25% (mass fraction of solute, same below) sodium phosphate aqueous solution, and the concentration of the mother liquor is 13%. The amount of water vaporized during the crystallization process is 5% of the feed amount. If the crystallization product amounts to 6000 kg/h, calculate the flow rate of the feed solution is ().

Options:
A. 8567.0kg/h
B. 8400.5kg/h
C. 9021.6kg/h
D. 8234.2kg/h
E. 9145.8kg/h
F. 8899.0kg/h
G. 8873.9kg/h
H. 8621.3kg/h
I. 8765.4kg/h
J. 8697.3kg/h
Answer: J
The boiling point of a NaCl aqueous solution with a known concentration of 0.25 at an absolute pressure of 19.6 kPa is 65.8°C. Use Duhring's rule to determine the boiling point of this solution at an absolute pressure of 50 kPa is ().

Options:
A. 86.78°C
B. 93.45°C
C. 91.56°C
D. 89.04°C
E. 84.67°C
F. 87.91°C
G. 92.49°C
H. 82.35°C
I. 90.12°C
J. 78.23°C
Answer: F
In a certain shell and tube heat exchanger, a fluid is heated from 20°C to 80°C using steam at 100°C. After six months of operation, due to the effect of fouling, the fluid's outlet temperature is only 70°C under the same operating conditions. What temperature should the heating steam be increased to in order to maintain the outlet temperature at 80°C?

Options:
A. 112°C
B. 135°C
C. 116°C
D. 150°C
E. 90°C
F. 95°C
G. 125°C
H. 108°C
I. 102°C
J. 140°C
Answer: C
Atmospheric air is heated in the annular gap of the casing with specifications of $\varPhi 100 \times 5 \, \text{mm}$ and $\varPhi 57 \times 3.5 \, \text{mm}$. Given: the air flow rate is 0.06 kg/s, and the inlet and outlet temperatures are 30°C and 50°C, respectively. Determine the heat transfer film coefficient of the pipe wall to the air is ().

Options:
A. $1 8. 9 3 \mathrm{W / m^{2} \! \cdot\! °C}$
B. $2 5. 3 5 \mathrm{W / m^{2} \! \cdot\! °C}$
C. $2 9. 7 5 \mathrm{W / m^{2} \! \cdot\! °C}$
D. $4 2. 9 0 \mathrm{W / m^{2} \! \cdot\! °C}$
E. $1 5. 6 4 \mathrm{W / m^{2} \! \cdot\! °C}$
F. $2 2. 8 2 \mathrm{W / m^{2} \! \cdot\! °C}$
G. $3 1. 8 6 \mathrm{W / m^{2} \! \cdot\! °C}$
H. $3 4. 7 1 \mathrm{W / m^{2} \! \cdot\! °C}$
I. $3 6. 2 0 \mathrm{W / m^{2} \! \cdot\! °C}$
J. $2 1. 4 8 \mathrm{W / m^{2} \! \cdot\! °C}$
Answer: F
In a tubular heat exchanger, the two fluids flow in parallel, with the inlet and outlet temperatures of the hot fluid being 130°C and 65°C, and the inlet and outlet temperatures of the cold fluid being 32°C and 48°C. If the two fluids are changed to counterflow while maintaining the same flow rates and inlet temperatures, estimate the mean temperature difference of the exchanger and the outlet temperatures of the two fluids.

Options:
A. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 9. 0 \mathrm{°C}
$$
B. $$
\Delta t^{\prime} {}_{\mathrm{m}}=6 0. 0 \mathrm{°C}
$$
C. $$
\Delta t^{\prime} {}_{\mathrm{m}}=4 8. 2 \mathrm{°C}
$$
D. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 6. 9 \mathrm{°C}
$$
E. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 7. 3 \mathrm{°C}
$$
F. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 1. 3 \mathrm{°C}
$$
G. $$
\Delta t^{\prime} {}_{\mathrm{m}}=4 5. 7 \mathrm{°C}
$$
H. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 2. 5 \mathrm{°C}
$$
I. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 4. 8 \mathrm{°C}
$$
J. $$
\Delta t^{\prime} {}_{\mathrm{m}}=5 5. 1 \mathrm{°C}
$$
Answer: H
Saturated steam in 400kPa with a flow of 50 kg/h condenses and is then cooled to 60°C. In this situation, the heat transfer amount of the heat object is ()

Options:
A. 38.25kW
B. 41.50kW
C. 35.15kW
D. 37.85kW
E. 36.60kW
F. 29.15kW
G. 33.70kW
H. 32.25kW
I. 34.40kW
J. 28.40kW
Answer: C
Filter a water suspension with a solid phase concentration of 15% (volume percentage). The filter cake has a water content of 40% (mass percentage), and the true density of the particles is $1 5 0 0 \, \text{kg/m}^{3}$. Calculate the yield of the filter cake $v$ is ().

Options:
A. 0.4492
B. 0.4408
C. 0.3921
D. 0.5071
E. 0.4823
F. 0.3657
G. 0.4135
H. 0.4286
I. 0.4659
J. 0.4756
Answer: H
Determine the maximum particle size for coal ash particles with a density of $2150 \, \text{kg/m}^3$ undergoing laminar settling in air at 20°C is ().

