MikaStars39/nano-eval huggingface dataset:
The electrical conductivity of ferrites is().

Options:
A. Less than that of paramagnetic materials
B. Equivalent to that of metals
C. Greater than that of electrolytic solutions
D. Less than that of ferromagnetic materials
E. Equal to that of diamagnetic substances
F. Similar to that of ferroelectric compounds
G. More than that of insulators
H. Equal to that of superconductors
Answer: D
Which of the following metals has highest specific gravity?

Options:
A. Iron
B. Lead
C. Nickel
D. Bronze
E. Silver
F. Aluminum
G. Copper
H. Zinc
I. Gold
J. Mercury
Answer: E
A patient from a region where corn is the staple food presents with symmetrical erythema on the extensor sides of the limbs, with mild erosion, and a tongue that is red and swollen like a strawberry. The patient reports memory loss, insomnia, and diarrhea. The most likely nutritional deficiency disease is ().

Options:
A. Beriberi
B. Zenker's Disease
C. Morgagni Herniation
D. Essential Fatty Acid Deficiency
E. Scurvy
F. Celiac Sprue
G. Turcot Syndrome
H. Epileptic Dermatitis
I. Wilson's Disorder
J. Riboflavin Deficiency Disease
Answer: H
The infinite cylinder with a radius of $R$ is uniformly charged, with a charge density of $\rho$. Setting the reference point for the electric potential on the axis, what is the magnitude of the potential outside the cylinder $(r \ge R)$?

Options:
A. $$
\frac{\rho R}{2 \, \varepsilon_{0}} \left( \mathrm{l n} \, \frac{R} {r} \right)
$$
B. $$
\frac{\rho R^{2}} {8 \, \varepsilon_{0}} \left( 2 \mathrm{l n} \, \frac{r} {R} \,-\, 1 \right)
$$
C. $$
\frac{\rho R^{2}} {2 \, \varepsilon_{0}} \left( \mathrm{l n} \, \frac{R} {r} \right)
$$
D. $$
\frac{\rho R^{2}} {4 \, \varepsilon_{0}} \left( 2 \mathrm{l n} \, \frac{R} {r} \,-\, 1 \right)
$$
E. $$
\frac{\rho R^{2}} {12 \, \varepsilon_{0}} \left( 2 \mathrm{l n} \, \frac{R} {r} \,-\, 1 \right)
$$
F. $$
\frac{\rho R^{2}} {4 \, \varepsilon_{0}} \left( 2 \mathrm{l n} \, \frac{r} {R} \,+\, 1 \right)
$$
G. $$
\frac{\rho R^{2}} {4 \, \varepsilon_{0}} \left( \mathrm{l n} \, \frac{R}{r} \,+\, 2 \right)
$$
H. $$
\frac{\rho R^{2}} {6 \, \varepsilon_{0}} \left( \mathrm{l n} \, \frac{r} {R} \,-\, 1 \right)
$$
I. $$
\frac{\rho R^{2}} {4 \, \varepsilon_{0}} \left( \mathrm{l n} \, \frac{r}{R} \,-\, 1 \right)
$$
J. $$
\frac{\rho R^{2}} {4 \, \varepsilon_{0}} \left( 3 \mathrm{l n} \, \frac{R} {r} \,-\, 1 \right)
$$
Answer: D
What is the magnitude of the interaction force between two dipoles separated by a distance $r$, with dipole moments $\boldsymbol{p}_{1}$ and $\boldsymbol{p}_{2}$ aligned parallel to their connecting line?

Options:
A. $$F={\frac{3 \, p_{1} \, p_{2}} {4 \pi\varepsilon_{0} \, r^{4}}}$$
B. $$F={\frac{2 \, p_{1} \, p_{2}} { \pi\varepsilon_{0} \, r^{5}}}$$
C. $$F={\frac{5 \, p_{1} \, p_{2}} {2 \pi\varepsilon_{0} \, r^{4}}}$$
D. $$F={\frac{\, p_{1} \, p_{2}} {3 \pi\varepsilon_{0} \, r^{4}}}$$
E. $$
F={\frac{3 \, p_{1} \, p_{2}} {2 \pi\varepsilon_{0} \, r^{4}}}
$$
F. $$F={\frac{3 \, p_{1} \, p_{2}} { \pi\varepsilon_{0} \, r^{3}}}$$
G. $$F={\frac{3 \, p_{1} \, p_{2}} {2 \pi\varepsilon_{0} \, r^{6}}}$$
H. $$F={\frac{3 \, p_{1} \, p_{2}} {2 \pi\varepsilon_{0} \, r^{5}}}$$
I. $$F={\frac{4 \, p_{1} \, p_{2}} { \pi\varepsilon_{0} \, r^{4}}}$$
J. $$F={\frac{\, p_{1} \, p_{2}} {\pi\varepsilon_{0} \, r^{4}}}$$
Answer: E
The coil of a galvanometer has 50 turns and encloses an area of $6 \, \mathrm{cm}^{2}$, with the magnetic field $B$ in the swinging area equal to 0.01 T. The elastic constant of the torsion wire is $K=10^{6} \, \mathrm{N \cdot m / (degree)}$. If a current of 1 mA passes through, what is the deflection angle of this coil?

Options:
A. $$
\alpha=4 0^{\circ} \operatorname{or} 1 6 0^{\circ}
$$
B. $$
\alpha=3 5^{\circ} \operatorname{or} 1 4 5^{\circ}
$$
C. $$
\alpha=2 5^{\circ} \operatorname{or} 1 5 5^{\circ}
$$
D. $$
\alpha=3 2^{\circ} \operatorname{or} 1 5 2^{\circ}
$$
E. $$
\alpha=2 0^{\circ} \operatorname{or} 1 4 0^{\circ}
$$
F. $$
\alpha=5 0^{\circ} \operatorname{or} 1 7 0^{\circ}
$$
G. $$
\alpha=4 5^{\circ} \operatorname{or} 1 6 5^{\circ}
$$
H. $$
\alpha=1 5^{\circ} \operatorname{or} 1 3 5^{\circ}
$$
I. $$
\alpha=3 0^{\circ} \operatorname{or} 1 5 0^{\circ}
$$
J. $$
\alpha=1 0^{\circ} \operatorname{or} 1 2 0^{\circ}
$$
Answer: I
Supply a 220 V, 50 Hz AC power source to an inductive load with a power factor of 0.6, where the load absorbs power of 550 W. What is the power output of the source after adding a capacitor in series?

Options:
A. $$
1 \ 6 3 0 \ \mathbf{w}
$$
B. $$
1 \ 5 2 8 \ \mathbf{w}
$$
C. $$
1 \ 6 0 5 \ \mathbf{w}
$$
D. $$
1 \ 4 7 5 \ \mathbf{w}
$$
E. $$
1 \ 5 3 5 \ \mathbf{w}
$$
F. $$
1 \ 3 8 5 \ \mathbf{w}
$$
G. $$
1 \ 4 8 0 \ \mathbf{w}
$$
H. $$
1 \ 4 2 0 \ \mathbf{w}
$$
I. $$
1 \ 3 9 0 \ \mathbf{w}
$$
J. $$
1 \ 4 5 5 \ \mathbf{w}
$$
Answer: B
What adapter kit is used when launching the MK 25 marker from sonobuoy launchers?

Options:
A. The MK 28 MOD 4 adapter kit
B. The MK 32 MOD 1 adapter kit
C. The MK 29 MOD 3 adapter kit
D. The MK 35 MOD 1 adapter kit
E. The MK 33 MOD 2 adapter kit
F. The MK 34 MOD 0 adapter kit
G. The MK 36 MOD 3 adapter kit
H. The MK 30 MOD 2 adapter kit
I. The MK 31 MOD 0 adapter kit
J. The MK 27 MOD 5 adapter kit
Answer: F
When the MK 25 marine location marker is going to be sonobuny launched, what component should be installed around the base?

Options:
A. A MK 37 MOD 0 coupling sleeve
B. A MK 29 MOD 3 securing band
C. A MK 31 MOD 2 sealing flange
D. A MK 30 MOD 0 attachment plate
E. A MK 35 MOD 0 positioning cap
F. A MK 34 MOD 0 adapter kit
G. A MK 28 MOD 1 base gasket
H. A MK 33 MOD 1 mounting bracket
I. A MK 36 MOD 0 adjustment ring
J. A MK 32 MOD 1 fitment collar
Answer: F
Patient, female, 65 years old, was found to have a mass in the right breast during a medical examination. The patient has no family history of tumors. Biopsy pathology diagnosed as invasive ductal carcinoma of the breast, but the patient refused surgery. Six months later, the patient developed metastasis to the right axillary and neck lymph nodes, as well as the lungs and liver. The patient passed away one year after diagnosis. The most likely molecular genetic alteration in this patient is ____.

