MikaStars39/nano-eval huggingface dataset:
It is known that the length of each monomer unit of cis-polyisoprene is $0.46 \mathrm{~nm}$, and $\overline{{{h^{2}}}}=16.2 n$. What is the segment length of the statistical equivalent freely jointed chain of this macromolecule? (Note: $n$ here is the number of monomer units)

Options:
A. $$
0. 6 6 2 \mathrm{~ n m}
$$
B. $$
0. 5 8 4 \mathrm{~ n m}
$$
C. $$
0. 5 1 9 \mathrm{~ n m}
$$
D. $$
0. 7 8 4 \mathrm{~ n m}
$$
E. $$
0. 3 5 2 \mathrm{~ n m}
$$
F. $$
0. 4 0 8 \mathrm{~ n m}
$$
G. $$
0. 7 7 3 \mathrm{~ n m}
$$
H. $$
0. 1 9 4 \mathrm{~ n m}
$$
I. $$
0. 6 2 1 \mathrm{~ n m}
$$
J. $$
0. 2 9 6 \mathrm{~ n m}
$$
Answer: E
Which can be transmitted on the data lines of the system bus?

Options:
A. Scent
B. Melody
C. all signals
D. Temperature
E. Handshake (acknowledge) signals
F. Flavor
G. Emotion
H. Instruction
I. Texture
J. Voltage
Answer: H
In a 16-bit bus system, if the clock frequency is 100MHz and the bus data cycle transmits one byte in 5 clock cycles, what is the data transfer rate of the bus?

Options:
A. $$
6 0 \times1 0^{6} ( \mathrm{B / s} )
$$
B. $$
3 2 \times1 0^{6} ( \mathrm{B / s} )
$$
C. $$
5 0 \times1 0^{6} ( \mathrm{B / s} )
$$
D. $$
4 0 \times1 0^{6} ( \mathrm{B / s} )
$$
E. $$
1 0 \times1 0^{6} ( \mathrm{B / s} )
$$
F. $$
2 5 \times1 0^{6} ( \mathrm{B / s} )
$$
G. $$
3 6 \times1 0^{6} ( \mathrm{B / s} )
$$
H. $$
4 4 \times1 0^{6} ( \mathrm{B / s} )
$$
I. $$
2 0 \times1 0^{6} ( \mathrm{B / s} )
$$
J. $$
4 8 \times1 0^{6} ( \mathrm{B / s} )
$$
Answer: D
There is a (7, 4) code with the polynomial G(x) = $x^{3}$ + x + 1. Write out the cyclic redundancy check code for the codeword 1001 is ().

Options:
A. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 1 0 1 0 1 0
$$
B. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 1 1 0 0 0 1
$$
C. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 0 0 1 1 1 0
$$
D. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=0 0 1 0 0 1 0
$$
E. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=0 1 0 1 1 0 0
$$
F. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 0 0 0 0 1 1
$$
G. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 1 0 0 1 1 1
$$
H. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=0 0 0 1 0 1 1
$$
I. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=0 1 1 0 1 0 1
$$
J. $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 1 1 1 0 0 0
$$
Answer: C
When a cache system miss occurs, it is common for information to be transmitted from the main memory to the CPU, and it is also necessary to write the information into the cache. During this process, what is the data width for writing the information?

Options:
A. Frame
B. Cluster
C. Segment
D. Cell
E. Page
F. Chunk
G. Block
H. Word
I. Byte
J. Line
Answer: G
What is the largest integer that a float type (i.e., IEEE 754 single-precision floating-point format) can represent?

Options:
A. $$
2^{1 2 7}-2^{1 0 6}
$$
B. $$
2^{1 2 2}-2^{1 0 8}
$$
C. $$
2^{1 1 5}-2^{1 0 7}
$$
D. $$
2^{1 2 5}-2^{1 0 2}
$$
E. $$
2^{1 2 4}-2^{1 0 5}
$$
F. $$
2^{1 2 3}-2^{1 0 0}
$$
G. $$
2^{1 2 8}-2^{1 0 4}
$$
H. $$
2^{1 2 0}-2^{1 0 9}
$$
I. $$
2^{1 2 6}-2^{1 0 3}
$$
J. $$
2^{1 0 9}-2^{1 0 1}
$$
Answer: G
When using n+1 bits (including 1 sign bit) to represent a fixed-point integer, the range of representable digits is $0 \! \leqslant\! | \mathrm{N} | \! \leqslant\! 2^{n} \!-\! 1$. What is the range of representable values when using n+1 bits (including 1 sign bit) to represent a fixed-point decimal?

Options:
A. $$
2^{-n} \leqslant N \leqslant 2^{n} - 1
$$
B. $$
2^{-n} \leqslant N < 1
$$
C. $$
0 \leqslant| N | \leqslant1-2^{-n}
$$
D. $$
-1 \leqslant N < 2^{n}
$$
E. $$
-2^{-n} \leqslant N \leqslant 1
$$
F. $$
0 \leqslant N \leqslant 2^{n-1} - 1
$$
G. $$
0 \leqslant N < 2^{n} + 1
$$
H. $$
-2^{n} \leqslant N \leqslant 0
$$
I. $$
-1 \leqslant N \leqslant 2^{-n} - 1
$$
J. $$
0 \leqslant N \leqslant 2^{-n}
$$
Answer: C
The clock speed of a certain CPU is 10MHz. Given that each machine cycle contains an average of 4 clock cycles, the average instruction execution speed of this machine is 1 MIPS. To achieve an average instruction execution speed of 800,000 instructions per second, what clock speed should the CPU chip have?

Options:
A. 2MHz
B. 200MHz
C. 400MHz
D. 80MHz
E. 40MHz
F. 8.5MHz
G. 20MHz
H. 300MHz
I. 60MHz
J. 120MHz
Answer: D
By reviewing the literature, learn about R. Willstätter's method for synthesizing cyclooctatetraene. Some have questioned his results. Without considering modern characterization techniques, which of the following is a method to verify that his product is cyclooctatetraene?

Options:
A. Monitoring cyclooctatetraene reaction yield and comparing it against theoretical predictions.
B. Observing cyclooctatetraene's color change with the application of thin-layer chromatography.
C. Subjecting cyclooctatetraene to X-ray crystallography for analysis of molecular structure.
D. Cross-referencing known hydrocarbon data with cyclooctatetraene via nuclear magnetic resonance.
E. Using infrared spectroscopy to test cyclooctatetraene bonds and analyze results.
F. Evaluating cyclooctatetraene flame test for characteristic color and combustion products.
G. Performing gas chromatography for cyclooctatetraene and checking for peak retention.
H. After catalytic hydrogenation reduction of cyclooctatetraene, cyclooctane is obtained, which can be identified using the Liebig method or other methods.
I. Determining cyclooctatetraene molecular weight through the freezing point depression method.
J. Analyzing elemental composition of cyclooctatetraene with Karl Fischer titration technique.
Answer: H
Based on the components obtained from the hydrolysis of individual peptides, deduce the sequence of amino acid residues in the peptide:
The components containing arginine, proline, glycine, serine, and phenylalanine decompose into the following fragments: Arg-Pro-Pro, Gly-Phe-Ser, Pro-Phe-Arg, Pro-Gly-Phe, Ser-Pro-Phe.
It is ____.

Options:
A. Phe-Pro-Arg-Gly-Ser Pro-Gly-Glu-Phe-Pro (echoes viable assembly).
B. Phe-Ser-Pro-Gly-Gly Pro-Pro-Glu-Phe-Phe (imitates theoretical chain).
C. Gly-Ser-Pro-Arg-Phe Phe-Ser-Glu-Pro-Phe (portrays alternate sequence).
D. Ser-Phe-Arg-Pro-Phe Gly-Pro-Glu-Pro-Phe (suggests common sequence).
E. Pro-Gly-Phe-Ser-Pro Phe-Phe-Glu-Pro-Pro (can be a cyclic polypeptide).
F. Gly-Phe-Arg-Pro-Pro Phe-Ser-Glu-Gly-Phe (resembles plausible chain).
G. Arg-Phe-Pro-Gly-Gly Pro-Ser-Glu-Phe-Arg (appears linear variant).
H. Ser-Gly-Pro-Phe-Phe Pro-Phe-Glu-Arg-Arg (mimics potential structure).
I. Pro-Arg-Ser-Phe-Gly Pro-Phe-Glu-Phe-Gly (likewise conceivable layout).
J. Gly-Arg-Ser-Pro-Pro Phe-Phe-Glu-Phe-Gly (resembles linear arrangement).
Answer: E
The dominance relationships among the multiple alleles determining coat color in domestic rabbits are as follows: \($c^{\mathrm{c h}}$\) is dominant over \($c^{\mathrm{h}}$\). Among them, \($c^{\mathrm{b}}$\) determines the Himalayan phenotype. What proportion of the offspring will exhibit the Himalayan phenotype in the cross \($C c^{\mathrm{c h}} \times c^{\mathrm{c h}} c^{\mathrm{b}}$\)?