Options:
A. $$
4 3 . 7 7 \mu\mathrm{m}
$$
B. $$
6 6 . 5 8 \mu\mathrm{m}
$$
C. $$
4 9 . 2 7 \mu\mathrm{m}
$$
D. $$
5 2 . 1 1 \mu\mathrm{m}
$$
E. $$
2 1 . 3 9 \mu\mathrm{m}
$$
F. $$
8 8 . 5 2 \mu\mathrm{m}
$$
G. $$
1 0 . 8 9 \mu\mathrm{m}
$$
H. $$
7 7. 4 3 \mu\mathrm{m}
$$
I. $$
9 9 . 6 6 \mu\mathrm{m}
$$
J. $$
3 3 . 9 5 \mu\mathrm{m}
$$
Answer: H
The water at a temperature of 293K is led from the water tower to the workshop using a $\phi11 4 \times4 \mathrm{mm}$ seamed steel pipe, with a calculated length (the sum of the straight pipe length and the equivalent length of local obstacles) of 150m. The water level in the water tower is maintained constant and is 12m higher than the outlet of the drainage pipe. Try to determine what the water flow rate in this pipeline is ().

Options:
A. $$
7 6. 3 \mathrm{m}^{3} / \mathrm{h}
$$
B. $$
8 9. 6 \mathrm{m}^{3} / \mathrm{h}
$$
C. $$
9 1. 4 \mathrm{m}^{3} / \mathrm{h}
$$
D. $$
6 2. 7 \mathrm{m}^{3} / \mathrm{h}
$$
E. $$
8 0. 1 \mathrm{m}^{3} / \mathrm{h}
$$
F. $$
6 9. 5 \mathrm{m}^{3} / \mathrm{h}
$$
G. $$
8 5. 2 \mathrm{m}^{3} / \mathrm{h}
$$
H. $$
7 0. 8 \mathrm{m}^{3} / \mathrm{h}
$$
I. $$
5 4. 9 \mathrm{m}^{3} / \mathrm{h}
$$
J. $$
5 8. 4 \mathrm{m}^{3} / \mathrm{h}
$$
Answer: A
A sphere with a diameter of 8.5 inches and a weight of 16 pounds-force (similar to a bowling ball), calculate its free-fall velocity under gravity as it passes through the standard atmospheric pressure at the horizon is().

Options:
A. $$
4 8 5 \mathrm{ft} / \mathrm{s e c}
$$
B. $$
6 3 8 \mathrm{ft} / \mathrm{s e c}
$$
C. $$
4 1 2 \mathrm{ft} / \mathrm{s e c}
$$
D. $$
7 0 2 \mathrm{ft} / \mathrm{s e c}
$$
E. $$
3 9 3 \mathrm{ft} / \mathrm{s e c}
$$
F. $$
3 5 0 \mathrm{ft} / \mathrm{s e c}
$$
G. $$
5 4 7 \mathrm{ft} / \mathrm{s e c}
$$
H. $$
7 9 1 \mathrm{ft} / \mathrm{s e c}
$$
I. $$
5 9 0 \mathrm{ft} / \mathrm{s e c}
$$
J. $$
6 2 0 \mathrm{ft} / \mathrm{s e c}
$$
Answer: C
The stress $s$ and strength $r$ of a certain component are known to follow a log-normal distribution, with their means and standard deviations being $\mu_{s}=60000 \mathrm{kPa}$, $\sigma_{s}=20000 \mathrm{kPa}$, $\mu_{r}=100000 \mathrm{kPa}$, $\sigma_{r}=10000 \mathrm{kPa}$. Try to calculate the reliability of this component.

Options:
A. 0.96950
B. 0.73950
C. 0.94950
D. 0.99950
E. 0.88950
F. 0.97950
G. 0.95950
H. 0.92950
I. 0.85950
J. 0.90950
Answer: C
A blade of an axial flow pump is subjected to a mean concentrated load of $P=5 \times 10^{4} \, \mathrm{N}$, with a standard deviation $\sigma_{p}=5 \times 10^{3} \, \mathrm{N}$. The point of action is at a distance $a = 0.1\, \mathrm{m}$ from the root, with a standard deviation $\sigma_{\mathrm{a}}=1\, \mathrm{mm}$. The mean strength of the material is $\mu_{r}=186\, \mathrm{MPa}$. Determine the minimum size of the pump blade pivot at a reliability of $R=0.99$.

Options:
A. 80mm
B. 60mm
C. 90mm
D. 95mm
E. 85mm
F. 65mm
G. 70mm
H. 100mm
I. 75mm
J. 55mm
Answer: I
To consume 0.1000 mol/L HCl solution $20-25 \, \mathrm{ml}$ for titration, how many grams of the standard reagent $\mathrm{Na_{2}CO_{3}}$ should be used?

Options:
A. $0.18g$
B. $0.17g$
C. $0.16g$
D. $0.14g$
E. $0.20g$
F. $0.15g$
G. $0.19g$
H. $0.11g$
I. $0.12g$
J. $0.13g$
Answer: J
Using a 0.1000 mol/L HCl standard solution to titrate a monoacidic weak base $\mathbf{B}$ via potentiometric titration, 40.00 ml of the HCl standard solution is consumed at the stoichiometric point. When 16.00 ml of the HCl standard solution is added, the solution's pH = 6.20. Calculate the $K_{b}$ value of $\mathbf{B}^{-}$.

Options:
A. 2.56
B. 3.22
C. 9.31
D. 4.18
E. 6.75
F. 12.45
G. 5.67
H. 10.89
I. 7.98
J. 11.34
Answer: I
In a 0.10 mol/L $\mathrm{AlF}_{6}^{3-}$ solution, the concentration of free $\mathbf{F}^{-}$ is 0.010 mol/L. What is the concentration of free $\mathrm{Al}^{3+}$ in the solution?