Options:
A. KRAS codon 12 alteration
B. EGFR mutation present
C. BRAF V600E mutation found
D. HER2 gene amplification
E. TP53 gene rearrangement
F. ALK gene translocation
G. CDH1 promoter methylation
H. PIK3CA exon 9 mutation
I. BRCA1 gene deletion
J. PTEN loss of function
Answer: D
The width of the one-way motor vehicle lane on a certain road section is 8 meters, with intersections spaced 300 meters apart. Both ends use signal control with a green signal ratio of 0.48, and there is a median strip between the motor vehicle lane and the non-motorized vehicle lane. Calculate the design traffic capacity for this section of the road as ( ).

Options:
A. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 0 \times1 3 0. 5 9 5 \times1. 7 9 \times0. 5 8 4 \;=\; 2 3 9 8 \, ( \mathrm{p e u / h} )
$$
B. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 0 \times1 0 9. 9 4 1 \times1. 9 2 \times0. 4 9 9 \;=\; 2 1 3 8 \, ( \mathrm{p e u / h} )
$$
C. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 0 \times1 1 1. 3 4 6 \times1. 8 7 \times0. 5 3 8 \;=\; 2 0 1 6 \, ( \mathrm{p e u / h} )
$$
D. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 0 \times1 2 0. 3 4 7 \times2. 0 0 \times0. 4 5 0 \;=\; 2 4 5 0 \, ( \mathrm{p e u / h} )
$$
E. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times0. 9 \times9 8. 2 6 1 \times1. 8 3 \times0. 5 9 7 \;=\; 1 8 5 4 \, ( \mathrm{p e u / h} )
$$
F. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 0 \times1 2 0. 1 9 8 \times2. 1 2 \times0. 5 0 3 \;=\; 2 6 3 4 \, ( \mathrm{p e u / h} )
$$
G. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 1 \times1 4 5. 6 8 4 \times1. 7 0 \times0. 5 6 5 \;=\; 2 4 8 4 \, ( \mathrm{p e u / h} )
$$
H. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 1 \times1 1 8. 9 7 3 \times1. 6 5 \times0. 5 2 7 \;=\; 2 2 1 2 \, ( \mathrm{p e u / h} )
$$
I. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times0. 9 \times9 0. 8 8 6 \times1. 9 0 \times0. 6 1 2 \;=\; 1 5 9 0 \, ( \mathrm{p e u / h} )
$$
J. $$
C_{0} \;=\; C \cdot\gamma\cdot\eta\cdot\beta\cdot n^{\prime} \;=\; 1 8 0 0 \times1. 1 \times1 5 0. 3 1 1 \times1. 7 5 \times0. 5 4 2 \;=\; 2 2 5 5 \, ( \mathrm{p e u / h} )
$$
Answer: C
At the end of the 19th century, Dutch scientist van't Hoff noted, based on numerous experiments, that for every 10 K increase in temperature, the reaction rate increases by a factor of $2-4$. Assuming these experiments were conducted around 27°C, what is the range of activation energy $E_{s}$ for the chemical reactions involved?

Options:
A. $$
1 0 2. 3 \sim1 5 0. 4 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
B. $$
6 5. 0 \sim1 1 3. 9 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
C. $$
3 0. 1 \sim5 5. 8 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
D. $$
9 0. 0 \sim1 4 5. 3 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
E. $$
9 8. 5 \sim2 0 0. 7 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
F. $$
8 0. 2 \sim1 2 5. 4 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
G. $$
3 9. 4 \sim8 2. 6 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
H. $$
5 2. 1 \sim6 6. 8 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
I. $$
5 3. 6 \sim1 0 7. 2 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
J. $$
4 7. 9 \sim8 9. 1 \mathrm{~ k J \cdot m o l^{-1} ~}
$$
Answer: I
Given that the saturated vapor pressures of W(s) at 2600 K and 3000 K are $7.213 \times 10^{-5} \, \text{Pa}$ and $9.173 \times 10^{-3} \, \text{Pa}$, respectively, what is the molar enthalpy of sublimation $\Delta H_{m}^{\ominus}$ of W(s)? What is the saturated vapor pressure of W(s) at 3200 K?

Options:
A. $$
7 9 5. 4 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 6. 2 4 {\times} 1 0^{-2} \mathrm{~ P a}
$$
B. $$
7 8 5. 6 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 6. 5 7 {\times} 1 0^{-2} \mathrm{~ P a}
$$
C. $$
7 7 5. 6 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 7. 1 2 {\times} 1 0^{-2} \mathrm{~ P a}
$$
D. $$
7 6 5. 8 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 7. 5 8 {\times} 1 0^{-2} \mathrm{~ P a}
$$
E. $$
8 0 5. 7 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 5. 7 6 {\times} 1 0^{-2} \mathrm{~ P a}
$$
F. $$
8 1 0. 4 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 5. 5 9 {\times} 1 0^{-2} \mathrm{~ P a}
$$
G. $$
8 0 1. 3 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 5. 9 8 {\times} 1 0^{-2} \mathrm{~ P a}
$$
H. $$
7 9 0. 1 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 6. 6 9 {\times} 1 0^{-2} \mathrm{~ P a}
$$
I. $$
7 8 0. 2 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 6. 8 9 {\times} 1 0^{-2} \mathrm{~ P a}
$$
J. $$
7 8 9. 9 \mathrm{~ k J ~ \cdot~ m o l}^{-1},\ 6. 3 5 {\times} 1 0^{-2} \mathrm{~ P a}
$$
Answer: B
Dissociation equilibrium constants for the triprotic acid arsenic acid $\mathrm{H_{3}AsO}_{4}$ are $K_{1}=5.5 \times 10^{-3}$, $K_{2}=1.7 \times 10^{-7}$, $K_{3}=5.1 \times 10^{-12}$. What initial concentration of $\mathrm{H}_{3}\mathrm{AsO}_{4}$ is required to achieve $c \, (\mathrm{AsO}_{4}^{3-}) = 4.0 \times 10^{-17} \, \mathrm{mol \cdot dm}^{-3}$?

Options:
A. $$
4. 4 9 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
B. $$
0. 0 7 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
C. $$
0. 1 1 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
D. $$
1. 0 2 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
E. $$
3. 5 7 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
F. $$
0. 2 9 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
G. $$
2. 3 4 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
H. $$
0. 4 5 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
I. $$
5. 1 3 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
J. $$
0. 0 8 \ \mathrm{m o l} \cdot\mathrm{d m}^{-3}
$$
Answer: C
A solution contains $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$, both at a concentration of $0.10 \ \mathrm{mol} \cdot \mathrm{dm}^{-3}$. If the requirement is that only $\mathrm{Fe(OH)}_3$ precipitates and no $\mathrm{Fe(OH)}_2$ precipitates, determine the pH range that the solution should be controlled within. Known values are the solubility product $K_{\mathrm{sp}}^{\ominus}=2.8 \times 10^{-39}$ for $\mathrm{Fe(OH)}_3$ and $K_{\mathrm{sp}}^{\ominus}=4.9 \times 10^{-17}$ for $\mathrm{Fe(OH)}_2$.

Options:
A. $$
1. 5 \sim4. 0
$$
B. $$
3. 0 \sim8. 5
$$
C. $$
4. 5 \sim6. 6
$$
D. $$
3. 5 \sim5. 9
$$
E. $$
2. 8 \sim6. 3
$$
F. $$
5. 0 \sim7. 8
$$
G. $$
6. 0 \sim9. 2
$$
H. $$
4. 1 \sim7. 3
$$
I. $$
1. 8 \sim4. 2
$$
J. $$
2. 2 \sim5. 0
$$
Answer: E
The most effective method to differentiate an isodense subdural hematoma from an intracranial tumor is ().