Options:
A. 0.05
B. 0.50
C. 0.35
D. 0.15
E. 1
F. 0
G. 0.20
H. 0.30
I. 0.25
J. 0.10
Answer: F
Wild-type haploid Neurospora can synthesize tryptophan on its own, but the mutant allele \(td\) causes it to lose this function. Mutants with the genotype \(id\) require the addition of tryptophan to the medium in order to grow. This phenotype is suppressed by the allele \(su\), so strains carrying both the \(su\) and \(id\) mutant genes are no longer dependent on tryptophan. The alleles \(su\) and \(td\) are independently assorted. What is the ratio of tryptophan-dependent to non-dependent types in the progeny of the above cross?

Options:
A. 3:1
B. 1:1
C. 2:1
D. 1:3
E. 3:2
F. 0:4
G. 2:2
H. 0:3
I. 4:1
J. 1:2
Answer: D
Brown eyes (B) are dominant over blue eyes (b), and right-handedness (R) is dominant over left-handedness (r). A brown-eyed, right-handed man marries a blue-eyed, right-handed woman, and their first child has blue eyes and is left-handed. If this couple has another child, what are the possible phenotypes and their likely ratios?

Options:
A. Blue-eyed right dominance: Brown-eyed left dominance: Brown-eyed right dominance: Blue-eyed left dominance = 2:1:3:3
B. Blue-eyed left dominance: Brown-eyed left dominance: Blue-eyed right dominance: Brown-eyed right dominance = 1:1:2:3
C. Brown-eyed right dominance: Blue-eyed right dominance: Brown-eyed left dominance: Blue-eyed left dominance = 3:3:1:1
D. Brown-eyed left dominance: Blue-eyed right dominance: Brown-eyed right dominance: Blue-eyed left dominance = 3:2:3:1
E. Brown-eyed right dominance: Blue-eyed right dominance: Brown-eyed left dominance: Blue-eyed left dominance = 3:2:3:2
F. Brown-eyed left dominance: Blue-eyed left dominance: Brown-eyed right dominance: Blue-eyed right dominance = 6:2:3:3
G. Brown-eyed right dominance: Brown-eyed left dominance: Blue-eyed right dominance: Blue-eyed left dominance = 3:1:3:1
H. Blue-eyed left dominance: Brown-eyed right dominance: Blue-eyed right dominance: Brown-eyed left dominance = 1:2:3:3
I. Blue-eyed right dominance: Blue-eyed left dominance: Brown-eyed right dominance: Brown-eyed left dominance = 3:1:3:2
J. Blue-eyed right dominance: Brown-eyed right dominance: Blue-eyed left dominance: Brown-eyed left dominance = 2:3:3:1
Answer: C
Red fruit is dominant over yellow fruit, two-chamber fruit is dominant over multi-chamber fruit, and long vines are dominant over short vines. A breeder has pure lines of red fruit, two-chamber, short vines, and yellow fruit, multi-chamber, long vines, and he needs a strain with red fruit, multi-chamber, and long vines. If the two pure lines are crossed and their F1 and F2 generations are planted, what is the proportion of the phenotype he needs appearing in the F2 generation? What is the proportion where all three traits are homozygous?

Options:
A. 9/128,1/9
B. 12/64,1/10
C. 9/32,1/6
D. 27/64,3/16
E. 15/64,1/11
F. 9/64,1/9
G. 3/64,1/12
H. 3/16,1/8
I. 1/64,1/4
J. 18/64,2/9
Answer: F
The B locus and C locus are tightly linked, such that no recombination has ever been observed between them. When BBcc is crossed with bbCC, and then the F1 generation is self-fertilized, what phenotypes will appear in F2, and in what proportions?

Options:
A. 1 bC/Bc, 2 BB/bC, 1 bC/bB
B. 1 Bc/Bc, 2 Bc/bB, 1 bC/bb
C. 2 Bc/Bb, 1 Bb/bC, 1 bC/bC
D. 1 Bc/Bb, 2 Bc/Bc, 1 bC/bC
E. 0 Bc/Bc, 2 bC/bC, 2 Bc/bC
F. 1 BB/Bc, 2 Bc/bC, 1 bc/bB
G. 1 bC/Bb, 2 Bc/bC, 1 bc/Bc
H. 1 bC/Bc, 2 Bc/Bb, 1 bC/bC
I. 1 Bc/Bc,
2 Bc/bC,
1 bC/bC
J. 3 Bc/Bc, 0 Bc/bC, 1 bC/bC
Answer: I
A dominant allele of an X-linked gene in humans causes hypophosphatemia. What is the probability that the son of an affected male who marries a normal female will have the condition?

Options:
A. 0
B. 1
C. 50
D. 25
E. 100
F. 90
G. 5
H. 75
I. 10
J. 20
Answer: A
In the conjugation experiment, there is an $Hfr\ a^{+} b^{+} \operatorname{Str}^{s} \times \operatorname{F}^{-} a^{-} b^{-} \operatorname{Str}^{r}$ cross, where it is known that genes $a$ and $b$ control nutrient requirements. The hybrid strains were first inoculated on a complete medium containing streptomycin to grow, and then 100 colonies were tested on different media, with the following results:
(1) With the addition of substance $a$, 40 colonies were obtained.
(2) With the addition of substance $b$, 20 colonies were obtained.
(3) On the minimal medium, 10 colonies were obtained.
Write out the genotype of the third type of colony and calculate the recombination frequency between genes $a$ and $b$ is().

Options:
A. $$
a^{+} b^{+},{50} \%$$
B. $$
a^{+} b^{-},{40} \%$$
C. $$
a^{-} b^{+},{80} \%$$
D. $$
a^{-} b^{+},{10} \%$$
E. $$
a^{-} b^{-},{90} \%$$
F. $$
a^{+} b^{-},{30} \%$$
G. $$
a^{+} b^{+},{80} \%$$
H. $$
a^{-} b^{-},{60} \%$$
I. $$
a^{+} b^{+},{0} \%$$
J. $$
a^{+} b^{+},{20} \%$$
Answer: G
When a plant's genotype is aab6, the height of the plant is 40 cm, and when the genotype is AABB, the height is 60 cm. Assume that each dominant allele contributes additively to the height. In the F2 generation produced by self-crossing of F1, what proportion of the plants have a height of 50 cm?

Options:
A. 3/16
B. 4/16
C. 6/16
D. 2/16
E. 12/16
F. 5/16
G. 7/16
H. 9/16
I. 10/16
J. 8/16
Answer: C
A point moves along a straight line $x$, with its acceleration changing according to the following rule: $a = ct - k^{2}x$, where $x$ is the coordinate of the point, and $c$ and $k$ are constants. When $t=0$, $x=\dot{x}=0$. Determine the law of motion of the point.

Options:
A. $x=\frac{k}{c^{3}}( ct-\sin kt )$
B. $x=\frac{c}{k^{2}}( kt-\sin ct )$
C. $x=\frac{c}{k^{2}}( t-\cos kt )$
D. $x=\frac{c}{k^{3}}( \sin kt+kt )$
E. $x=\frac{k}{c^{3}}( kt-\sin ct )$
F. $x=\frac{k}{c^{2}}( \sin kt-ct )$
G. $x=\frac{c}{k^{3}}( kt+\sin kt )$
H. $x=\frac{c}{k^{2}}( \sin ct-kt )$
I. $x=\frac{c}{k^{3}}( \cos kt-kt )$
J. $x=\frac{c}{k^{3}}( kt-\sin kt )$
Answer: J
The transition section of the railway from a straight line to a certain curve is described by the following equation $y=\frac{x^{2}} {2000}$, where $x$ and $y$ are measured in meters. The motion of the train along the track is governed by $s=\frac{t^{2}} {10}$, where the origin of the arc coordinate is selected at $x=0$, $s$ is in meters, and $t$ is in seconds. Find the train's speed, tangential acceleration, and total acceleration when $x=1000$.