Options:
A. $$
8. 6 \times1 0^{-1 2} ( \mathrm{m o l / L} )
$$
B. $$
2. 5 \times1 0^{-1 2} ( \mathrm{m o l / L} )
$$
C. $$
6. 4 \times1 0^{-1 2} ( \mathrm{m o l / L} )
$$
D. $$
3. 3 \times1 0^{-1 3} ( \mathrm{m o l / L} )
$$
E. $$
9. 8 \times1 0^{-1 3} ( \mathrm{m o l / L} )
$$
F. $$
1. 1 \times1 0^{-1 1} ( \mathrm{m o l / L} )
$$
G. $$
4. 7 \times1 0^{-1 2} ( \mathrm{m o l / L} )
$$
H. $$
7. 2 \times1 0^{-1 3} ( \mathrm{m o l / L} )
$$
I. $$
0. 1 \times1 0^{-1 2} ( \mathrm{m o l / L} )
$$
J. $$
5. 9 \times1 0^{-1 4} ( \mathrm{m o l / L} )
$$
Answer: F
When $\mathbf{Ca}^{2+}$ and $\mathbf{Mg}^{2+}$ coexist, the pH condition for titration of $\mathbf{Ca}^{2+}$ with EDTA without the use of a masking agent is ( ).

Options:
A. $pH10$
B. $pH8$
C. $pH6$
D. $pH5$
E. $pH11$
F. $pH4$
G. $pH9$
H. $pH7$
I. $pH12$
J. $pH3$
Answer: I
In a medium of 1.0 mol/L $\mathrm{H_{2}SO_{4}}$, titrate a 0.1000 mol/L $\mathrm{Fe}^{2+}$ solution with a 0.1000 mol/L Ce solution. If the indicator chosen is $( \varphi_{\mathrm{ln}}^{\Theta^{\prime}} \ =\ 0.84 \mathrm{V} \ )$, set up the titration end-point $TE (\%)$ is().(Given: $\varphi_{Fe^{3+}/Fe^{2+}}^{\Theta^{\prime}} = 0.68 \mathrm{V}, \varphi_{Ce^{4+}/Ce^{3+}}^{\Theta^{\prime}} = 1.44 \mathrm{V}$)

Options:
A. $$
- 1. 1 \%
$$
B. $$
- 0. 2 \%
$$
C. $$
1. 2 \%
$$
D. $$
- 0. 8 \%
$$
E. $$
- 0. 6 \%
$$
F. $$
1. 0 \%
$$
G. $$
0. 5 \%
$$
H. $$
0. 3 \%
$$
I. $$
- 0. 4 \%
$$
J. $$
0. 9 \%
$$
Answer: B
Weigh a sample of $0.3675 \mathbf{g} \ \mathbf{BaCl}_{2} \cdot 2 \mathbf{H}_{2} \mathbf{O}$, and how many ml of 0.5 mol/L $\mathrm{H_{2}SO_{4}}$ solution are needed to precipitate the barium as $\mathrm{BaSO_{4}}$?

Options:
A. $8.3ml$
B. $9.1ml$
C. $6.7ml$
D. $4.5ml$
E. $10.2ml$
F. $7.4ml$
G. $1.9ml$
H. $2.8ml$
I. $5.2ml$
Answer: D
Immerse the pH glass electrode and the saturated calomel electrode in a standard buffer solution with a pH of 6.86, and measure the electromotive force as 0.352V. When measuring another unknown solution, the electromotive force is measured as 0.296V. What is the pH of the unknown solution?

Options:
A. 6.10
B. 7.00
C. 6.67
D. 6.92
E. 5.45
F. 6.29
G. 7.23
H. 5.91
I. 5.55
J. 5.99
Answer: H
To neutralize 25.00 ml of a purified weak acid solution with unknown composition, 44.60 ml of 0.1050 mol/L standard $\mathrm{NaOH}$ is required. An equal amount of base is added to 50.00 ml of this weak acid to form a buffer solution. To determine the buffer solution's $\mathrm{pH}$, a sufficient amount of indicator is added to achieve a concentration of $5.00 \times 10^{-4} \mathrm{mol/L}$. Using a 1.00 cm cuvette, the absorbance of the solution is measured to be 0.378 at 485 nm and 0.298 at 625 nm. What is the pH of the solution?

Options:
A. 7.01
B. 6.77
C. 6.02
D. 8.57
E. 5.45
F. 7.89
G. 4.62
H. 8.23
I. 9.11
J. 5.78
Answer: B
Predict the content of para-xylene in a mixed sample of xylene. Weigh 110.0 mg of the sample, add 30.0 mg of para-xylene reference material, and measure using the reverse-phase chromatography method. The chromatographic peak areas before and after adding the reference material are: para-xylene: $A_{para} 40.0, A_{para}^{\prime} 104.2$; meta-xylene: $A_{meta} 141.8, A_{meta}^{\prime} 156.2$. What is the percentage content of para-xylene?