Options:
A. Perform an ultrasound check
B. Apply genetic sequencing
C. Measure intracranial pressure
D. Conduct a tissue biopsy
E. Obtain a cerebrospinal fluid
F. Utilize PET imaging analysis
G. Use non-enhanced CT scan
H. Perform an enhanced scan
I. Evaluate blood serum levels
J. Inspect with MRI contrast dye
Answer: H
A male, 45 years old and had tuberculosis 20 years ago. For the past 3 months, he has experienced coughing, with occasional blood-streaked sputum. X-ray examination shows a 3 cm x 2.5 cm shadow in the right upper lung, with blurred and rough edges and calcification points inside. The rest of the lung fields are clear. Three sputum tests for cancer cells are negative. The most likely diagnosis is?

Options:
A. Pneumonia
B. Asthma
C. Chronic Bronchitis
D. Pleural Effusion
E. Lung Cancer
F. Pulmonary Embolism
G. Pulmonary Fibrosis
H. Bronchitis
I. Lung Abscess
J. Sarcoidosis
Answer: E
Which of the following kidney lesions does not have calcification?

Options:
A. Autosomal dominant polycystic kidney disease
B. Primary hyperoxaluria
C. Renal tubular acidosis
D. Nephrocalcinosis
E. Urolithiasis
F. Cystic renal dysplasia
G. Chronic pyelonephritis
H. Acute glomerulonephritis
I. Medullary sponge kidney
J. Idiopathic hypercalciuria
Answer: H
Someone forgot the last digit of a phone number, so he dials randomly. Calculate the probability that he connects to the desired number in no more than three attempts, given that the last digit is an odd number. What is this probability?

Options:
A. $$
P =\frac{4} {5}
$$
B. $$
P =\frac{1} {3}
$$
C. $$
P =\frac{3} {5}
$$
D. $$
P =\frac{2} {3}
$$
E. $$
P =\frac{5} {8}
$$
F. $$
P =\frac{1} {4}
$$
G. $$
P =\frac{1} {2}
$$
H. $$
P =\frac{3} {4}
$$
I. $$
P =\frac{1} {5}
$$
J. $$
P =\frac{2} {5}
$$
Answer: C
Assume the diameter of an oxygen molecule \( $d = 3 \times 10^{-10} \mathrm{~m}$ \). Calculate the mean free path of oxygen molecules under standard conditions, and determine to what pressure (Pa) the temperature must drop to 0 °C for the mean free path of oxygen molecules to increase to 1 cm?

Options:
A. $$
0 . 9 9 5 \mathrm{~ P a}
$$
B. $$
1 . 3 4 0 \mathrm{~ P a}
$$
C. $$
0. 9 4 2 \mathrm{~ P a}
$$
D. $$
1 . 2 3 0 \mathrm{~ P a}
$$
E. $$
1 . 1 5 0 \mathrm{~ P a}
$$
F. $$
0 . 8 6 9 \mathrm{~ P a}
$$
G. $$
1 . 0 5 5 \mathrm{~ P a}
$$
H. $$
1 . 0 8 0 \mathrm{~ P a}
$$
I. $$
0 . 8 5 7 \mathrm{~ P a}
$$
J. $$
0 . 7 9 2 \mathrm{~ P a}
$$
Answer: C
Under $101.325 \, \text{kPa}$ and $423 \, \text{K}$, compress $1 \, \text{mol} \, \text{NH}_3 (\text{g})$ isothermally to a volume of $10 \, \text{dm}^3$. Calculate the minimum work required.
(1) Assume it is an ideal gas.
(2) Assume it follows the van der Waals equation. Given the van der Waals constants: $a = 0.417 \, \text{Pa} \cdot \text{m}^6 \, \text{mol}^{-2}$, $b = 3.71 \times 10^{-5} \, \text{m}^3 \, \text{mol}^{-1}$.

Options:
A. $$
4 \ 2 1 3 \ \mathrm{J}
$$
B. $$
3 \ 8 9 0 \ \mathrm{J}
$$
C. $$
4 \ 7 3 1 \ \mathrm{J}
$$
D. $$
4 \ 8 5 2 \ \mathrm{J}
$$
E. $$
4 \ 3 4 5 \ \mathrm{J}
$$
F. $$
3 \ 6 2 5 \ \mathrm{J}
$$
G. $$
5 \ 0 2 9 \ \mathrm{J}
$$
H. $$
5 \ 4 0 8 \ \mathrm{J}
$$
I. $$
5 \ 1 0 7 \ \mathrm{J}
$$
J. $$
3 \ 9 5 6 \ \mathrm{J}
$$
Answer: E
Liquid A and B form an ideal solution. There is a vapor phase with a mole fraction of A at $0.4$, placed in a piston cylinder, and the vapor is slowly compressed at a constant temperature. It is known that $p_{\mathrm{A}}^{*}$ and $p_{\mathrm{B}}^{*}$ are $0.4 \times p^{\Theta}$ and $1.2 \times p^{\Theta}$ respectively ($p^{\Theta}$ is the standard atmospheric pressure). Calculate the total vapor pressure when the liquid begins to condense.

Options:
A. $$
0. 5 0 0 \ 8
$$
B. $$
0. 7 4 2 \ 8
$$
C. $$
0. 6 0 2 \ 4
$$
D. $$
0. 6 6 3 \ 9
$$
E. $$
0. 7 1 5 \ 6
$$
F. $$
0. 7 8 9 \ 1
$$
G. $$
0. 9 3 4 \ 5
$$
H. $$
0. 5 9 9 \ 3
$$
I. $$
0. 6 6 6 \ 7
$$
J. $$
0. 8 0 1 \ 2
$$
Answer: I
At 262.5 K, dissolving 3.30 mol of $\mathrm{KCl (s)}$ in 1.0 kg of water forms a saturated solution, with the saturated solution and ice coexisting in equilibrium at this temperature. Taking pure water as the standard state, calculate the activity and activity coefficient of water in the saturated solution. (It is known that the molar freezing point depression of water is $\Delta_{\mathrm{f r e}} H_{\mathrm{m}}=601 \mathrm{~J \cdot~mol^{-1}}$.)

Options:
A. 0.9300,1.060
B. 0.9250,1.065
C. 0.9350,1.053
D. 0.9480,1.043
E. 0.9155,1.073
F. 0.9205,1.068
G. 0.9321,1.058
H. 0.9600,1.038
I. 0.9439,1.048
J. 0.9550,1.033
Answer: I
At 360 K, water (A) and isobutanol (B) are partially miscible, with the mole fraction of isobutanol in the aqueous phase $x_{\mathrm{B}} = 0.021$. It is known that isobutanol in the aqueous phase follows Henry's Law, with the Henry's constant $k_{x,B} = 1.58 \times 10^6 \text{ Pa}$. Calculate the partial pressures of water and isobutanol in the vapor phase in equilibrium with this system. (Given that the molar enthalpy of vaporization of water is $40.66 \text{ kJ} \cdot \text{mol}^{-1}$ and does not change with temperature. Assume the gas is ideal.)

Options:
A. $$
5 3. 6 7 \mathrm{~ k P a}
$$
B. $$
4 9. 3 8 \mathrm{~ k P a}
$$
C. $$
4 8. 0 2 \mathrm{~ k P a}
$$
D. $$
6 1. 8 0 \mathrm{~ k P a}
$$
E. $$
6 0. 7 9 \mathrm{~ k P a}
$$
F. $$
5 2. 3 6 \mathrm{~ k P a}
$$
G. $$
5 1. 4 4 \mathrm{~ k P a}
$$
H. $$
5 5. 2 1 \mathrm{~ k P a}
$$
I. $$
5 4. 2 0 \mathrm{~ k P a}
$$
J. $$
4 7. 5 9 \mathrm{~ k P a}
$$
Answer: F
At 373 K, the reaction $2 \, \mathrm{NaHCO}_{3 (\mathrm{s})} = \mathrm{Na}_{2}\mathrm{CO}_{3 (\mathrm{s})} + \mathrm{CO}_{2 (\mathrm{g})} + \mathrm{H}_{2}\mathrm{O (\mathrm{g})}$ has an equilibrium constant $K_{p}^{\Theta} = 0.231$. In a vacuum container with a volume of $10^{-2} \, \mathrm{m}^{3}$, $0.1 \, \mathrm{mol}$ of $\mathrm{Na}_{2}\mathrm{CO}_{3 (\mathrm{s})}$ is introduced, along with $0.2 \, \mathrm{mol}$ of $\mathrm{H}_{2}\mathrm{O (\mathrm{g})}$. The question is, what is the minimum amount of $\mathrm{CO}_{2 (\mathrm{g})}$ that needs to be introduced to ensure that all of the $\mathrm{Na}_{2}\mathrm{CO}_{3 (\mathrm{s})}$ is converted into $\mathrm{NaHCO}_{3 (\mathrm{s})}$?