Options:
A. $\text{20.0m/s}$
$0.170\mathrm{m/s}^{2}$
$0.255\mathrm{m/s}^{2}$
B. $\text{19.3m/s}$
$0.175\mathrm{m/s}^{2}$
$0.240\mathrm{m/s}^{2}$
C. $\text{19.0m/s}$
$0.165\mathrm{m/s}^{2}$
$0.275\mathrm{m/s}^{2}$
D. $\text{22.8m/s}$
$0.178\mathrm{m/s}^{2}$
$0.235\mathrm{m/s}^{2}$
E. $\text{21.9m/s}$
$0.155\mathrm{m/s}^{2}$
$0.245\mathrm{m/s}^{2}$
F. $\text{18.5m/s}$
$0.165\mathrm{m/s}^{2}$
$0.260\mathrm{m/s}^{2}$
G. $\text{21.4m/s}$
$0.162\mathrm{m/s}^{2}$
$0.258\mathrm{m/s}^{2}$
H. $\text{20.7m/s}$
$0.150\mathrm{m/s}^{2}$
$0.270\mathrm{m/s}^{2}$
I. $\text{23.5m/s}$
$0.160\mathrm{m/s}^{2}$
$0.250\mathrm{m/s}^{2}$
J. $\text{22.0m/s}$
$0.182\mathrm{m/s}^{2}$
$0.265\mathrm{m/s}^{2}$
Answer: G
A point moves in the $x-y$ plane, with its radius given by $\boldsymbol{r}=2 t^{2} \boldsymbol{i} + \frac{2}{3} t^{3} \boldsymbol{j}$, where $r$ is measured in centimeters and $t$ in seconds. Find the radius of curvature $\rho$ and the velocity $v$ when $t=2s$.

Options:
A. $$
\rho=2 0. 4 \mathrm{m}, \; \; v=1 1. 0 \mathrm{m} / \mathrm{s}
$$
B. $$
\rho=1 9. 1 \mathrm{m}, \; \; v=1 0. 5 \mathrm{m} / \mathrm{s}
$$
C. $$
\rho=1 2. 4 \mathrm{m}, \; \; v=1 2. 9 \mathrm{m} / \mathrm{s}
$$
D. $$
\rho=1 7. 4 \mathrm{m}, \; \; v=8. 9 \mathrm{m} / \mathrm{s}
$$
E. $$
\rho=1 3. 5 \mathrm{m}, \; \; v=1 3. 7 \mathrm{m} / \mathrm{s}
$$
F. $$
\rho=1 6. 5 \mathrm{m}, \; \; v=1 0. 8 \mathrm{m} / \mathrm{s}
$$
G. $$
\rho=1 3. 7 \mathrm{m}, \; \; v=1 1. 9 \mathrm{m} / \mathrm{s}
$$
H. $$
\rho=1 8. 2 \mathrm{m}, \; \; v=9. 7 \mathrm{m} / \mathrm{s}
$$
I. $$
\rho=1 5. 8 \mathrm{m}, \; \; v=1 2. 1 \mathrm{m} / \mathrm{s}
$$
J. $$
\rho=1 4. 3 \mathrm{m}, \; \; v=1 1. 3 \mathrm{m} / \mathrm{s}
$$
Answer: J
The wind is blowing from the southwest at a speed of $v_{w} = 100 \text{ km/h}$. The airplane's nose is pointing 15° south of west, with a course of due west. Determine the airplane's speed relative to the air, $v_{r}$, and its speed relative to the ground, $v_{a}$.

Options:
A. $$
260 km/h
$$
$$
280km/h
$$
B. $$
280 km/h
$$
$$
250km/h
$$
C. $$
268 km/h
$$
$$
255km/h
$$
D. $$
285 km/h
$$
$$
245km/h
$$
E. $$
275 km/h
$$
$$
260km/h
$$
F. $$
273 km/h
$$
$$
264km/h
$$
G. $$
282 km/h
$$
$$
240km/h
$$
H. $$
255 km/h
$$
$$
265km/h
$$
I. $$
265 km/h
$$
$$
270km/h
$$
J. $$
290 km/h
$$
$$
258km/h
$$
Answer: F
The torque machine can generate a large amount of torque on the $O$ axis. The active component is the gear on the $C$ axis, which drives a screw with a pitch of $3mm$. When the screw rotates, it causes the internally threaded sleeve $B$ to move closer to point $C$. Given that the rotational speed of the screw is $100 rpm$, and the crank $OA=20cm$ is in a vertical position, find the angular acceleration $\varepsilon$ of $OA$ at this moment.

Options:
A. $$
5. 6 4 \times1 0^{-5} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
B. $$
0. 8 9 \times1 0^{-6} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
C. $$
7. 2 4 \times1 0^{-3} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
D. $$
- 3. 5 9 \times1 0^{-4} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
E. $$
- 9. 8 7 \times1 0^{-4} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
F. $$
- 4. 6 0 \times1 0^{-4} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
G. $$
3. 3 1 \times1 0^{-4} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
H. $$
6. 7 9 \times1 0^{-5} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
I. $$
1. 4 8 \times1 0^{-2} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
J. $$
2. 7 2 \times1 0^{-3} \mathbf{r} \mathrm{a d} / \mathbf{s}^{2}
$$
Answer: D
A spherical rigid container with a diameter of 1m has a vacuum level of 752.5 mmHg after the air is evacuated. If the local atmospheric pressure is 0.101 MPa, calculate: How much force in Newtons is exerted on the surface of the container?

Options:
A. $$
1.215 {\times} 10^{6} \, \mathrm{N}
$$
B. $$
1.305 {\times} 10^{6} \, \mathrm{N}
$$
C. $$
1.261 {\times} 10^{6} \, \mathrm{N}
$$
D. $$
1.100 {\times} 10^{6} \, \mathrm{N}
$$
E. $$
1.201 {\times} 10^{6} \, \mathrm{N}
$$
F. $$
1.460 {\times} 10^{6} \, \mathrm{N}
$$
G. $$
1.318 {\times} 10^{6} \, \mathrm{N}
$$
H. $$
1.180 {\times} 10^{6} \, \mathrm{N}
$$
I. $$
1.250 {\times} 10^{6} \, \mathrm{N}
$$
J. $$
1.270 {\times} 10^{6} \, \mathrm{N}
$$
Answer: C
In a certain process, a gas absorbs 50J of heat, and at the same time, the thermodynamic energy increases by 84J. Is this process one of expansion or compression? How much work is done on the surroundings in joules?

Options:
A. $$
- 66 \mathrm{J}
$$
B. $$
- 34 \mathrm{J}
$$
C. $$
- 84 \mathrm{J}
$$
D. $$
+ 66 \mathrm{J}
$$
E. $$
+ 84 \mathrm{J}
$$
F. $$
+ 34 \mathrm{J}
$$
G. $$
+ 50 \mathrm{J}
$$
H. $$
- 100 \mathrm{J}
$$
I. $$
+ 100 \mathrm{J}
$$
J. $$
- 50 \mathrm{J}
$$
Answer: B
The parameters of the pressurized water entering the 30mm inner diameter pipe of the steam generator are 10MPa and 30°C. Upon exiting the pipe, the parameters are 9MPa and 400°C. If the inlet volumetric flow rate is $\mathrm{3 L / s}$, find the heating rate. It is known that at the initial state $h=134.8 \mathrm{kJ} / \mathrm{kg}$ and $v=0.0010 \mathrm{m}^{3} / \mathrm{kg}$; at the final state $h=3117.5 \mathrm{kJ} / \mathrm{kg}$ and $v=0.0299 \mathrm{m}^{3} / \mathrm{kg}$.