Options:
A. $$
3 0. 8 \% $$
B. $$
3 5. 0 \% $$
C. $$
4 0. 5 \% $$
D. $$
2 5. 4 \%
$$
E. $$
2 3. 7 \% $$
F. $$
1 5. 6 \% $$
G. $$
2 9. 4 \% $$
H. $$
2 7. 5 \% $$
I. $$
2 0. 1\%
$$
J. $$
1 8. 9 \% $$
Answer: I
When analyzing the drawing of non-uniform gradient free seepage infiltration lines, for slopes with $i > 0$, there is a normal water depth N-N line. How many zones can it be divided into?

Options:
A. 3
B. 10
C. 1
D. 4
E. 7
F. 5
G. 2
H. 9
I. 8
J. 6
Answer: G
A certain steel plate boiler air duct has a length of $l=100 \mathrm{m}$, with a cross-sectional dimension of $400 \mathrm{mm} \times 200 \mathrm{mm}$. The average airflow speed inside the pipe is $V=10 \mathrm{m/s}$, with an absolute roughness of the steel plate $\Delta=0.15 \mathrm{mm}$. The air temperature is $20°C$. What is the pressure loss $\Delta p$ when air passes through this duct?

Options:
A. $$400Pa$$
B. $$405Pa$$
C. $$375Pa$$
D. $$395Pa$$
E. $$382Pa$$
F. $$360Pa$$
G. $$385Pa$$
H. $$390Pa$$
I. $$365Pa$$
J. $$370Pa$$
Answer: E
The heat capacity of copper between $20^{\circ} \ \mathrm{C}$ and its melting point can be expressed as $C_{\mathrm{p}} = 22.6 + 6.27 \times 10^{-3} \, T \mathrm{~ J / (mol \cdot K)}$. The heat of fusion for copper is $13,290 \, \mathrm{J/mol}$, and the equilibrium solidification temperature is $1356 \, \mathrm{K}$. Under adiabatic conditions, what supercooling is required for $1 \, \mathrm{mol}$ of copper to completely solidify without the temperature rising back to the melting point?

Options:
A. $$
3 7 5 \ ( \mathrm{K} )
$$
B. $$
5 1 5 \ ( \mathrm{K} )
$$
C. $$
7 7 0 \ ( \mathrm{K} )
$$
D. $$
4 4 8 \ ( \mathrm{K} )
$$
E. $$
3 2 0 \ ( \mathrm{K} )
$$
F. $$
2 9 0 \ ( \mathrm{K} )
$$
G. $$
6 2 5 \ ( \mathrm{K} )
$$
H. $$
8 4 0 \ ( \mathrm{K} )
$$
I. $$
5 5 0 \ ( \mathrm{K} )
$$
J. $$
6 6 5 \ ( \mathrm{K} )
$$
Answer: D
A lossless transmission line with a characteristic impedance of 50Ω in an air medium connects a 500 MHz transmitter with an antenna having an input impedance of 70Ω. The positions and values of the maximum and minimum voltage and current on the transmission line are ().

Options:
A. $$
U_{\mathrm{\scriptsize~ m ax}}=2 9. 9 9 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=2 7. 9 9 \mathbf{V}
$$
B. $$
U_{\mathrm{\scriptsize~ m ax}}=2 3. 5 8 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=1 5. 9 2 \mathbf{V}
$$
C. $$
U_{\mathrm{\scriptsize~ m ax}}=2 8. 3 2 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=2 3. 0 0 \mathbf{V}
$$
D. $$
U_{\mathrm{\scriptsize~ m ax}}=2 8. 0 0 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=2 2. 4 5 \mathbf{V}
$$
E. $$
U_{\mathrm{\scriptsize~ m ax}}=2 5. 7 4 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=1 9. 6 5 \mathbf{V}
$$
F. $$
U_{\mathrm{\scriptsize~ m ax}}=2 6. 4 6 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=1 8. 9 0 \mathbf{V}
$$
G. $$
U_{\mathrm{\scriptsize~ m ax}}=2 7. 0 1 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=2 0. 5 5 \mathbf{V}
$$
H. $$
U_{\mathrm{\scriptsize~ m ax}}=3 0. 5 0 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=2 5. 4 7 \mathbf{V}
$$
I. $$
U_{\mathrm{\scriptsize~ m ax}}=1 8. 6 0 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=1 1. 2 3 \mathbf{V}
$$
J. $$
U_{\mathrm{\scriptsize~ m ax}}=1 9. 3 7 \mathbf{V}
$$
$$
U_{\mathrm{m i n}}=1 2. 0 2 \mathbf{V}
$$
Answer: F
Consider a granite column with a cross-sectional area of $A$ and a length of $l$, connected at both ends to other rock blocks. Suppose the temperature of the column suddenly drops by 40°C, while the distance between the two ends remains unchanged. Given that the linear expansion coefficient of granite is $a = 7 \times 10^{-6} / °C$ (α is the amount of elongation or shortening per unit length for each degree increase or decrease), what is the stress induced within the column due to contraction?

Options:
A. $75kg/cm^{2}$
B. $60kg/cm^{2}$
C. $55kg/cm^{2}$
D. $65kg/cm^{2}$
E. $50kg/cm^{2}$
F. $95kg/cm^{2}$
G. $90kg/cm^{2}$
H. $80kg/cm^{2}$
I. $85kg/cm^{2}$
J. $70kg/cm^{2}$
Answer: J
A long plate with a centrally penetrating crack is subjected to uniform tensile forces at both ends. The plate width is $W = 200 \, \mathrm{mm}$ and the thickness is $h = 10 \, \mathrm{mm}$. The total applied tensile force is $P = 1.26 \, \mathrm{MN}$. The total length of the crack is 20 mm. It is known that the tensile yield limit of the material is $\sigma_{0.2} = 1120 \, \mathrm{MPa}$. Determine the stress intensity factor $K_{1}$ at the crack tip. If considering the plastic zone correction at the crack tip, to what value will $K_{1}$ increase?