Options:
A. $$
0. 4 0 \mathrm{~ m o l ~}
$$
B. $$
0. 3 4 \mathrm{~ m o l ~}
$$
C. $$
0. 1 5 \mathrm{~ m o l ~}
$$
D. $$
0. 2 1 \mathrm{~ m o l ~}
$$
E. $$
0. 5 2 \mathrm{~ m o l ~}
$$
F. $$
0. 1 8 \mathrm{~ m o l ~}
$$
G. $$
0. 4 7 \mathrm{~ m o l ~}
$$
H. $$
0. 2 6 \mathrm{~ m o l ~}
$$
I. $$
0. 5 5 \mathrm{~ m o l ~}
$$
J. $$
0. 3 0 \mathrm{~ m o l ~}
$$
Answer: B
A potential method for large-scale hydrogen production is to pass a mixed gas of $\mathrm{CH_{4} (g)} + \mathrm{H_{2}O (g)}$ through a heated catalyst bed. If the molar ratio of the feed gas is $n_{\mathrm{H_{2}O}} : n_{\mathrm{CH_{4}}} = 5 : 1$, with a temperature of 873 K and a pressure of $100 \ \mathrm{kPa}$, and assuming only the following two reactions occur:
$$
\begin{array} {l l}
\mathrm{CH_{4} (g) + H_{2}O (g) \Longrightarrow CO (g) + 3 H_{2} (g)} & \Delta_{\mathrm{r}} G_{\mathrm{m}}^{\mathrm{\Theta}} (1) = 4.435 \ \mathrm{kJ \cdot mol}^{-1} \\
\mathrm{CO (g) + H_{2}O (g) \Longrightarrow CO_{2} (g) + H_{2} (g)} & \Delta_{\mathrm{r}} G_{\mathrm{m}}^{\mathrm{\Theta}} (2) = -6.633 \ \mathrm{kJ \cdot mol}^{-1} \\
\end{array}
$$
Calculate the composition of the equilibrium dry gas, expressed in mole fractions, after achieving equilibrium and removing $\mathrm{H_{2}O (g)}$.

Options:
A. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,+\, ( \, x \,+y \, ) \,-\, ( \, 3 \, x \,- y \, ) \,-\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
B. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,+\, ( \, x \,-y \, ) \,+\, ( \, 3 \, x \,+\, y \, ) \,+\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
C. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,+\, ( \, x \,+y \, ) \,-\, ( \, x \,+ 2 y \, ) \,-\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
D. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,+x \, )
\,+\, ( \, x \,+y \, ) \,+\, ( \, 3 \,+ x \,- y \, ) \,+\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
E. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,+x \, )
\,+\, ( \, x \,-y \, ) \,-\, ( \, 3 \, x \,+\, y \, ) \,-\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
F. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,+\, ( \, x \,+y \, ) \,+\, ( \, 2 \, x \,+\, y \, ) \,-\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
G. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,+x \, )
\,-\, ( \, x \,-y \, ) \,+\, ( \, 3 \, x \,+ 2 y \, ) \,+\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
H. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,+x \, )
\,+\, ( \, x \,+y \, ) \,+\, ( \, 3 \,- x \,+\, y \, ) \,-\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
I. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,-\, ( \, x \,+y \, ) \,+\, ( \, x \,+\, 3 y \, ) \,+\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
J. $$
n_{\mathbb{total}}^{\prime}=\left[ \begin{array} {l} {{{( \, 1 \,-x \, )
\,-\, ( \, x \,-y \, ) \,+\, ( \, 3 \,- x \,+ y \, ) \,+\, y \,}}} \\ \end{array} \right] \mathrm{m o l}
$$
Answer: B
A solution of $\mathrm{Na_{2}SO_{4}}$ with a known concentration of 0.001 mol·dm$^{-3}$ has a conductivity of $0.026 \, \mathrm{S \cdot m^{-1}}$. When this solution becomes saturated with $\mathrm{CaSO_{4}}$, the conductivity increases to $0.070 \, \mathrm{S \cdot m^{-1}}$. It is also known that the molar conductivities of $\mathrm{Na^{+}}$ and $\frac{1}{2} \mathrm{Ca^{2+}}$ are $A_{\mathrm{m, Na^{+}}} = 5.0 \times 10^{-3} \, \mathrm{S \cdot m^{2} \cdot mol^{-1}}$ and $A_{\mathrm{m, \frac{1}{2}Ca^{2+}}} = 6.0 \times 10^{-3} \, \mathrm{S \cdot m^{2} \cdot mol^{-1}}$, respectively. Calculate the solubility product of $\mathrm{CaSO_{4}}$. (assuming all activity coefficients are 1).

Options:
A. $$
5. 7 7 \times1 0^{-5}
$$
B. $$
2. 1 1 \times1 0^{-7}
$$
C. $$
6. 0 3 \times1 0^{-8}
$$
D. $$
1. 5 5 \times1 0^{-4}
$$
E. $$
3. 9 9 \times1 0^{-6}
$$
F. $$
5. 0 0 \times1 0^{-5}
$$
G. $$
4. 1 0 \times1 0^{-5}
$$
H. $$
4. 0 4 \times1 0^{-6}
$$
I. $$
2. 5 5 \times1 0^{-6}
$$
J. $$
3. 0 0 \times1 0^{-6}
$$
Answer: H
In a container with a volume of $28.5 L$, there is $0.3 kg$ of $\mathrm{NH_{3}} \ (\mathrm{gas})$. The measured temperature is $348.2 K$. What is the pressure?

Options:
A. $$
1 \ 7 0 2. \ 7 \ \mathrm{k P a}
$$
B. $$
1 \ 5 7 5. \ 4 \ \mathrm{k P a}
$$
C. $$
1 \ 6 4 3. \ 9 \ \mathrm{k P a}
$$
D. $$
1 \ 6 1 9. \ 0 \ \mathrm{k P a}
$$
E. $$
1 \ 5 8 0. \ 3 \ \mathrm{k P a}
$$
F. $$
1 \ 6 6 0. \ 5 \ \mathrm{k P a}
$$
G. $$
1 \ 5 9 9. \ 8 \ \mathrm{k P a}
$$
H. $$
1 \ 6 7 2. \ 1 \ \mathrm{k P a}
$$
I. $$
1 \ 7 4 5. \ 2 \ \mathrm{k P a}
$$
J. $$
1 \ 7 1 1. \ 6 \ \mathrm{k P a}
$$
Answer: H
For an ideal gas reaction at a temperature of 1000 K, $2 \mathrm{SO}_{3} \left( \mathrm{\bf~g} \right) = 2 \mathrm{SO}_{2} \left( \mathrm{\bf~g} \right) + \mathrm{O}_{2} \left( \mathrm{\bf~g} \right)$, with an equilibrium constant $K_{p} = 29.0 \ \mathrm{kPa}$, the $\Delta_{\varepsilon} G^{\Theta}$ for this reaction is _____.

Options:
A. $$
5 1. 6 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
B. $$
1 0. 3 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
C. $$
4 2. 8 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
D. $$
4 9. 5 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
E. $$
5 8. 2 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
F. $$
3 5. 1 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
G. $$
2 5. 7 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
H. $$
2 2. 4 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
I. $$
4 6. 9 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
J. $$
6 1. 0 \mathrm{~ k J ~ \cdot~ m o l^{-1} ~}
$$
Answer: B
An ammonia compression refrigeration device employing a throttle valve has a theoretical compressor power of $50 kW$, with an ammonia evaporation temperature of $-15°C$. At the compressor inlet, the ammonia is in a wet vapor state, and after reversible adiabatic compression, it exits the compressor as dry saturated vapor with a saturation temperature of $25°C$. What is the refrigeration capacity of this device in kW?