Options:
A. $$
8990.4\mathrm{kW}
$$
B. $$
8456.7\mathrm{kW}
$$
C. $$
9214.5\mathrm{kW}
$$
D. $$
8800.0\mathrm{kW}
$$
E. $$
9530.1\mathrm{kW}
$$
F. $$
7689.4\mathrm{kW}
$$
G. $$
9875.6\mathrm{kW}
$$
H. $$
8972.2\mathrm{kW}
$$
I. $$
8300.3\mathrm{kW}
$$
J. $$
9123.8\mathrm{kW}
$$
Answer: H
When the medical oxygen bag is empty, it is in a flat state, with an internal volume of zero. It is connected to a steel oxygen cylinder with a pressure of 14 MPa and a temperature of 17°C for inflation. After inflation, the oxygen bag bulges, with a volume of $0.008 \mathrm{m}^3$ and a pressure of 0.15 MPa. Because the inflation process is very rapid, the heat exchange between the oxygen bag and the atmosphere can be ignored. Additionally, since the mass of gas filled in the oxygen bag is very small compared to the mass of the gas inside the steel cylinder, the parameters of the oxygen inside the cylinder can be assumed to remain unchanged. Assume that oxygen can be treated as an ideal gas, with its thermodynamic energy and enthalpy expressed as $\left\{u\right\}_{\mathrm{kJ}/\mathrm{kg}}=0.657\left\{T\right\}_{\mathrm{K}}$, and $\left\{h\right\}_{\mathrm{kJ}/\mathrm{kg}}=0.917\left\{T\right\}_{\mathrm{K}}$. The ideal gas follows the equation $pV=mR_{\mathrm{g}}T$. Calculate the mass of oxygen filled in the oxygen bag. For oxygen, $R_{\mathrm{g}}=260 \mathrm{J}/(\mathrm{kg}\cdot\mathrm{K})$.

Options:
A. $$
315.40 \mathrm{K},0.0150 \mathrm{kg}
$$
B. $$
312.00 \mathrm{K},0.0145 \mathrm{kg}
$$
C. $$
309.90 \mathrm{K},0.0154 \mathrm{kg}
$$
D. $$
310.80 \mathrm{K},0.0149 \mathrm{kg}
$$
E. $$
311.50 \mathrm{K},0.0152 \mathrm{kg}
$$
F. $$
313.20 \mathrm{K},0.0147 \mathrm{kg}
$$
G. $$
317.60 \mathrm{K},0.0139 \mathrm{kg}
$$
H. $$
314.10 \mathrm{K},0.0138 \mathrm{kg}
$$
I. $$
313.50 \mathrm{K},0.0140 \mathrm{kg}
$$
J. $$
316.30 \mathrm{K},0.0142 \mathrm{kg}
$$
Answer: F
At the initial state, the air has a temperature of $T_{1}=480 \mathrm{K}$ and a pressure of $p_{1}=0.2 \mathrm{MPa}$. Through a process of state change, it is heated to $T_{2}=1100 \mathrm{K}$, at which point the pressure is $p_{2}=0.5 \mathrm{MPa}$. Calculate the internal energy $u_{1}$, $u_{2}$, the change in internal energy $\Delta u$, the enthalpy $h_{1}$, $h_{2}$, and the change in enthalpy $\Delta h$ for 1 kg of air. (1) According to the average specific heat capacity table.

Options:
A. $$
671.4 \mathbf{kJ} / \mathbf{kg}
$$
B. $$
678.3 \mathbf{kJ} / \mathbf{kg}
$$
C. $$
690.0 \mathbf{kJ} / \mathbf{kg}
$$
D. $$
679.1 \mathbf{kJ} / \mathbf{kg}
$$
E. $$
663.5 \mathbf{kJ} / \mathbf{kg}
$$
F. $$
680.7 \mathbf{kJ} / \mathbf{kg}
$$
G. $$
672.8 \mathbf{kJ} / \mathbf{kg}
$$
H. $$
694.2 \mathbf{kJ} / \mathbf{kg}
$$
I. $$
705.1 \mathbf{kJ} / \mathbf{kg}
$$
J. $$
688.9 \mathbf{kJ} / \mathbf{kg}
$$
Answer: B
$\mathrm{CO_{2}}$ flows through a cooler in a constant pressure process, with $p_{1}=p_{2}=0.105 \ \mathrm{MPa}$, and the temperature cools from $600 \mathrm{K}$ to $366 \mathrm{K}$. Try using the arithmetic mean of specific heat capacity to calculate the change in thermodynamic energy, the change in enthalpy, and the change in entropy for $1 \ \mathrm{kg} \ \mathrm{CO_{2}}$.

Options:
A. $$
-0.5120 \mathrm{kJ} / \mathrm{kg}
$$
B. $$
-0.4732 \mathrm{kJ} / \mathrm{kg}
$$
C. $$
-0.5388 \mathrm{kJ} / \mathrm{kg}
$$
D. $$
-0.4821 \mathrm{kJ} / \mathrm{kg}
$$
E. $$
-0.4903 \mathrm{kJ} / \mathrm{kg}
$$
F. $$
-0.5673 \mathrm{kJ} / \mathrm{kg}
$$
G. $$
-0.4517 \mathrm{kJ} / \mathrm{kg}
$$
H. $$
-0.4689 \mathrm{kJ} / \mathrm{kg}
$$
I. $$
-0.5254 \mathrm{kJ} / \mathrm{kg}
$$
J. $$
-0.4996 \mathrm{kJ} / \mathrm{kg}
$$
Answer: E
Ammonia with a dryness of 0.6 and temperature of 0°C is heated in a rigid container with a volume of 200 L until the pressure reaches $p_{2}=1 \ \mathrm{MPa}$. Calculate the amount of heat added.

Options:
A. $$
750. 1 \mathrm{kJ}
$$
B. $$
730. 6 \mathrm{kJ}
$$
C. $$
650. 0 \mathrm{kJ}
$$
D. $$
740. 9 \mathrm{kJ}
$$
E. $$
678. 7 \mathrm{kJ}
$$
F. $$
721. 3 \mathrm{kJ}
$$
G. $$
700. 0 \mathrm{kJ}
$$
H. $$
735. 2 \mathrm{kJ}
$$
I. $$
695. 3 \mathrm{kJ}
$$
J. $$
710. 5 \mathrm{kJ}
$$
Answer: F
3 kg of air undergoes reversible adiabatic expansion from $p_{1}=1 \mathrm{~MPa}$, $T_{1}=900 \mathrm{~K}$ to $p_{2}=0.1 \mathrm{~MPa}$. Assuming the specific heat capacity is constant and the adiabatic index $\kappa=1.4$, calculate the process work and technical work.

Options:
A. $$
1350.20 \mathrm{k J}
$$
B. $$
1400.75 \mathrm{k J}
$$
C. $$
1295.30 \mathrm{k J}
$$
D. $$
1306.50 \mathrm{k J}
$$
E. $$
1325.90 \mathrm{k J}
$$
F. $$
1250.34 \mathrm{k J}
$$
G. $$
1375.80 \mathrm{k J}
$$
H. $$
1310.10 \mathrm{k J}
$$
I. $$
1280.45 \mathrm{k J}
$$
J. $$
1205.65 \mathrm{k J}
$$
Answer: D
Drop a metal rod with a mass of $m=0.36 \ \mathrm{kg}$ into water with a mass of $m_{w}=9 \ \mathrm{kg}$. Initially, the temperature of the metal rod is $T_{\mathrm{m, 1}}=1060 \ \mathrm{K}$, and the temperature of the water is $T_{\mathrm{w}}=295 \ \mathrm{K}$. The specific heat capacities of the metal rod and the water are $c_{\mathrm{m}}=420 \ \mathrm{J/(kg \cdot K)}$ and $c_{\mathrm{w}}=4187 \ \mathrm{J/(kg \cdot K)}$, respectively. Find: the final temperature $T_{c}$ and the change in entropy for the metal rod, the water, and the isolated system they form is(). Assume the container is adiabatic.

