MikaStars39/nano-eval huggingface dataset:
A factory produces 1,000 kg per day of nylon-66 with an average relative molecular mass of 18,000, and the relative molecular mass is controlled by an excess of adipic acid. When the degree of reaction of hexamethylenediamine is 0.998, how many kilograms of hexamethylenediamine and adipic acid are needed per day?

Options:
A. $$
5 3 4 \mathrm{g},\ 7 0 1 \mathrm{k g}
$$
B. $$
5 5 0 \mathrm{g},\ 6 5 3 \mathrm{k g}
$$
C. $$
5 8 0 \mathrm{g},\ 6 9 0 \mathrm{k g}
$$
D. $$
5 1 4 \mathrm{g},\ 6 5 3 \mathrm{k g}
$$
E. $$
4 9 8 \mathrm{g},\ 6 8 5 \mathrm{k g}
$$
F. $$
5 1 2 \mathrm{g},\ 6 5 1 \mathrm{k g}
$$
G. $$
5 1 4 \mathrm{g},\ 6 4 8 \mathrm{k g}
$$
H. $$
5 1 4 \mathrm{g},\ 7 0 5 \mathrm{k g}
$$
I. $$
4 5 0 \mathrm{g},\ 7 1 0 \mathrm{k g}
$$
J. $$
6 0 0 \mathrm{g},\ 6 5 3 \mathrm{k g}
$$
Answer: D
Given the following data and relationships: Trans configuration $( t ), \varphi_{i}=0, U ( t )=0$; Gauche configuration $( g\ or\ g^{\prime} ), \varphi_{i}=\pm120, U ( g\ or\ g^{\prime})=3.34 \textrm{kJ} \cdot\mathrm{mol}^{-1}$, $T = 298 \mathrm{~K}, R = 8.31 \mathrm{~J \cdot~ K^{-1} ~ \cdot~ mol^{-1} ~, ~} \mathrm{~ \overline{{{{\cos \varphi_t}}}} ~}=\sum_{i=1}^{3} N_{i} \cos \varphi_{i} {\Big/} \sum_{i=1}^{3} N_{i}$, where $N_{i}=\exp \Bigl( {\frac{-U_{i}} {R T}} \Bigr)$. What is the maximum elongation ratio of the polyethylene chain when the bond numbers are $n=100$ and $n=1000$, respectively?

Options:
A. $2.97,\ 9.5$
B. $4.05,\ 11.3$
C. $3.65,\ 12.3$
D. $2.85,\ 8.9$
E. $3.39,\ 10.7$
F. $3.00,\ 10.0$
G. $4.21,\ 11.8$
H. $2.73,\ 9.1$
I. $3.47,\ 10.9$
J. $3.11,\ 10.2$
Answer: E
What does CPU stand for?

Options:
A. Core Processor Entity, Cache, Arithmetic
B. Computational Processing Core, Control Device
C. Central Power Unit, Encoder, Controller
D. Arithmetic Unit, Controller, and Cache
E. Binary Processor, Data Encoder, Controller
F. Control Panel Unit, Arithmetic Processor, Core
G. Central Processing Entity, Cache Switcher
H. Central Unit, Device Controller, Arithmetic
I. Computational Unit, Cache Handler, Control
J. Central Unit, Arithmetic Handler, Encoder
Answer: D
The clock frequency of a certain synchronous bus is 100MHz, with a width of 32 bits, and the address/data lines are multiplexed. Each transmission of an address or data occupies one clock cycle. If the bus supports burst mode transmission, what is the minimum time required for a "main memory write" bus transaction to transfer 128 bits of data?

Options:
A. 20ns
B. 100ns
C. 40ns
D. 70ns
E. 10ns
F. 80ns
G. 90ns
H. 60ns
I. 30ns
J. 50ns
Answer: J
An 8K×8-bit dynamic RAM chip has an internal structure arranged in a 256×256 format, with an access cycle of $0.1\mu\mathrm{s}$. What is the refresh interval for the distributed refresh method?