Options:
A. $$
- 4 6 0. 8 9 k J / k g
$$
B. $$
- 4 1 5. 3 3 k J / k g
$$
C. $$
- 4 0 0. 0 0 k J / k g
$$
D. $$
- 4 2 5. 4 7 k J / k g
$$
E. $$
- 3 5 0. 2 5 k J / k g
$$
F. $$
- 4 5 0. 6 3 k J / k g
$$
G. $$
- 4 8 5. 7 0 k J / k g
$$
H. $$
- 4 9 9. 9 9 k J / k g
$$
I. $$
- 4 3 5. 5 2 k J / k g
$$
J. $$
- 3 8 0. 1 1 k J / k g
$$
Answer: D
$\mathrm{SO}_{2}$ is a bent molecule with a molecular weight of 64.06. The product of its three principal moments of inertia is $ABC = 9.819 \times 10^{-123} \ \mathrm{kg}^{3} \cdot \mathrm{m}^{6}$. The three vibrational frequencies are $\nu_{1}=1575 \times 10^{10}$ Hz, $\nu_{2}=3456 \times 10^{10}$ Hz, and $\nu_{3}=4083 \times 10^{10}$ Hz. What is the entropy of $1 \ \mathrm{mol \ SO}_{2}$ gas at 1 atmosphere pressure and temperature of $25^{\circ} \mathrm{C}$ ?

Options:
A. $$140.5$$
B. $$102.4$$
C. $$198.7$$
D. $$160.6$$
E. $$189.9$$
F. $$210.2$$
G. $$125.8$$
H. $$156.1$$
I. $$230.0$$
J. $$175.3$$
Answer: D
You are given a 50W motor and assume the outside air temperature is 27°C. You are given a 50W motor and asked how much time is needed at 0°C to freeze 2kg of water?

Options:
A. $$
1. 3 \times1 0^{3} \mathrm{s}
$$
B. $$
2. 1 \times 1 0^{3} \mathrm{s}
$$
C. $$
2. 9 \times 1 0^{3} \mathrm{s}
$$
D. $$
1. 7 \times 1 0^{3} \mathrm{s}
$$
E. $$
2. 4 \times 1 0^{3} \mathrm{s}
$$
F. $$
3. 6 \times 1 0^{3} \mathrm{s}
$$
G. $$
1. 1 \times 1 0^{3} \mathrm{s}
$$
H. $$
1. 5 \times 1 0^{3} \mathrm{s}
$$
I. $$
1. 9 \times 1 0^{3} \mathrm{s}
$$
J. $$
2. 5 \times 1 0^{3} \mathrm{s}
$$
Answer: A
A clean glass tube with a diameter of 2mm is filled with water at 10°C to a height of 35mm. What is the actual hydrostatic height of the water ?

Options:
A. $$
2 1. 3 4 {\mathrm{m m}}
$$
B. $$
1 9. 8 6 {\mathrm{m m}}
$$
C. $$
2 3. 0 4 {\mathrm{m m}}
$$
D. $$
1 8. 9 2 {\mathrm{m m}}
$$
E. $$
2 2. 1 8 {\mathrm{m m}}
$$
F. $$
2 0. 7 5 {\mathrm{m m}}
$$
G. $$
1 8. 7 9 {\mathrm{m m}}
$$
H. $$
1 9. 5 3 {\mathrm{m m}}
$$
I. $$
2 0. 6 7 {\mathrm{m m}}
$$
J. $$
1 9. 1 1 {\mathrm{m m}}
$$
Answer: B
A reaction turbine has a rotor with 18 blades, each with a thickness of 0.2 inches. The radius $r_{1}=10$ inches, angle $B, =65^\circ$, and radius $r_{3}=$ 6 inches, with an angle $\beta_{2}=122^\circ$. The depth of the fluid flow passage between the two sides of the turbine $B$ is 4 inches. When this rotor rotates at 180 revolutions per minute, the water flow rate is 7.5 cubic feet per second. Assuming that there is no hydraulic impact when the water enters and exits the blades, what is the torque delivered by the water and the horsepower applied to the shaft at given the inlet and outlet conditions?

Options:
A. $$
1 9 3. 8\ \mathrm{f t\cdot l b f},\ 4. 8 9\ \mathrm{h p}
$$
B. $$
1 5 0. 9\ \mathrm{f t\cdot l b f},\ 4. 3 7\ \mathrm{h p}
$$
C. $$
1 3 9. 2\ \mathrm{f t\cdot l b f},\ 5. 1 9\ \mathrm{h p}
$$
D. $$
2 0 2. 6\ \mathrm{f t\cdot l b f},\ 5. 9 1\ \mathrm{h p}
$$
E. $$
1 7 4. 3\ \mathrm{f t\cdot l b f},\ 7. 1 4\ \mathrm{h p}
$$
F. $$
1 2 9. 5\ \mathrm{f t\cdot l b f},\ 5. 6 2\ \mathrm{h p}
$$
G. $$
2 1 0. 2\ \mathrm{f t\cdot l b f},\ 4. 2 5\ \mathrm{h p}
$$
H. $$
1 4 5. 7\ \mathrm{f t\cdot l b f},\ 6. 3 0\ \mathrm{h p}
$$
I. $$
1 8 3. 4\ \mathrm{f t\cdot l b f},\ 6. 2 8\ \mathrm{h p}
$$
J. $$
1 6 8. 1\ \mathrm{f t\cdot l b f},\ 5. 4 6\ \mathrm{h p}
$$
Answer: I
Water is flowing through a pipe with a diameter of 150mm at a flow rate of 100L/s. If the pipe suddenly expands to a diameter of 200mm through a diffuser with a total cone angle of 20°, what is the resulting head loss?

Options:
A. $$
0. 1 3 1 0 {\mathrm{m}}
$$
B. $$
0. 1 0 9 8 {\mathrm{m}}
$$
C. $$
0. 1 1 9 5 {\mathrm{m}}
$$
D. $$
0. 1 0 7 2 {\mathrm{m}}
$$
E. $$
0. 1 4 4 5 {\mathrm{m}}
$$
F. $$
0. 1 2 1 3 {\mathrm{m}}
$$
G. $$
0. 1 1 8 7 {\mathrm{m}}
$$
H. $$
0. 1 3 2 9 {\mathrm{m}}
$$
I. $$
0. 1 2 3 4 {\mathrm{m}}
$$
J. $$
0. 1 0 5 6 {\mathrm{m}}
$$
Answer: G
Give an analysis of the water surface line in a rectangular channel made of concrete ($n=0.013$). The channel is 10 ft wide, with a flow rate of 400 ft³/sec, and the bottom slope suddenly drops from 0.0150 to 0.0016. What is the energy loss caused by the formation of a hydraulic jump?

Options:
A. $$
5. 8 9 \mathrm{h p}
$$
B. $$
7. 0 8 \mathrm{h p}
$$
C. $$
8. 4 7 \mathrm{h p}
$$
D. $$
8. 1 0 \mathrm{h p}
$$
E. $$
7. 4 5 \mathrm{h p}
$$
F. $$
6. 4 5 \mathrm{h p}
$$
G. $$
5. 3 2 \mathrm{h p}
$$
H. $$
9. 2 3 \mathrm{h p}
$$
I. $$
7. 6 9 \mathrm{h p}
$$
J. $$
6. 9 1 \mathrm{h p}
$$
Answer: I
What is the gravitational flow rate through the Venturi tube? Given that the air temperature is 20°C and the pressure is 700 kN/m², assume the pressure at the throat is 400 kN/m². The diameters at the inlet and the throat are 250 mm and 125 mm, respectively. Assume $C = 0.985$.

Options:
A. $$
1 8 5. 6 N / s
$$
B. $$
1 9 5. 7 N / s
$$
C. $$
1 9 0. 8 N / s
$$
D. $$
1 8 2. 4 N / s
$$
E. $$
2 1 0. 5 N / s
$$
F. $$
2 0 3. 9 N / s
$$
G. $$
1 8 8. 0 N / s
$$
H. $$
1 9 7. 1 N / s
$$
I. $$
2 0 6. 2 N / s
$$
J. $$
2 1 2. 3 N / s
$$
Answer: H
Air flows out from a large container through a converging-diverging nozzle with a throat diameter of 2.0 inches. The internal pressure of the tank is 50 psia, and the temperature is $80^{\circ} \mathrm{F}$. The external pressure is 13.5 psia. If the flow in the diverging section is supersonic and the exit pressure is 13.5 psia, what is the area at cross section 3 assuming isentropic flow ?