Options:
A. $$
294.9 \mathrm{K},-0.1856kJ/K,0.3781kJ/K,0.1925 {\mathrm{k J}} / {\mathrm{K}}
$$
B. $$
296.3 \mathrm{K},-0.1750kJ/K,0.3550kJ/K,0.1800 {\mathrm{k J}} / {\mathrm{K}}
$$
C. $$
293.7 \mathrm{K},-0.1798kJ/K,0.3607kJ/K,0.1909 {\mathrm{k J}} / {\mathrm{K}}
$$
D. $$
297.7 \mathrm{K},-0.1801kJ/K,0.3820kJ/K,0.2019 {\mathrm{k J}} / {\mathrm{K}}
$$
E. $$
298.8 \mathrm{K},-0.1950kJ/K,0.3952kJ/K,0.2002 {\mathrm{k J}} / {\mathrm{K}}
$$
F. $$
301.5 \mathrm{K},-0.1501kJ/K,0.3502kJ/K,0.2001 {\mathrm{k J}} / {\mathrm{K}}
$$
G. $$
300.0 \mathrm{K},-0.1905kJ/K,0.3905kJ/K,0.2050 {\mathrm{k J}} / {\mathrm{K}}
$$
H. $$
295.2 \mathrm{K},-0.1804kJ/K,0.3704kJ/K,0.1900 {\mathrm{k J}} / {\mathrm{K}}
$$
I. $$
299.8 \mathrm{K},-0.2002kJ/K,0.4005kJ/K,0.2003 {\mathrm{k J}} / {\mathrm{K}}
$$
J. $$
298.1 \mathrm{K},-0.1918kJ/K,0.3939kJ/K,0.2021 {\mathrm{k J}} / {\mathrm{K}}
$$
Answer: J
The front end of the gas engine serves as a diffuser section, followed by the compression section. If the airflow enters the diffuser section at a speed of 900 km/h, with an inflow temperature of -5°C and a pressure of 50 kPa. When the airflow exits the diffuser section and enters the compression section, its speed is 80 m/s, and the flow cross-sectional area is 80% of the entry cross-sectional area. Determine the pressure of the airflow as it enters the compression section.

Options:
A. $$
175.6kPa
$$
B. $$
220.1kPa
$$
C. $$
180.5kPa
$$
D. $$
165.2kPa
$$
E. $$
215.7kPa
$$
F. $$
190.7kPa
$$
G. $$
195.3kPa
$$
H. $$
200.4kPa
$$
I. $$
230.8kPa
$$
J. $$
205.9kPa
$$
Answer: E
In the compressor, the temperature of the compressed gas should not be excessively high, with the extreme limit being set at $150^\circ \mathrm{C}$. For a single-cylinder compressor, the pressure and temperature of the intake air are $p_{1}=0.1 \mathrm{MPa}, \; \; t_{1}=20^\circ \mathrm{C}$, with an intake volume of $250 \mathrm{m}^{3}/\mathrm{h}$. If the cooling water flowing through the cylinder liner of the compressor is $465 \mathrm{kg}/\mathrm{h}$ and the temperature rise is $14^\circ \mathrm{C}$, find the required power of the compressor.