Options:
A. $$
3 . 6 8 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
B. $$
3. 8 3 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
C. $$
3 . 4 5 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
D. $$
4 . 0 2 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
E. $$
4 . 1 0 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
F. $$
4 . 3 0 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
G. $$
3 . 9 5 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
H. $$
4 . 1 7 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
I. $$
3 . 5 0 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
J. $$
4 . 2 1 \times1 0^{3} \mathrm{N / m m}^{3 / 2}
$$
Answer: B
A certain brick masonry column has a cross-sectional dimension of $490 \, \mathrm{mm} \times 620 \,\mathrm{mm} \, ( \, b \times h \, )$, with a calculated brick column height of $H_{0}=4.8 \, \mathrm{m}$. It uses MU10 grade sintered perforated bricks (with a porosity of 33%) and is built with M7.5 grade cement mortar. The quality control level of the masonry construction is Class $\mathbf{B}$.
Question: Which of the following values is closest to the design value of the compressive strength of this brick column ($\mathrm{kN/mm^{2}}$)?

Options:
A. 1.25
B. 1.19
C. 1.52
D. 1.26
E. 1.28
F. 1.21
G. 1.23
H. 1.20
I. 1.24
J. 1.27
Answer: C
A set of composite brick columns, with a sectional height $h=620 \text{ mm}$ in the direction of eccentricity of the axial force, is subjected to an axial force design value of 872 kN and a bending moment design value of 25.8 kN·$\mathbf{m}$. To which of the following values is the initial eccentricity $e (\text{mm})$ of the axial force in this composite brick column closest?

Options:
A. 31.0
B. 30.7
C. 33.2
D. 34.8
E. 26.9
F. 28.4
G. 35.6
H. 32.5
I. 29.7
J. 27.3
Answer: A
A bridge on a first-class highway consists of a main bridge and approach bridges. Its structure: the main bridge is a three-span (70m + 100m + 70m) variable cross-section prestressed concrete continuous box girder; each approach bridge consists of 5 spans of 40m prestressed concrete small box-shaped section girders. The abutment is of an embedded ribbed slab structure, with the wing wall length being 3500mm and the retaining wall thickness $400 \mathrm{mm}$; the expansion joints at both ends of the main bridge and approach bridges are 160mm. The clear width of the bridge carriageway is 15m, and the total width is 17.5m. Please determine which value below is closest to the calculated total length of the bridge (m).

Options:
A. 625.50
B. 655.40
C. 647.96
D. 640.65
E. 672.30
F. 699.20
G. 679.15
H. 682.45
I. 610.25
J. 630.80
Answer: C
Assuming that the T-shaped section beam bridge deck is a rigid connection slab, the center-to-center distance of the main beams is 2.4m, the spacing of the cross beams is 6m, and the top layer of the slab is paved with 0.15m. When considering only the rear axle wheel load of a vehicle acting in the transverse direction of the bridge, determine which of the following values is closest to the distribution width value in the vertical span direction of the slab?

Options:
A. 5.2m
B. 4.2m
C. 6.0m
D. 2.8m
E. 4.5m
F. 3.0m
G. 4.0m
H. 3.8m
I. 5.5m
J. 3.5m
Answer: F
Under the conditions of a total pressure of 10.13 kPa and a temperature of 298 K, a gas mixture composed of $\mathrm{N_{2}}$ (A) and He (B) diffuses through a capillary tube that is 0.02 m long with an average diameter of $5 \times 10^{-6} \mathrm{m}$. It is known that the mole fraction at one end is 0.8 and at the other end is 0.2. The flux ratio for this system is given by $N_{\mathrm{A}} / N_{\mathrm{B}}=\ {\sqrt{M_{\mathrm{B}} / M_{\mathrm{A}}}}$. Under the diffusion conditions, the average diffusion coefficient of $\mathrm{N_{2}}$ is $D = 6.98 \times 10^{-5} \mathrm{m}^{2} / \mathrm{s}$, and the viscosity is $1.8 \times 10^{-5} \, \mathrm{Pa} \cdot \mathrm{s}$. Calculate the diffusion flux of $\mathrm{N_{2}}$, $N_{\mathrm{A}}$.

Options:
A. $$
2. 4 8 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
B. $$
3. 1 7 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
C. $$
6. 2 3 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
D. $$
4. 5 8 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
E. $$
5. 4 5 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
F. $$
1. 0 5 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
G. $$
5. 9 6 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
H. $$
7. 9 0 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
I. $$
9. 3 7 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
J. $$
8. 0 1 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
Answer: D
At the bottom of a test tube, there is methanol at a temperature of 298K. The distance between the liquid surface and the top of the test tube is 80mm, and at the top of the test tube, air at 298K and 101.3kPa gently blows across. It is known that the saturation vapor pressure of methanol at 298K is 16.8kPa, and the diffusion coefficient of methanol in air is $1.5 3 \times 10^{-5} \, {\mathrm{m}}^{2}$/s. Calculate the time required for the liquid surface to drop by 2mm.