Options:
A. $$
0. 0 2 9 4 {\mathrm{f t}}^{2}
$$
B. $$
0. 0 2 8 0 {\mathrm{f t}}^{2}
$$
C. $$
0. 0 2 7 5 {\mathrm{f t}}^{2}
$$
D. $$
0. 0 3 1 2 {\mathrm{f t}}^{2}
$$
E. $$
0. 0 1 8 3 {\mathrm{f t}}^{2}
$$
F. $$
0. 0 2 5 7 {\mathrm{f t}}^{2}
$$
G. $$
0. 0 2 6 1 {\mathrm{f t}}^{2}
$$
H. $$
0. 0 1 7 9 {\mathrm{f t}}^{2}
$$
I. $$
0. 0 1 9 8 {\mathrm{f t}}^{2}
$$
J. $$
0. 0 3 0 6 {\mathrm{f t}}^{2}
$$
Answer: F
A water turbine, with an outlet flow rate of $200 \, \mathrm{ft}^3/\mathrm{sec}$, a rotational speed of $150 \, \mathrm{r/min}$, and a net head of 81 ft, achieves a maximum efficiency of 87%. The turbine drives a motor operating on a 60 Hz current. Under the same operating conditions with a net head of 40.5 ft, how many poles are required for the motor to meet these working conditions?

Options:
A. 49
B. 46
C. 53
D. 52
E. 38
F. 48
G. 50
H. 45
I. 51
J. 54
Answer: J
For an n-type GaAs with a thickness of 0.08 cm, a current of 50 mA is applied in the $x$ direction, and a magnetic field of 0.5 T is applied in the $z$ direction, resulting in a Hall voltage of -0.4 mV. What is the mobility of the charge carriers?

Options:
A. $$
8. 5 3 \, \times\, 1 0^{3} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
B. $$
1. 1 9 \, \times\, 1 0^{2} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
C. $$
4. 7 2 \, \times\, 1 0^{4} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
D. $$
5. 6 7 \, \times\, 1 0^{2} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
E. $$
2. 4 7 \, \times\, 1 0^{4} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
F. $$
6. 8 4 \, \times\, 1 0^{2} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
G. $$
7. 9 6 \, \times\, 1 0^{3} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
H. $$
7. 4 1 \, \times\, 1 0^{4} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
I. $$
3. 5 8 \, \times\, 1 0^{3} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
J. $$
9. 3 1 \, \times\, 1 0^{3} \, \mathrm{[ \ c m^{2} / V \cdot s ]}
$$
Answer: A
What are the thermoelectric power and Peltier coefficient of n-type PoTe with a conductivity of 2000 S/cm, an electron mobility of $6000 \ \mathrm{cm}^{2} / ( \mathrm{V} \cdot \mathrm{s} )$, and an effective electron mass of $0.2 \ m_{0}$, assuming long-wavelength acoustic scattering at room temperature?

Options:
A. $$
- 1. 9 5 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 4 7. 8 ( \mathrm{m V} )
$$
B. $$
- 1. 7 0 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 6. 2 ( \mathrm{m V} )
$$
C. $$
- 2. 0 1 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 4 9. 3 ( \mathrm{m V} )
$$
D. $$
- 1. 6 5 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 9. 1 ( \mathrm{m V} )
$$
E. $$
- 1. 9 0 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 4 8. 9 ( \mathrm{m V} )
$$
F. $$
- 1. 7 2 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 5. 6 ( \mathrm{m V} )
$$
G. $$
- 1. 7 9 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 3. 8 ( \mathrm{m V} )
$$
H. $$
- 1. 8 3 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 1. 7 ( \mathrm{m V} )
$$
I. $$
- 1. 8 5 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 0. 2 ( \mathrm{m V} )
$$
J. $$
- 1. 6 7 \times1 0^{-4} ( \mathrm{V} / \mathrm{K} ),\ 5 7. 4 ( \mathrm{m V} )
$$
Answer: G
What is the injection ratio of GaAs and $\mathrm{Al}_{0.3} \mathrm{Ga}_{0.7} \mathrm{As}$ at 300K?

Options:
A. $$
3. 7 \times 1 0^{7}
$$
B. $$
2. 6 \times 1 0^{6}
$$
C. $$
4. 8 \times 1 0^{5}
$$
D. $$
7. 3 \times 1 0^{7}
$$
E. $$
5. 1 \times 1 0^{5}
$$
F. $$
5. 5 \times1 0^{6}
$$
G. $$
4. 9 \times 1 0^{6}
$$
H. $$
8. 0 \times 1 0^{6}
$$
I. $$
9. 4 \times 1 0^{5}
$$
J. $$
6. 2 \times 1 0^{6}
$$
Answer: F
The relative permittivity of silicon, $\varepsilon_{\mathrm{n}} = 12$, and the mobility, $\mu_{\mathrm{n}} = 1350 \mathrm{cm}^2/(\mathrm{V} \cdot \mathrm{s})$. For an n-type silicon sample with a resistivity of $3 \Omega \cdot \mathrm{cm}$, at what distance from the surface to the boundary of the space charge region does strong inversion begin, such that the intrinsic level is exactly at this point in the space charge region?

Options:
A. $$
1. 3 \times1 0^{-5} ( \mathrm{\, c m} )
$$
B. $$
1. 7 \times1 0^{-5} ( \mathrm{\, c m} )
$$
C. $$
1. 1 \times1 0^{-5} ( \mathrm{\, c m} )
$$
D. $$
1. 8 \times1 0^{-5} ( \mathrm{\, c m} )
$$
E. $$
1. 2 \times1 0^{-5} ( \mathrm{\, c m} )
$$
F. $$
1. 5 \times1 0^{-5} ( \mathrm{\, c m} )
$$
G. $$
1. 6 \times1 0^{-5} ( \mathrm{\, c m} )
$$
H. $$
0. 9 \times1 0^{-5} ( \mathrm{\, c m} )
$$
I. $$
2. 0 \times1 0^{-5} ( \mathrm{\, c m} )
$$
J. $$
1. 4 \times1 0^{-5} ( \mathrm{\, c m} )
$$
Answer: F
A metal plate is positioned $0.4 μm$ away from an n-type silicon, forming a parallel-plate capacitor. The relative dielectric constant of the dry air between them is $ε_n = 1$. When a negative voltage is applied to the metal end, the semiconductor is in a depletion state. Ignoring the work function difference between the metal and semiconductor, what should be the electric potential $V_c$ on the metal plate for the depletion layer width to just reach its maximum value? ($N_D = 10^{16} cm^{−3}$)

Options:
A. $$
2 0. 9 9 ( \mathrm{V} )
$$
B. $$
3 1. 4 5 ( \mathrm{V} )
$$
C. $$
1 6. 3 7 ( \mathrm{V} )
$$
D. $$
3 0. 1 3 ( \mathrm{V} )
$$
E. $$
2 5. 8 0 ( \mathrm{V} )
$$
F. $$
1 9. 6 6 ( \mathrm{V} )
$$
G. $$
1 8. 5 4 ( \mathrm{V} )
$$
H. $$
2 7. 1 2 ( \mathrm{V} )
$$
I. $$
2 9. 0 1 ( \mathrm{V} )
$$
J. $$
2 2. 6 8 ( \mathrm{V} )
$$
Answer: J
If a silicon abrupt junction is set with impurity concentrations on both sides of $N_{\mathrm{A}}=10^{17}/\mathrm{cm}^{3}$ and $N_{\mathrm{D}}=4.5 \times 10^{15}/\mathrm{cm}^{3}$. What is the value of $x_{\mathrm{D}}$ when a reverse bias voltage of 10V is applied to the junction?

Options:
A. $$
3. 0 1 \times1 0^{-5} ( \mathrm{\, c m} )
$$
B. $$
2. 0 4 \times1 0^{-6} ( \mathrm{\, c m} )
$$
C. $$
3. 5 4 \times1 0^{-6} ( \mathrm{\, c m} )
$$
D. $$
4. 0 2 \times1 0^{-5} ( \mathrm{\, c m} )
$$
E. $$
1. 1 2 \times1 0^{-5} ( \mathrm{\, c m} )
$$
F. $$
1. 8 9 \times1 0^{-6} ( \mathrm{\, c m} )
$$
G. $$
2. 9 3 \times1 0^{-6} ( \mathrm{\, c m} )
$$
H. $$
1. 5 6 \times1 0^{-6} ( \mathrm{\, c m} )
$$
I. $$
2. 6 7 \times1 0^{-6} ( \mathrm{\, c m} )
$$
J. $$
2. 3 3 \times1 0^{-6} ( \mathrm{\, c m} )
$$
Answer: B
A $1 ( \Omega \cdot \mathrm{cm} )$ n-type silicon sample is uniformly illuminated, generating non-equilibrium carriers with an electron-hole pair generation rate of $10^{17} \text{ cm}^{-3} \cdot \text{s}^{-1}$. Assuming the sample has a lifetime of $10 \mu \text{s}$ and a surface recombination velocity of 100 cm/s, how many holes recombine within three diffusion lengths from the surface per unit time and per unit area?