Options:
A. $$
18.4kW
$$
B. $$
17.3kW
$$
C. $$
19.9kW
$$
D. $$
22.7kW
$$
E. $$
24.1kW
$$
F. $$
21.8kW
$$
G. $$
25.5kW
$$
```
H. $$
20.6kW
$$
I. $$
16.7kW
$$
J. $$
23.4kW
$$
Answer: A
A certain flow of air flows turbulently inside the steam heater pipes, with the temperature rising from 20°C to 80°C. Saturated steam with a pressure of 198.64 kPa (absolute pressure) condenses outside the pipes. Now, due to production needs, the air flow increases by 20%, while its inlet and outlet temperatures remain unchanged. How much should the pressure of the saturated steam be increased to accomplish this task? Assume that the thermal resistance of the pipe wall and fouling can be neglected.

Options:
A. 190.34kPa
B. 215.47kPa
C. 235.45kPa
D. 199.56kPa
E. 245.11kPa
F. 217.65kPa
G. 229.83kPa
H. 205.29kPa
I. 239.92kPa
J. 221.78kPa
Answer: G
Design a shell-and-tube condenser to use cold water to condense alcohol vapor, with a production capacity of 4000 kg·h$^{-1}$ of industrial alcohol. The inlet and outlet temperatures of the cooling water are 20°C and 40°C, respectively, and the operation is at atmospheric pressure. It is known that the heat transfer film coefficient of alcohol vapor is 1700 W·m$^{-2}$·K$^{-1}$, and the latent heat of vaporization of alcohol is 925 kJ·kg$^{-1}$. The boiling point is 78°C. What is the heat transfer coefficient $K$?

Options:
A. 750W·m$^{-2}$·K$^{-1}$
B. 780W·m$^{-2}$·K$^{-1}$
C. 800W·m$^{-2}$·K$^{-1}$
D. 720W·m$^{-2}$·K$^{-1}$
E. 770W·m$^{-2}$·K$^{-1}$
F. 730W·m$^{-2}$·K$^{-1}$
G. 790W·m$^{-2}$·K$^{-1}$
H. 740W·m$^{-2}$·K$^{-1}$
I. 760W·m$^{-2}$·K$^{-1}$
J. 810W·m$^{-2}$·K$^{-1}$
Answer: B
When drying a certain wet material with hot air, the following is known: the initial temperature of the air is 20°C, and the initial moisture content is 0.006 kg of water per kg of dry air. To ensure the quality of the dried product, the temperature of the air entering the dryer must not exceed 90°C. If the air is preheated to the maximum permissible temperature of 90°C and sent into a hypothetical ideal dryer, the exit temperature of the air is set at 60°C. What is the thermal efficiency of evaporating each kilogram of water?

Options:
A. 42.86%
B. 39.35%
C. 45.81%
D. 41.25%
E. 46.75%
F. 44.67%
G. 40.12%
H. 47.28%
I. 48.09%
J. 43.54%
Answer: A
For a first-order liquid phase reaction $\mathcal{A}\longrightarrow\mathbb{R}$, when conducted in a continuous stirred-tank reactor (CSTR), the conversion rate can reach 50%. What is the conversion rate if the process is transferred to a plug flow reactor (PFR) with the same effective volume, while keeping the reaction temperature, initial volumetric flow rate, and initial concentration unchanged?

Options:
A. 63.2%
B. 81.3%
C. 54.1%
D. 52.5%
E. 69.5%
F. 48.9%
G. 59.7%
H. 64.8%
I. 77.8%
J. 45.0%
Answer: A
The depth of the pile foundations for a river-crossing railway bridge is calculated according to the following assumptions: the pile foundations and the load must be balanced by the pressure from the soil at the bottom of the pile foundation and the friction on the sides of the pile foundation. The soil is saturated fine sand, which can be considered liquid. Assume the load on the pile foundation is 1500 kN, the weight of the pile foundation is 80 kN per meter of height, the pile foundation rises 9 m above the riverbed, the water level is 6 m above the riverbed, the bottom area of the pile foundation is $3.5 \mathrm{m}^{2}$, and the lateral area per meter of height is $7 \; \mathrm{m}^{2}$. The weight of sand saturated with water is 18 kN per cubic meter, the weight of water is 10 kN per cubic meter, and the pile is made of stone, enclosed in a steel casing, with a coefficient of friction with the sand of 0.18. What is the depth $h$ at which the pile foundation is buried ?
When calculating friction, the average lateral pressure per square meter can be taken as equal to 10 (6+0.9 h) kN.

Options:
A. $$
12.5 m
$$
B. $$
9.5 m
$$
C. $$
12 m
$$
D. $$
11 m
$$
E. $$
8 m
$$
F. $$
13 m
$$
G. $$
15 m
$$
H. $$
10 m
$$
I. $$
14 m
$$
J. $$
10.5 m
$$
Answer: D
On a ship with a displacement of 45,000 kN, a cargo weighing 300 kN is moved from the bow to a point 60 m from the stern. How much does the center of gravity of the ship and cargo as a whole shift?

Options:
A. $$
1.5 m
$$
B. $$
1.0 m
$$
C. $$
3.2 m
$$
D. $$
0.49 m
$$
E. $$
0.7 m
$$
F. $$
0.9 m
$$
G. $$
0.4 m
$$
H. $$
3.8 m
$$
I. $$
2.1 m
$$
J. $$
5.0 m
$$
Answer: G
A rigid body rotates around a fixed point. At a certain moment, the angular velocity vector of the rigid body projects onto the coordinate axes as $\sqrt{3}$, $\sqrt{5}$, $\sqrt{7}$. What is the velocity $v$ of a point on the rigid body with coordinates (V12, √20, √28) at this moment ?

Options:
A. $$2\sqrt{2}$$
B. $$1.5\sqrt{5}$$
C. $$0.9$$
D. $$\frac{\sqrt{3}}{2}$$
E. $$5$$
F. $$0$$
G. $$3\sqrt{3}$$
H. $$\sqrt{10}$$
I. $$2.5$$
J. $$4.2$$
Answer: F
A heavy object with a mass of 1000 kg, together with a sports car, moves along the horizontal bridge of an overhead crane at a speed of $v=1$ m/s. The distance from the center of mass of the object to the suspension point is $l=5 \mathrm{~m}$. When the crane suddenly stops, the object continues to move due to inertia, swinging around the suspension point. What is the maximum tension in the steel cable when the object swings ?

Options:
A. $$45 0 0 0 0 \mathrm{~ N}$$
B. $$30 0 0 0 0 \mathrm{~ N}$$
C. $$15 0 0 0 0 \mathrm{~ N}$$
D. $$35 0 0 0 0 \mathrm{~ N}$$
E. $$50 0 0 0 0 \mathrm{~ N}$$
F. $$20 0 0 0 0 \mathrm{~ N}$$
G. $$25 0 0 0 0 \mathrm{~ N}$$
H. $$1 0 0 0 0 \mathrm{~ N}$$
I. $$40 0 0 0 0 \mathrm{~ N}$$
J. $$55 0 0 0 0 \mathrm{~ N}$$
Answer: H
The rocket launches vertically from the lunar surface with an effective exhaust velocity of $v_{e}=2000 \ \mathrm{m/s}$. The Tsiolkovsky number $z$ is 5. To make the rocket reach a velocity of $v=3000 \ \mathrm{m/s}$, what is the burn time of the fuel ? ( It is assumed that the gravitational acceleration near the moon remains constant 1.62 m/s. )

Options:
A. $$\approx4min 9 s$$
B. $$\approx3min 15 s$$
C. $$\approx1min 55 s$$
D. $$\approx2min 50 s$$
E. $$\approx3min 2 s$$
F. $$\approx2min 16 s$$
G. $$\approx3min 7 s$$
H. $$\approx1min 8 s$$
I. $$\approx2min 4 s$$
J. $$\approx1min 5 s$$
Answer: I
For a perfect gas with $p=101,300 \mathrm{kPa}$ and $T=20 \mathrm{°C}$, it is known that $\mu=2 \times 10^{-5} \mathrm{Pa \cdot s}$, $\nu=15 \mathrm{mm}^2/s$, and $\mathcal{R}=8314 \mathrm{J}/(\mathrm{kg} \cdot \mathrm{mol} \cdot \mathrm{K})$. What is the molecular weight $M$?

Options:
A. 20.17
B. 44.01
C. 72.14
D. 64.12
E. 22.99
F. 10.81
G. 39.95
H. 18.02
I. 28.08
J. 32.06
Answer: J
Equation of motion for the steady two-dimensional flow of an ideal fluid along streamlines and their normal directions is().

Options:
A. $$
V \frac{\partial V} {\partial s}=f_{n}-\frac{1} {\rho} \frac{\partial\phi} {\partial n}
$$
$$
- \frac{V^{2}} {R_{p}}=f_{s}-\frac{1} {\rho} \ \frac{\partial p} {\partial s}
$$
B. $$
V \frac{\partial V} {\partial s}=f_{s}-\frac{1} {\rho} \frac{\partial p} {\partial s}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{s}-\frac{1} {\rho} \ \frac{\partial p} {\partial n}
$$
C. $$
V \frac{\partial V} {\partial p}=f_{n}-\frac{1} {\rho} \frac{\partial p} {\partial s}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{s}-\frac{1} {\rho} \ \frac{\partial n} {\partial phi}
$$
D. $$