Options:
A. $$
\ 5. \ 8 9 \times1 0^{4} \, \mathrm{s}
$$
B. $$
\ 4. \ 5 2 \times1 0^{4} \, \mathrm{s}
$$
C. $$
\ 2. \ 3 9 \times1 0^{4} \, \mathrm{s}
$$
D. $$
\ 6. \ 5 4 \times1 0^{4} \, \mathrm{s}
$$
E. $$
\ 1. \ 9 5 \times1 0^{4} \, \mathrm{s}
$$
F. $$
\ 3. \ 1 7 \times1 0^{4} \, \mathrm{s}
$$
G. $$
\ 4. \ 2 1 \times1 0^{4} \, \mathrm{s}
$$
H. $$
\ 4. \ 0 8 \times1 0^{4} \, \mathrm{s}
$$
I. $$
\ 3. \ 5 4 \times1 0^{4} \, \mathrm{s}
$$
J. $$
\ 2. \ 7 3 \times1 0^{4} \, \mathrm{s}
$$
Answer: I
The solute composition of a certain mixed gas is $y_{1}=0.60$. After chemical absorption, the solute composition decreases to $y_{2}=0.02$. When the amount of absorbent is sufficiently large, the equilibrium partial pressure of the solute is zero. Calculate the total number of gas-phase mass transfer units according to high composition absorption and low composition absorption, respectively.

Options:
A. 3.467,3.601
B. 3.849,3.401
C. 4.121,2.903
D. 4.753,2.912
E. 4.120,3.759
F. 3.358,3.965
G. 3.798,3.500
H. 3.002,4.001
I. 2.941,3.980
J. 2.950,2.852
Answer: B
In a continuous distillation column, separate the mixture composed of carbon disulfide and carbon tetrachloride. It is known that the feed stream flow rate is 14,000 kg/h, with a composition $a_{F}$ of 0.3 (mass fraction of carbon disulfide, the same below). If the bottom product composition $a_{\mathbf{w}}$ must not exceed 0.05 and the recovery rate of the distillate is 90%, find the flow rate and composition of the distillate, expressed in terms of molar flow rate and mole fraction respectively.

Options:
A. $$
D \!=\! 5 7. 6 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 7 6 8 7
$$
B. $$
D \!=\! 5 5. 8 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 7 9 8 0
$$
C. $$
D \!=\! 5 8. 5 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 7 5 6 7
$$
D. $$
D \!=\! 5 4. 9 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 7 4 1 5
$$
E. $$
D \!=\! 6 1. 7 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 7 9 4 5
$$
F. $$
D \!=\! 6 3. 4 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 8 3 9 2
$$
G. $$
D \!=\! 5 9. 0 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 8 0 1 2
$$
H. $$
D \!=\! 6 2. 3 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 8 2 2 1
$$
I. $$
D \!=\! 6 4. 1 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 8 2 8 3
$$
J. $$
D \!=\! 6 0. 2 \mathrm{k m o l / h}, \; \; x_{D} \!=\! 0. 8 0 4 4
$$
Answer: J
In a multi-stage cross-flow extraction apparatus, water is used as a solvent to extract acetaldehyde from an acetaldehyde-toluene mixture with an acetaldehyde mass fraction of 0.06. It is known that the processing capacity of the feed is 600 kg/h, and it is required that the mass fraction of acetaldehyde in the final raffinate phase does not exceed 0.005. The amount of water used in each stage is 125 kg/h. Under operating conditions, water and toluene are considered completely immiscible, and the equilibrium relationship expressed by the mass ratio of acetaldehyde is $Y=2.2 X$. Use the analytical method to determine the required number of theoretical stages.

Options:
A. n=10.5
B. n=7.0
C. n=5.0
D. n=4.5
E. n=7.5
F. n=3.0
G. n=6.5
H. n=9.0
I. n=8.5
J. n=11.0
Answer: G
Given that after 5 hours, the liquid level drops from 0.011 m to 0.021 m from the top. Under experimental conditions, the density of acetone is 790 kg/m³, and the saturated vapor pressure is 23.98 kPa. Calculate the diffusion coefficient of acetone in air at 293 K and 98.68 kPa using the evaporation tube method.

Options:
A. $$
6. \ 0 8 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
B. $$
2. \ 0 5 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
C. $$
3. \ 0 9 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
D. $$
5. \ 0 3 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
E. $$
7. \ 0 4 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
F. $$
8. \ 0 6 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
G. $$
0. \ 0 5 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
H. $$
1. \ 0 7 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
I. $$
4. \ 0 1 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
J. $$
9. \ 0 2 \times1 0^{-5} \ {\bf m}^{2} / {\bf s}
$$
Answer: H
In a circular tube with a diameter of 0.01m and a length of 0.30m, $\mathrm{C O_{2}}$ gas undergoes steady-state molecular diffusion through $\mathrm{N_{2}}$. The temperature of $\mathrm{N_{2}}$ inside the tube is 298K, and the total pressure is 101.3kPa. The partial pressures of $\mathrm{C O_{2}}$ at both ends of the tube are 60.8kPa and 6.8kPa, respectively. Calculate the diffusion flux of $\mathrm{C O_{2}}$.