Options:
A. $$
4.7 \times 10^{14} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
B. $$
1.5 \times 10^{18} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
C. $$
2. 9 \times1 0^{1 5} ( 1 / \mathrm{c m}^{2} \cdot\mathrm{s} )
$$
D. $$
3.1 \times 10^{16} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
E. $$
6.3 \times 10^{17} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
F. $$
7.8 \times 10^{15} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
G. $$
9.2 \times 10^{16} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
H. $$
8.0 \times 10^{13} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
I. $$
5.9 \times 10^{13} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
J. $$
1.4 \times 10^{14} (1/\mathrm{cm}^{2} \cdot \mathrm{s})
$$
Answer: C
Calculate the resistivity of intrinsic silicon at room temperature. Assume the electron and hole mobilities are $1350 \, \mathrm{cm}^2/(\mathrm{V} \cdot \mathrm{s})$ and $500 \, \mathrm{cm}^2/(\mathrm{V} \cdot \mathrm{s})$, respectively. After doping with one part per million of arsenic (As), assuming full ionization of the impurities, by how many times does the conductivity increase compared to intrinsic Si?

Options:
A. $$
1. 4 1 {\times} 1 0^{6}
$$
B. $$
1. 5 3 {\times} 1 0^{6}
$$
C. $$
1. 4 7 {\times} 1 0^{5}
$$
D. $$
1. 5 8 {\times} 1 0^{5}
$$
E. $$
1. 9 4 {\times} 1 0^{6}
$$
F. $$
1. 2 5 {\times} 1 0^{6}
$$
G. $$
1. 7 3 {\times} 1 0^{5}
$$
H. $$
1. 6 8 {\times} 1 0^{6}
$$
I. $$
1. 5 9 {\times} 1 0^{4}
$$
J. $$
1. 3 2 {\times} 1 0^{6}
$$
Answer: B
How many quantum states per unit volume are there between the energies $E = E_{c}$ and $E = E_{c} + 100 \left( \frac{h^{2}}{8 m_{n}^{\ast} L^{2}} \right)$?

Options:
A. $$
5 0 0 \pi/ 3 L^{2}
$$
B. $$
3 0 0 \pi/ 2 L^{3}
$$
C. $$
4 0 0 0 \pi/ L^{3}
$$
D. $$
2 0 0 0 \pi/ 3 L^{2}
$$
E. $$
2 5 0 \pi/ 3 L^{3}
$$
F. $$
1 0 0 \pi/ 6 L^{3}
$$
G. $$
9 0 0 \pi/ 4 L^{3}
$$
H. $$
1 0 0 0 \pi/ 3 L^{3}
$$
I. $$
1 5 0 0 \pi/ L^{3}
$$
J. $$
8 0 0 \pi/ L^{3}
$$
Answer: H
Given that the electron energy band of a one-dimensional crystal can be written as
$$
E(k) = \frac{h^2}{m_0 a^2} \left( \frac{7}{8} - \cos 2\pi k a + \frac{1}{8} \cos 6\pi k a \right)
$$
where $a$ is the lattice constant. What is the effective mass of electrons at the top of the energy band?

Options:
A. $$
2. 6 5 m_{0}
$$
B. $$
4. 1 2 m_{0}
$$
C. $$
- 3. 5 2 m_{0}
$$
D. $$
- 4. 1 8 m_{0}
$$
E. $$
- 5. 2 6 m_{0}
$$
F. $$
- 0. 7 4 m_{0}
$$
G. $$
0. 8 9 m_{0}
$$
H. $$
1. 0 8 m_{0}
$$
I. $$
- 6. 3 3 m_{0}
$$
J. $$
3. 9 1 m_{0}
$$
Answer: D
A square flat plate inclined at a 30° angle to the vertical, with a side length of 40 cm, has saturated water vapor at 1.013 × 10° Pa condensing on it. The average wall temperature is 96°C. Try to calculate the amount of condensate per hour. If the flat plate is inclined at a 30° angle to the horizontal, what percentage of the current amount will the condensate be?

Options:
A. $$
1 1. 8 \mathrm{k g / h}
$$
B. $$
1 4. 4 \mathrm{k g / h}
$$
C. $$
1 4. 0 \mathrm{k g / h}
$$
D. $$
1 0. 8 \mathrm{k g / h}
$$
E. $$
1 2. 8 \mathrm{k g / h}
$$
F. $$
1 3. 5 \mathrm{k g / h}
$$
G. $$
1 5. 2 \mathrm{k g / h}
$$
H. $$
1 1. 1 \mathrm{k g / h}
$$
I. $$
1 0. 5 \mathrm{k g / h}
$$
J. $$
1 2. 2 \mathrm{k g / h}
$$
Answer: J
Given that the vector $A = a_{r} \Big( \frac{1} {r} \Big) + a_{r} \Big( \frac{2} {r} \Big)$ is in the cylindrical coordinate system, find the expression of this vector in the Cartesian coordinate system is ().

Options:
A. $$
A=a_{x} \, \frac{y-x} {y^{2}+x^{2}}+a_{x} \, \frac{x-y} {x^{2}+y^{2}}
$$
B. $$
A=a_{x} \, \frac{x-2 y} {x^{2}+y^{2}}+a_{x} \, \frac{y-2 x} {x^{2}+y^{2}}
$$
C. $$
A=a_{x} \, \frac{x^{2}-y} {y^{2}+x}+a_{x} \, \frac{y^{2}-x} {x^{2}+y}
$$
D. $$
A=a_{x} \, \frac{x+y} {x^{2}-y^{2}}+a_{x} \, \frac{y+x} {y^{2}-x^{2}}
$$
E. $$
A=a_{x} \, \frac{2 x-y} {y^{2}+x^{2}}+a_{x} \, \frac{2 y-x} {y^{2}+x^{2}}
$$
F. $$
A=a_{x} \, \frac{y-2 x} {x^{2}-y^{2}}+a_{x} \, \frac{x-2 y} {y^{2}-x^{2}}
$$
G. $$
A=a_{x} \, \frac{2 y-x} {x^{2}+y^{2}}+a_{x} \, \frac{2 x-y} {x^{2}+y^{2}}
$$
H. $$
A=a_{x} \, \frac{x-y} {x^{2}+y^{2}}+a_{x} \, \frac{y-x} {x^{2}+y^{2}}
$$
I. $$
A=a_{x} \, \frac{x+y^{2}} {x^{2}-y}+a_{x} \, \frac{y+x^{2}} {y^{2}-x}
$$
J. $$
A=a_{x} \, \frac{2 y+x} {x^{2}+y^{2}}+a_{x} \, \frac{2 x+y} {y^{2}+x^{2}}
$$
Answer: B
A non-charged conducting spherical shell with a radius of $R$ is placed in a uniform electric field $E_{0}$. Imagine this spherical shell is divided into two hemispherical shells by a plane perpendicular to $E_{0}$. What magnitude of external force is needed to keep these two hemispherical shells from separating?

Options:
A. $$\frac{11}4\pi\varepsilon_0E_0^2R^2.$$
B. $$\frac54\pi\varepsilon_0E_0^2R^2.$$
C. $$\frac10\pi\varepsilon_0E_0^2R^2.$$
D. $$\frac13\pi\varepsilon_0E_0^2R^2.$$
E. $$\frac32\pi\varepsilon_0E_0^2R^2.$$
F. $$\pi\varepsilon_0E_0^2R^2.$$
G. $$\frac94\pi\varepsilon_0E_0^2R^2.$$
H. $$\frac83\pi\varepsilon_0E_0^2R^2.$$
I. $$\frac25\pi\varepsilon_0E_0^2R^2.$$
J. $$\frac7{10}\pi\varepsilon_0E_0^2R^2.$$
Answer: G
Water at a temperature of 20°C flows through a horizontal circular pipe with an inner diameter of 10mm at a mass flow rate of 2kg/h. Calculate the shear stress of the fluid at a point located halfway between the wall and the center after the flow is fully developed is ().