V \frac{\partial V} {\partial n}=f_{n}-\frac{1} {\rho} \frac{\partial p} {\partial s}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{s}-\frac{1} {\rho} \ \frac{\partial n} {\partial p}
$$
E. $$
V \frac{\partial V} {\partial s}=f_{n}-\frac{1} {\rho} \frac{\partial n} {\partial phi}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{p}-\frac{1} {\rho} \ \frac{\partial phi} {\partial n}
$$
F. $$
V \frac{\partial V} {\partial n}=f_{s}-\frac{1} {\rho} \frac{\partial n} {\partial s}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{p}-\frac{1} {\rho} \ \frac{\partial\phi} {\partial n}
$$
G. $$
V \frac{\partial V} {\partial n}=f_{s}-\frac{1} {\rho} \frac{\partial\phi} {\partial s}
$$
$$
- \frac{V^{2}} {R_{n}}=f_{n}-\frac{1} {\rho} \ \frac{\partial p} {\partial s}
$$
H. $$
V \frac{\partial V} {\partial s}=f_{p}-\frac{1} {\rho} \frac{\partial n} {\partial p}
$$
$$
- \frac{V^{2}} {R_{n}}=f_{n}-\frac{1} {\rho} \ \frac{\partial\phi} {\partial s}
$$
I. $$
V \frac{\partial V} {\partial p}=f_{p}-\frac{1} {\rho} \frac{\partial\phi} {\partial n}
$$
$$
- \frac{V^{2}} {R_{s}}=f_{n}-\frac{1} {\rho} \ \frac{\partial n} {\partial p}
$$
J. $$
V \frac{\partial V} {\partial n}=f_{s}-\frac{1} {\rho} \frac{\partial p} {\partial phi}
$$
$$
- \frac{V^{2}} {R_{p}}=f_{n}-\frac{1} {\rho} \ \frac{\partial\phi} {\partial s}
$$
Answer: B
An aircraft is flying at a constant subsonic speed. Onboard, a Pitot tube measures $p = 82 \, \text{kN/m}^2$, $p = 54 \, \text{kN/m}^2$, and a total temperature gauge records $T_0 = 288 \, \text{K}$. The speed of the aircraft is ().

Options:
A. 229.8m/s
B. 269.4m/s
C. 284.0m/s
D. 254.6m/s
E. 315.5m/s
F. 299.7m/s
G. 245.1m/s
H. 178.3m/s
I. 192.5m/s
J. 213.7m/s
Answer: D
Glycerin with a flow rate of 20 L/s passes through a 45-meter-long circular pipe with a diameter of 100 mm, inclined at 15° to the horizontal. The dynamic viscosity (μ) of the glycerin is 0.9 Ns/m², and its density (ρ) is 1260 kg/m³. The inlet pressure is 590 kN/m². Neglecting end effects, the average shear stress on the wall surface is ().

Options:
A. $$
0. 3 6 1 1 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
B. $$
0. 1 1 4 5 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
C. $$
0. 3 8 4 7 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
D. $$
0. 2 6 9 2 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
E. $$
0. 2 2 7 4 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
F. $$
0. 1 5 7 2 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
G. $$
0. 2 9 5 8 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
H. $$
0. 1 8 3 6 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
I. $$
0. 2 0 1 9 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
J. $$
0. 0 9 4 8 ~ \mathrm{k N} / \mathrm{m}^{2}
$$
Answer: H
Known exact solution of the plane stagnation flow $U_{\bullet}=cx$: $O_{2}=0.292\sqrt{\frac{v}{c}},\tau_{\bullet}=1.233\mu cx\sqrt{\frac{c}{\nu}}$, $H= \frac {\delta _1}{\delta _2}= 2.21.$ Try using Squire's method to determine the value of H is ().

Options:
A. 3.30
B. 1.98
C. 3.15
D. 2.58
E. 2.45
F. 3.05
G. 1.75
H. 1.89
I. 2.65
J. 2.36
Answer: J
The air, with an average velocity of V=21.5 m/s, flows through a smooth pipe with an inner diameter of 40mm. The air density ρ is 1.225 kg/m³, and the dynamic viscosity coefficient μ is 1.8 × 10⁻⁵ Pa·s. We now intend to replace the air with water for a model experiment to determine the friction factor λ, where the water has a μ of 1.12 × 10⁻³ Pa·s and a ρ of 1000 kg/m³. If the measured pressure drop in a 1-meter long water pipe is 107.5 N/m², what is the value of λ?

Options:
A. $\lambda$=0.0029
B. $\lambda$=0.0025
C. $\lambda$=0.0043
D. $\lambda$=0.0041
E. $\lambda$=0.0037
F. $\lambda$=0.0032
G. $\lambda$=0.0027
H. $\lambda$=0.0028
I. $\lambda$=0.0035
J. $\lambda$=0.0038
Answer: F
In a gas cylinder with a volume of 1.77 m³, there was originally a certain amount of CO with an absolute pressure of 103.4 kPa at a temperature of 21°C. Later, 1.36 kg of CO was pumped in, and the temperature after the input was measured at 24°C. What is the absolute pressure is after the input ?

Options:
A. 185kPa
B. 180kPa
C. 175kPa
D. 176kPa
E. 172kPa
F. 169kPa
G. 158kPa
H. 190kPa
I. 167kPa
J. 162kPa
Answer: E
The diameter of the pipeline is $d \!=\! 25 \ \mathrm{mm}$, with $l_{1} \!=\! 8 \ \mathrm{m}$, $l_{2} \!=\! 1 \ \mathrm{m}$, and $H \!=\! 5 \ \mathrm{m}$. The nozzle diameter is $d_{0} = 10 \ \mathrm{mm}$. The elbow loss coefficient is $\zeta_{2} = 0.1$, the nozzle loss coefficient $\zeta_{3} = 0.1$, and the friction factor is $\lambda = 0.03$. The spray height $h$ is ().

Options:
A. 5.79m
B. 2.86m
C. 1.95m
D. 4.17m
E. 4.72m
F. 6.03m
G. 3.11m
H. 2.48m
I. 5.21m
J. 3.59m
Answer: J
$N$ identical mercury droplets carry the same type of charge and reach the same electric potential $U$. After these small mercury droplets merge into one large mercury droplet, what will be the electric potential $U'$ of the large mercury droplet? (Assume the mercury droplets are spherical.)

Options:
A. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N \cdot U^3
$$
B. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=\sqrt[3]{N^{2}} ~U
$$
C. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N^{1/3} / U
$$
D. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=\log(N) ~U^2
$$
E. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N^{-3} ~U
$$
F. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N^2 ~U^{-1}
$$
G. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N^{2/3} ~U^3
$$
H. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=\frac{U}{N^2}
$$
I. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=\sqrt{N} ~U
$$
J. $$
R=r \sqrt[3]{N}
$$
$$
U^{\prime}=N^{2/3} ~U^{-2}
$$
Answer: B
Assuming that the electromotive force of each battery is $E_{0}=2 \ \ \mathrm{V}$ and the internal resistance is $r_{0}=0.5 \ \ \Omega$. To ensure a current of $I=8 \ \ \mathrm{A}$ in a circuit with resistance $R=5 \ \ \Omega$, what is the minimum number of batteries $N$ needed? These batteries are connected in series in groups of $m$ each, what is the value of $m$?

Options:
A. $N=150,\ m=3$
B. $N=200,\ m=4$
C. $N=170,\ m=3$
D. $N=190,\ m=5$
E. $N=130,\ m=6$
F. $N=160,\ m=4$
G. $N=180,\ m=2$
H. $N=165,\ m=5$
I. $N=140,\ m=6$
J. $N=175,\ m=2$
Answer: F
A wire is bent into a $\Pi$ shape, with a mass of $m$. The upper segment is of length $l$, and it is situated in a uniform magnetic field with a magnetic flux density of $B$, where $B$ is perpendicular to the wire. The two ends of the wire below are inserted into two cups of mercury, which are connected to an external power source with a switch. When the switch $\mathrm{K}$ is turned on, the wire jumps out of the mercury cups to a height of $h$. What is the amount of electrical charge $q$ passing through the wire?

Options:
A. $$
q={\frac{m} {B l}} {\sqrt{g h}}
$$
B. $$
q={\frac{m} {2 B l}} {\sqrt{g h}}
$$
C. $$
q={\frac{m} {B l}} {\sqrt{2 h g}}
$$
D. $$
q={\frac{m} {B^2 l}} {\sqrt{2 g h}}
$$
E. $$
q={\frac{l} {B m}} {\sqrt{2 g h}}
$$
F. $$
q=-{\frac{m} {B l}} {\sqrt{2 g h}}
$$
G. $$
q={\frac{m} {B l}} {\sqrt{2 g h}}
$$
H. $$
q={\frac{m^2} {B l}} {\sqrt{2 g h}}
$$
I. $$
q={\frac{m} {B l^2}} {\sqrt{2 g h}}
$$
J. $$
q={\frac{m} {B l}} {\sqrt{4 g h}}
$$
Answer: G
An aircraft is flying 10 kilometers from a certain radio station, receiving a signal strength of $S=10 \mu\mathrm{W / m^{2}}$ from the station. What is the transmission power of the radio station (assuming the transmission is isotropic and ignoring Earth's reflection)?