Options:
A. $$
1.8 7 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
B. $$
1.9 0 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
C. $$
1.6 9 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
D. $$
2.0 4 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
E. $$
2.3 0 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
F. $$
1.7 5 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
G. $$
1.9 3 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
H. $$
1.9 8 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
I. $$
2.1 1 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
J. $$
2.5 6 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
Answer: G
Under conditions of 101.3 kPa and 20°C, ammonia mixed in air is absorbed using clean water in an isothermal countercurrent flow within a packed column. The mass flow rate of the mixed gas $G$ is $600 \mathrm{kg} / (\mathrm{m}^2 \cdot \mathrm{h})$, and the molar fractions of the gas phase entering and exiting the column are 0.05 and 0.000526, respectively. The mass flow rate of water $W$ is $800 \mathrm{kg} / (\mathrm{m}^2 \cdot \mathrm{h})$, and the height of the packing layer is $3 \mathsf{m}$. It is known that under the operating conditions, the equilibrium relationship is $Y_{\mathrm{e}}=0.9 X$, while $K_{G} a$ is proportional to $G^{0.8}$ and independent of $W$. If the operating pressure is doubled, calculate how the height of the packing layer should change to maintain the same composition of tail gas.

Options:
A. $$
\Delta Z=-1. 9 2 0 m
$$
B. $$
\Delta Z=-1. 4 5 6 m
$$
C. $$
\Delta Z=-1. 5 0 9 m
$$
D. $$
\Delta Z=-1. 9 8 5 m
$$
E. $$
\Delta Z=-2. 2 1 0 m
$$
F. $$
\Delta Z=-2. 0 1 2 m
$$
G. $$
\Delta Z=-2. 8 8 8 m
$$
H. $$
\Delta Z=-1. 6 7 8 m
$$
I. $$
\Delta Z=-1. 8 0 3 m
$$
J. $$
\Delta Z=-2. 3 4 5 m
$$
Answer: I
A single-impact test soil sample has a volume of $1000 \, \text{cm}^{3}$, with a measured density of $\rho = 1.95 \, \text{t/m}^{3}$ and a moisture content of $w = 18\%$. How much water needs to be added to prepare a soil sample with $w = 20\%$?

Options:
A. 0.32kg
B. 0.35kg
C. 0.31kg
D. 0.33kg
E. 0.30kg
F. 0.39kg
G. 0.37kg
H. 0.34kg
I. 0.36kg
J. 0.38kg
Answer: H
A saturated clay specimen undergoes a compression test in a compression apparatus. The original height of the soil sample is 20 mm, with an area of $30 \mathrm{cm}^{2}$. The total weight of the soil sample and the ring cutter is 1.756 N, and the weight of the ring cutter alone is 0.586 N. When the load increases from $p_{1} = 100 \, \mathrm{kPa}$ to $p_{2} = 200 \, \mathrm{kPa}$, the height of the soil sample decreases from 19.31 mm to 18.76 mm over 24 hours. After the test, the soil sample is dried, and the dry weight is measured to be 0.910 N. Determine the initial void ratio $e_{0}$ of the soil sample.

Options:
A. 0.845
B. 0.728
C. 0.752
D. 0.793
E. 0.812
F. 0.717
G. 0.765
H. 0.831
I. 0.703
J. 0.689
Answer: G
Conduct a direct shear test on a particular sand sample. When the vertical pressure $\sigma = 200 \text{ kPa}$, its shear strength $\tau_{f} = 116 \text{ kPa}$ is measured. If a triaxial shear test is conducted on this sand sample with an applied surrounding pressure of $\sigma_{3} = 100 \text{kPa}$, what level of major principal stress $\sigma_{1}$ needs to be applied for the sample to fail?

Options:
A. $$
3 9 5. 9 \mathbf{k P a}
$$
B. $$
6 1 2. 3 \mathbf{k P a}
$$
C. $$
3 6 2. 1 \mathbf{k P a}
$$
D. $$
4 0 0. 2 \mathbf{k P a}
$$
E. $$
3 4 8. 5 \mathbf{k P a}
$$
F. $$
5 5 0. 0 \mathbf{k P a}
$$
G. $$
4 5 3. 7 \mathbf{k P a}
$$
H. $$
5 2 3. 4 \mathbf{k P a}
$$
I. $$
5 6 8. 8 \mathbf{k P a}
$$
J. $$
4 9 0. 6 \mathbf{k P a}
$$
Answer: G
The foundation has a base width of $2 \mathrm{m}$ and is buried to a depth of $\mathrm{1 m}$. The subsoil is medium sand with a unit weight of $18 \mathrm{kN/m}^{3}$. The standard penetration test blow count is $N=21$. Determine the characteristic value of the foundation bearing capacity $f_{\mathrm{a}}$ is__.

Options:
A. $$
3 4 5. 5 \mathrm{k P a}
$$
B. $$
3 7 5. 0 \mathrm{k P a}
$$
C. $$
4 0 0. 2 \mathrm{k P a}
$$
D. $$
3 2 0. 9 \mathrm{k P a}
$$
E. $$
3 6 0. 1 \mathrm{k P a}
$$
F. $$
2 9 0. 4 \mathrm{k P a}
$$
G. $$
3 2 5. 6 \mathrm{k P a}
$$
H. $$
3 3 0. 7 \mathrm{k P a}
$$
I. $$
3 5 5. 9 \mathrm{k P a}
$$
J. $$
3 0 5. 8 \mathrm{k P a}
$$
Answer: G
A building has a rectangular foundation, with a length of $3.6 \mathrm{m}$, width of $2.0 \mathrm{m}$, and a burial depth of $1.5 \mathrm{m}$. The load above ground is $N = 900 \mathrm{kN}$. The foundation soil is uniform silty clay with $\gamma = 18 \mathrm{kN/m^{3}}$, $e_{0} = 1.0$, and $\alpha = 0.4 \mathrm{MPa}^{-1}$. Try using the standard method to calculate the final settlement at the center of the foundation (considering the empirical correction factor for settlement calculation, $p_{0} = f_{\mathrm{ak}}$).