Options:
A. $$
3. 0 4 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
B. $$
3. 3 1 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
C. $$
1. 9 8 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
D. $$
1. 6 2 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
E. $$
2. 5 6 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
F. $$
3. 5 0 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
G. $$
2. 9 7 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
H. $$
2. 7 5 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
I. $$
4. 1 8 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
J. $$
2. 8 3 \! \times\! 1 0^{-3} \mathrm{N / m}^{2}
$$
Answer: J
Using a pipe with an inner diameter of $27 \mathrm{mm}$, air is heated from $10°C$ to $100°C$. The air flow rate is $250 \mathrm{kg/h}$, and the outside of the pipe is heated with saturated steam at $120°C$ (not liquefied). Determine the required pipe length is ().

Options:
A. $$
5.12m
$$
B. $$
5.68m
$$
C. $$
4.08m
$$
D. $$
3.56m
$$
E. $$
4.95m
$$
F. $$
4.44m
$$
G. $$
3.41m
$$
H. $$
6.29m
$$
I. $$
6.02m
$$
J. $$
3.78m
$$
Answer: F
In a storage tank with a diameter of $2 \mathrm{m}$, there is ammonia water with a mass fraction of 0.1. Due to negligence, the tank is uncovered, allowing ammonia to evaporate through molecular diffusion. Assuming the diffusion occurs through a 5mm thick layer of still air, at 101kPa and 20°C, the molecular diffusion coefficient of ammonia is $1.8 \times 10^{-5} \mathrm{m}^{2} / \mathrm{s}$. Calculate the evaporation loss of ammonia over 12 hours is (). In the calculation, the change in ammonia water concentration is not considered. The phase equilibrium relationship of ammonia at 20°C is given by $\mathrm{P}_{\mathrm{kPa}} = 269 \mathrm{x}$, where x is the mole fraction.

Options:
A. $$
5. 7 6 {\times} 1 0^{3} \mathrm{m o l}
$$
B. $$
7. 8 1 {\times} 1 0^{3} \mathrm{m o l}
$$
C. $$
7. 2 1 {\times} 1 0^{3} \mathrm{m o l}
$$
D. $$
6. 5 0 {\times} 1 0^{3} \mathrm{m o l}
$$
E. $$
6. 6 6 {\times} 1 0^{3} \mathrm{m o l}
$$
F. $$
8. 0 9 {\times} 1 0^{3} \mathrm{m o l}
$$
G. $$
5. 9 4 {\times} 1 0^{3} \mathrm{m o l}
$$
H. $$
7. 5 2 {\times} 1 0^{3} \mathrm{m o l}
$$
I. $$
6. 0 3 {\times} 1 0^{3} \mathrm{m o l}
$$
J. $$
5. 8 8 {\times} 1 0^{3} \mathrm{m o l}
$$
Answer: E
Using a filter to process a certain suspension, first perform constant-rate filtration for 20 minutes to obtain 2 cubic meters of filtrate. Then maintain the same pressure difference for constant-pressure filtration for 40 minutes. How much filtrate is obtained in total (ignoring the resistance of the medium)?

Options:
A. $$
3. 7 4 \, {\mathrm{m}}^{3}
$$
B. $$
2. 8 5 \, {\mathrm{m}}^{3}
$$
C. $$
5. 9 8 \, {\mathrm{m}}^{3}
$$
D. $$
5. 5 3 \, {\mathrm{m}}^{3}
$$
E. $$
4. 4 7 \, {\mathrm{m}}^{3}
$$
F. $$
4. 1 9 \, {\mathrm{m}}^{3}
$$
G. $$
3. 9 6 \, {\mathrm{m}}^{3}
$$
H. $$
6. 1 0 \, {\mathrm{m}}^{3}
$$
I. $$
5. 0 2 \, {\mathrm{m}}^{3}
$$
J. $$
4. 8 0 \, {\mathrm{m}}^{3}
$$
Answer: E
With glucose as the carbon source and $\mathrm{NH}_{3}$ as the nitrogen source, when cultivating a certain bacterium under aerobic conditions, two-thirds of the carbon from glucose is converted into carbon elements within the bacterial cells. Given that the cell composition is $\mathrm{C_{4.4} H_{7.3} N_{0.86} O_{1.2}}$, and assuming the reaction products are only $\mathrm{CO_{2}}$ and $\mathrm{H_{2}O}$, try to calculate $Y_{x/s}$ and $Y_{x/o}$ is ().

Options:
A. $$
\begin{array} {c} {{Y_{x / s}=8 6. 4 / 1 8 8=0. 4 6 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 6. 4 / 1. 4 4^{*} 3 2=1. 8 4 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
B. $$
\begin{array} {c} {{Y_{x / s}=8 0. 2 / 1 8 2=0. 4 2 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 0. 2 / 1. 5 2^{*} 3 4=1. 6 4 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
C. $$
\begin{array} {c} {{Y_{x / s}=8 1. 0 / 1 8 3=0. 4 3 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 1. 0 / 1. 5 0^{*} 3 3=1. 6 3 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
D. $$
\begin{array} {c} {{Y_{x / s}=8 3. 8 / 1 8 7=0. 4 5 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 3. 8 / 1. 5 1^{*} 3 3=1. 6 8 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
E. $$
\begin{array} {c} {{Y_{x / s}=8 7. 1 / 1 8 4=0. 4 9 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 7. 1 / 1. 4 6^{*} 3 1=1. 8 3 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
F. $$
\begin{array} {c} {{Y_{x / s}=8 4. 0 / 1 8 1=0. 4 7 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 4. 0 / 1. 4 5^{*} 3 2=1. 8 2 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
G. $$
\begin{array} {c} {{Y_{x / s}=8 2. 5 / 1 8 5=0. 4 4 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 2. 5 / 1. 4 9^{*} 3 1=1. 7 0 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
H. $$
\begin{array} {c} {{Y_{x / s}=8 3. 1 / 1 8 0=0. 4 6 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 3. 1 / 1. 4 7^{*} 3 2=1. 7 7 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
I. $$
\begin{array} {c} {{Y_{x / s}=7 8. 2 / 1 9 0=0. 4 1 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=7 8. 2 / 1. 5 0^{*} 3 5=1. 6 5 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
J. $$
\begin{array} {c} {{Y_{x / s}=8 5. 3 / 1 8 6=0. 4 8 \, \mathrm{k g} \, / \mathrm{k g}}} \\ {{Y_{x / o}=8 5. 3 / 1. 4 8^{*} 3 0=1. 8 0 \, \mathrm{k g} \, / \mathrm{k g}}} \\ \end{array}
$$
Answer: H
In a certain leaf filter press operating under constant pressure, 4L of filtrate is obtained in the first 10 minutes, and 2L is obtained in the second 10 minutes. Calculate: How many liters of filtrate are obtained in the third 10 minutes?

Options:
A. 1.94L
B. 1.75L
C. 1.54L
D. 1.70L
E. 1.33L
F. 1.61L
G. 1.46L
H. 1.80L
I. 1.59L
J. 1.28L
Answer: C
The plan is to use a plate-and-frame filter press to filter a certain suspension under constant pressure, where the filtration constant is known as $K=7.5\times10^{-5}$ $\mathrm{m^{2}/s}$. It is required to obtain $10 \mathrm{m}^{3}$ of filtrate per operation cycle, with a filtration time of 0.5 hours. The suspension has a solid content of $\phi=0.015$ ($\mathrm{m}^{3}$ solid/$\mathrm{m}^{3}$ suspension), and the porosity of the filter cake is $\varepsilon=0.5$, with negligible resistance of the filter medium. There is a plate and frame filter press available, with the dimensions of the frame being $0.6\mathrm{m} \times 0.6\mathrm{m} \times 0.02\mathrm{m}$. If the requirement remains to obtain a filtrate volume of $10 \mathrm{m}^{3}$ per filtration cycle, after installing the required number of plates and frames based on filtration time and filter cake volume, how long will the actual filtration time be to obtain a filtrate volume of $10 \mathrm{m}^{3}$?

Options:
A. 19.6min
B. 29.9min
C. 28.5min
D. 50.4min
E. 45.7min
F. 36.0min
G. 54.3min
H. 32.8min
I. 41.1min
J. 23.2min
Answer: J