Options:
A. $$
5. \, 1 \times1 0^{4} \, \mathrm{~W}
$$
B. $$
4. \, 2 \times1 0^{4} \, \mathrm{~W}
$$
C. $$
3. \, 7 \times1 0^{4} \, \mathrm{~W}
$$
D. $$
2. \, 5 \times1 0^{4} \, \mathrm{~W}
$$
E. $$
1. \, 3 \times1 0^{4} \, \mathrm{~W}
$$
F. $$
6. \, 9 \times1 0^{4} \, \mathrm{~W}
$$
G. $$
7. \, 8 \times1 0^{4} \, \mathrm{~W}
$$
H. $$
9. \, 6 \times1 0^{4} \, \mathrm{~W}
$$
I. $$
0. \, 5 \times1 0^{4} \, \mathrm{~W}
$$
J. $$
8. \, 4 \times1 0^{4} \, \mathrm{~W}
$$
Answer: E
When sunlight strikes the ground perpendicularly, the energy per square centimeter reaching the ground per minute is 1.94 cal. Given that 1 cal equals 4.1868 J, what are the amplitudes of the electric field intensity $E$ and the magnetic field intensity $H$ of the sunlight on the ground, denoted as $E_{0}$ and $H_{0}$ respectively?

Options:
A. $$E_{0}=6. 0 9 \times1 0^{2}\mathrm{~V / m},\ H_{0}=1. 8 2\mathrm{~A} / \mathrm{m}$$
B. $$E_{0}=5. 4 8 \times1 0^{3}\mathrm{~V / m},\ H_{0}=7. 3 1\mathrm{~A} / \mathrm{m}$$
C. $$E_{0}=2. 9 1 \times1 0^{3}\mathrm{~V / m},\ H_{0}=8. 4 2\mathrm{~A} / \mathrm{m}$$
D. $$E_{0}=8. 3 3 \times1 0^{3}\mathrm{~V / m},\ H_{0}=3. 5 0\mathrm{~A} / \mathrm{m}$$
E. $$
E_{0}=1. 0 1 \times1 0^{3}\mathrm{~V / m},\ H_{0}=2. 6 8\mathrm{~A} / \mathrm{m}
$$
F. $$E_{0}=4. 1 7 \times1 0^{3}\mathrm{~V / m},\ H_{0}=5. 9 6\mathrm{~A} / \mathrm{m}$$
G. $$E_{0}=9. 9 9 \times1 0^{2}\mathrm{~V / m},\ H_{0}=1. 1 0\mathrm{~A} / \mathrm{m}$$
H. $$E_{0}=3. 7 4 \times1 0^{3}\mathrm{~V / m},\ H_{0}=2. 3 7\mathrm{~A} / \mathrm{m}$$
I. $$E_{0}=7. 2 5 \times1 0^{3}\mathrm{~V / m},\ H_{0}=4. 6 7\mathrm{~A} / \mathrm{m}$$
J. $$E_{0}=1. 5 0 \times1 0^{2}\mathrm{~V / m},\ H_{0}=6. 1 9\mathrm{~A} / \mathrm{m}$$
Answer: E
An alternating current passes through a resistor $R$. After a capacitor $C$ is connected in parallel with $R$, assume the current magnitude remains unchanged (i.e., the total current through the parallel circuit equals the current through $R$ when $C$ is not connected). If $R = 30 \mathrm{k} \Omega$ and $C = 0.33 \mu\mathrm{F}$, at what frequency does the voltage across $R$ decrease by 5%?

Options:
A. $$
6. 0~\mathrm{H z}
$$
B. $$
5. 9~\mathrm{H z}
$$
C. $$
5. 3~\mathrm{H z}
$$
D. $$
2. 5~\mathrm{H z}
$$
E. $$
8. 4~\mathrm{H z}
$$
F. $$
7. 2~\mathrm{H z}
$$
G. $$
4. 8~\mathrm{H z}
$$
H. $$
3. 7~\mathrm{H z}
$$
I. $$
1. 6~\mathrm{H z}
$$
J. $$
9. 1~\mathrm{H z}
$$
Answer: C
An object with mass $m$ vibrates along the $x$-axis under the influence of an elastic force $-k x$, a damping force $-\alpha\; {\frac{\mathrm{d} x} {\mathrm{d} t}}$, and a driving force $F_{0} \cos \omega t$. Due to the similarity of the motion equations (differential equations), its motion can be modeled by a series circuit of $R, L, C$ with an alternating voltage $\mathscr{E}=\mathscr{E}_{0} \sin \omega t$. What are the corresponding electrical quantities for mass $m$, stiffness coefficient $k$, damping coefficient $\alpha$, and the quality factor $Q$ of the driving force?

Options:
A. $$
Q={\frac{\alpha} {k}} \sim{\sqrt{\frac{L} {C}} R}
$$
B. $$
Q={\frac{m \alpha} {k}} \sim{\frac{C} {R}} \sqrt{L}
$$
C. $$
Q={\frac{k} {\alpha}} \sim{\frac{\sqrt{L C}} {R}}
$$
D. $$
Q={\frac{\alpha m} {\sqrt{k}}} \sim{\frac{R} {L}} \sqrt{\frac{C} {L}}
$$
E. $$
Q={\frac{\sqrt{k m}} {a}} \sim{\frac{1} {R}} \sqrt{\frac{L} {C}}
$$
F. $$
Q={\frac{k \alpha} {m}} \sim{\sqrt{L C}} R
$$
G. $$
Q={\frac{\sqrt{m \alpha}} {k}} \sim{R} \sqrt{\frac{C} {L}}
$$
H. $$
Q={\frac{k} {m}} \sim{\frac{R} {\sqrt{L C}}}
$$
I. $$
Q={\frac{m} {k}} \sim{\frac{L} {R}} \sqrt{C}
$$
J. $$
Q={\frac{\alpha} {\sqrt{m}}} \sim{\frac{R} {L}} \sqrt{C}
$$
Answer: E
The electric charge $Q$ is uniformly distributed on the surface of a sphere with radius $a$. When this sphere rotates around one of its fixed diameters at a constant angular velocity $\omega$, what is the magnetic field energy inside the sphere?

Options:
A. $$
\frac{\mu_{0} Q \omega^{2} a^{3}} {5 8 \pi}
$$
B. $$
\frac{\mu_{0} Q^{2} \omega^{3} a^{2}} {6 4 \pi}
$$
C. $$
\frac{\mu_{0} Q^{2} \omega a^{2}} {15 4 \pi}
$$
D. $$
\frac{\mu_{0} Q^{2} \omega a^{4}} {10 \pi}
$$
E. $$
\frac{\mu_{0} Q^{2} \omega^{2} a} {5 4 \pi}
$$
F. $$
\frac{\mu_{0} Q^{4} \omega^{2} a} {5 4 \pi^{2}}
$$
G. $$
\frac{\mu_{0} Q \omega^{2} a^{3}} {3 4 \pi}
$$
H. $$
\frac{\mu_{0} Q^{3} \omega a^{2}} {5 4 \pi}
$$
I. $$
\frac{\mu_{0} Q^{2} \omega^{2} a^{2}} {7 8 \pi}
$$
J. $$
\frac{\mu_{0} Q^{3} \omega^{2} a} {8 4 \pi}
$$
Answer: E
A superconducting ring with a radius of $R$ and self-inductance $L$ is placed in a uniform magnetic field with magnetic flux density $B$, with the axis of the ring perpendicular to $B$, and there is no current in the ring. Now the ring is rotated 90° around a diameter perpendicular to $B$, aligning its axis parallel to $B$. How much work is done by the external force?

Options:
A. $$
\frac{\pi^{3} R^{4} B^{2}} {L}
$$
B. $$
\frac{\pi^{2} R^{5} B^{2}} {2 L}
$$
C. $$
\frac{\pi^{2} R^{4} B} {L^2}
$$
D. $$
\frac{\pi R^{4} B^{3}} {2 L}
$$
E. $$
\frac{\pi^{4} R^{4} B^{2}} {3 L}
$$
F. $$
\frac{\pi^{2} R^{2} B^{3}} {2 L}
$$
G. $$
\frac{\pi^{2} R^{4} B^{2}} {2 L}
$$
H. $$
\frac{\pi^{2} R^{4} B^{2}} {L^2}
$$
I. $$
\frac{2 \pi^{3} R^{2} B^{2}} {L}
$$
J. $$
\frac{\pi R^{3} B^{2}} {L}
$$
Answer: G
An infinitely long straight cylindrical tube with a radius of $a$ is uniformly charged, and its surface charge density is $\sigma$. It starts rotating from rest at time $t=0$ with a constant angular acceleration $\alpha$ around its geometric axis. At time $t$, what is the induced electric field intensity $E_{R}$ at a location outside the tube at a distance $R$ from the axis?

Options:
A. $$
E_{R}=\frac{\mu_{0} a^{4} \pmb{\sigma} \times \pmb{\alpha}}{2 R^{2}}
$$
B. $$
E_{R}=\frac{\mu_{0} a^{3} \pmb{\sigma} \times \pmb{\alpha} R}{R^{2}}
$$
C. $$
E_{R}=\frac{\mu_{0} a^{3} R \times \pmb{\sigma} \pmb{\alpha}}{2 R^{2}}
$$
D. $$
E_{R}=\frac{\mu_{0} a^{3} \pmb{\sigma} R \times\pmb{\alpha}} {2 R^{2}}
$$
E. $$
E_{R}=\frac{\mu_{0} \pmb{\sigma} a^{3} R \times \pmb{\alpha}}{2 R^{4}}
$$
F. $$
E_{R}=\frac{\mu_{0} a^{2} \pmb{\sigma} R \times \pmb{\alpha}}{R^{2}}
$$
G. $$
E_{R}=\frac{\epsilon_{0} a^{3} \pmb{\sigma} \times \pmb{\alpha}}{2 R^{3}}
$$
H. $$
E_{R}=\frac{\mu_{0} a^{3} R \pmb{\sigma} \times \pmb{\alpha}}{2 R}
$$
I. $$
E_{R}=\frac{\mu_{0} a^{3} \pmb{\sigma} \pmb{\alpha} \times R}{2 R^{2}}
$$
J. $$
E_{R}=\frac{\mu_{0} a^{3} \pmb{\sigma} R \pmb{\alpha}}{2 R^{2}}
$$
Answer: D
At the interface between air $( \mu_{\mathrm{r}} = 1 )$ and soft iron $( \mu_{\mathrm{r}} = 7000 )$, the angle between the magnetic flux density in the soft iron and the normal to the interface is $85^{\circ}$. What is the angle between the magnetic flux density in the air and the normal to the interface?

Options:
A. $$
30^{\prime}
$$
B. $$
60^{\prime}
$$
C. $$
70^{\prime}
$$
D. $$
25^{\prime}
$$
E. $$
20^{\prime}
$$
F. $$
45^{\prime}
$$
G. $$
90^{\prime}
$$
H. $$
15^{\prime}
$$
I. $$
5. 6^{\prime}
$$
J. $$
10^{\prime}
$$
Answer: I
An air parallel plate capacitor has plates separated by 1.0 mm and a voltage of 1000 V applied. Neglecting edge effects, remove the power supply and fill the space between the two plates with gasoline of dielectric constant $e=2.0$, and then a voltage of 1000 V is applied, what is the electrostatic force per unit area on the plates at this time?

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