Options:
A. $$
7 7. 9 \mathrm{m m}
$$
B. $$
5 5. 7 \mathrm{m m}
$$
C. $$
6 9. 3 \mathrm{m m}
$$
D. $$
6 7. 5 \mathrm{m m}
$$
E. $$
5 8. 9 \mathrm{m m}
$$
F. $$
7 0. 8 \mathrm{m m}
$$
G. $$
7 3. 4 \mathrm{m m}
$$
H. $$
5 2. 6 \mathrm{m m}
$$
I. $$
8 2. 1 \mathrm{m m}
$$
J. $$
8 5. 2 \mathrm{m m}
$$
Answer: D
In the future, when humanity leaves Earth to live in space, some have designed a space village, which is a sealed, circular structure, with people living along the edge of the ring. To prevent inhabitants from experiencing weightlessness, the structure can rotate around the central axis. Assuming the diameter of this space village is 200m, at what rotational speed must it achieve around the central axis for people to experience an acceleration of $10 \mathrm{m/s}^{2}$, akin to living on Earth?

Options:
A. $$
1. 9 \times1 0^{-2} \, \mathrm{r / s}
$$
B. $$
3. 8 \times1 0^{-2} \, \mathrm{r / s}
$$
C. $$
6. 4 \times1 0^{-2} \, \mathrm{r / s}
$$
D. $$
3. 5 \times1 0^{-2} \, \mathrm{r / s}
$$
E. $$
2. 9 \times1 0^{-2} \, \mathrm{r / s}
$$
F. $$
3. 2 \times1 0^{-3} \, \mathrm{r / s}
$$
G. $$
5. 1 \times1 0^{-2} \, \mathrm{r / s}
$$
H. $$
2. 5 \times1 0^{-2} \, \mathrm{r / s}
$$
I. $$
4. 7 \times1 0^{-2} \, \mathrm{r / s}
$$
J. $$
4. 3 \times1 0^{-2} \, \mathrm{r / s}
$$
Answer: D
Three identical homogeneous spheres are placed on a smooth horizontal surface, each touching the others. A rope is wrapped around the three spheres at the height of their centers and tied together. A fourth identical sphere is then placed on top of the three spheres. Find the tension $T$ in the rope. What is the weight of each sphere $P$ ?

Options:
A. $$T=\frac{\sqrt{5}}{15}P$$
B. $$T=\frac{\sqrt{3}}{14}P$$
C. $$T=\frac{5}{24}P$$
D. $$T=\frac{2\sqrt{3}}{9}P$$
E. $$T=\frac{3}{16}P$$
F. $$T=\frac{\sqrt{6}}{18}P$$
G. $$T=\frac{\sqrt{7}}{20}P$$
H. $$T=\frac{7}{36}P$$
I. $$T=\frac{1}{8}P$$
J. $$T=\frac{\sqrt{2}}{12}P$$
Answer: F
A particle moves within a central force field, where the potential energy in the field is given by
$$
V ( r ) = -k \frac{\mathrm{e}^{-a r}} {r},
$$
where $k$ and $a$ are both positive constants.What is the expression for the force $F ( r )$ ?

Options:
A. $$
F ( r ) \approx-\frac{k} {r^{2}}.
$$
B. $$
F ( r ) \approx \frac{k e^{-r}} {a r}.
$$
C. $$
F ( r ) \approx -\frac{a k} {r}.
$$
D. $$
F ( r ) \approx \frac{k r} {a^{2}}.
$$
E. $$
F ( r ) \approx -\frac{a k r} {e^{r}}.
$$
F. $$
F ( r ) \approx -\frac{a^{2} k} {e^{r}}.
$$
G. $$
F ( r ) \approx -\frac{a k e^{r}} {r^{3}}.
$$
H. $$
F ( r ) \approx \frac{k e^{a r}} {r^{2}}.
$$
I. $$
F ( r ) \approx \frac{k r^{2}} {a}.
$$
J. $$
F ( r ) \approx \frac{k a} {r^{2}}.
$$
Answer: A
A cannonball with a mass of 6 kg is fired from the muzzle at an initial speed of 570 m/s. Assuming the cannonball travels 2 m inside the barrel and the gas pressure is constant.What is the average pressure of the explosive gas and the time the cannonball spends moving within the barrel ?

Options:
A. $$
P=4. 5 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 0 5 \ \mathrm{s}.
$$
B. $$
P=5. 1 2 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 1 0 \ \mathrm{s}.
$$
C. $$
P=5. 3 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 1 4 \ \mathrm{s}.
$$
D. $$
P=5. 2 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 1 3 \ \mathrm{s}.
$$
E. $$
P=4. 8 8 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 0 7 \ \mathrm{s}.
$$
F. $$
P=4. 6 5 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 1 2 \ \mathrm{s}.
$$
G. $$
P=4. 7 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 1 1 \ \mathrm{s}.
$$
H. $$
P=4. 9 8 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 0 9 \ \mathrm{s}.
$$
I. $$
P=5. 0 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 0 8 \ \mathrm{s}.
$$
J. $$
P=4. 9 0 \times1 0^{5} \ \mathrm{N}, \quad t=0. 0 0 6 \ \mathrm{s}.
$$
Answer: E