Options:
A. $$
4 9. 9 \mu\mathrm{s}
$$
B. $$
5 4. 2 \mu\mathrm{s}
$$
C. $$
6 0. 3 \mu\mathrm{s}
$$
D. $$
5 1. 2 \mu\mathrm{s}
$$
E. $$
5 5. 0 \mu\mathrm{s}
$$
F. $$
5 6. 8 \mu\mathrm{s}
$$
G. $$
5 0. 5 \mu\mathrm{s}
$$
H. $$
4 8. 6 \mu\mathrm{s}
$$
I. $$
5 3. 1 \mu\mathrm{s}
$$
J. $$
5 2. 4 \mu\mathrm{s}
$$
Answer: D
In various types of memory, both ROM and RAM use random access methods. What type of memory does not use random access methods?

Options:
A. Magnetic Disk
B. EEPROM
C. SSD
D. Flash Drive
E. CD-ROM
F. DRAM
G. Tape Drive
H. Hard Disk
I. Cache Memory
J. SRAM
Answer: E
In the input-output system of a program query method, assuming processing time is not considered, each query operation requires 100 clock cycles, and the CPU's clock frequency is 50MHz. Currently, there are two devices: a mouse and a hard disk. The CPU must query the mouse 30 times per second, and the hard disk transfers data in 32-bit word units, meaning it's queried by the CPU once per 32 bits, with a transfer rate of 2MB/s. Calculate the time ratio the CPU spends querying the disk is ().

Options:
A. 85%
B. 110%
C. 75%
D. 65%
E. 150%
F. 105%
G. 98%
H. 130%
I. 120%
J. 90%
Answer: F
The process of floating-point addition and subtraction generally includes steps such as aligning the decimal points, performing the mantissa operation, normalization, rounding, and overflow checking. Assume that both the exponent and mantissa of the floating-point numbers are represented using two's complement notation, with bit lengths of 5 and 7 respectively (including 2 sign bits each). Given two numbers $x=2^{7}\times29/32$ and $y=2^{5}\times5/8$, what is the final result of calculating $x+y$ using floating-point addition?

Options:
A. Invalid mantissa values.
B. Precision error detected.
C. Incorrect rounding.
D. Overflow occurred.
E. Zero result obtained.
F. Fraction part lost.
G. Overflow in mantissa.
H. Exponent misalignment.
I. Underflow occurred.
J. Subnormal number produced.
Answer: D
In a certain computer system, the main memory address has m bits, and the machine word length is n bits, where m > n. If the instruction set uses a fixed-length format, the direct register addressing mode has the fastest execution speed, while the memory indirect addressing mode has the slowest execution speed. If a variable-length format is used, the immediate addressing mode executes the fastest, and the memory indirect addressing mode executes the slowest. The direct addressing mode has the longest instruction length, so which addressing mode has the shortest instruction length?

Options:
A. Register Indirect Addressing Mode
B. Base Register Addressing Mode
C. Accumulator Addressing Mode
D. Stack Addressing Mode
E. Index Register Addressing Mode
F. Memory Direct Addressing Mode
G. Memory Indirect Addressing Mode
H. Relative Addressing Mode
I. Direct Register Addressing Mode
J. Immediate Addressing Mode
Answer: I
Dissolve 9.73 mg of 2.4-dimethyl-1,3-pentadiene in 10 mL of ethanol. Then dilute it to 1000 mL. Measure the ultraviolet absorption of this solution using a cuvette with path length of 1 cm. The absorbance \( $A$ \) is 1.02. Calculate the molar absorptivity coefficient \( $\varepsilon$ \) of the compound.

Options:
A. $$
\mathrm{ 2 5 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
B. $$
\mathrm{ 5 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
C. $$
\mathrm{ 9 5 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
D. $$
\mathrm{ 1 3 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
E. $$
\mathrm{ 1 5 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
F. $$
\mathrm{ 8 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
G. $$
\mathrm{ 1 2 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
H. $$
\mathrm{ 3 0 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
I. $$
\mathrm{ 2 0 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
J. $$
\mathrm{ 1 0 ~ 0 0 0 ~ L \cdot~ m o l^{-1} \cdot~ c m^{-1}}
$$
Answer: J
In industry, an alcoholic solution of sodium ethoxide is prepared by heating ethanol and sodium hydroxide in benzene. In the reaction system of ethanol, benzene, and water, water is the least component, and if it can be continuously removed, it will favor the forward reaction. Ethanol, benzene, and water form a ternary azeotropic mixture with a composition ratio of: ethanol 18.5%, benzene 74.1%, water 7.4%, and an azeotropic point of ____, which is distilled first.

Options:
A. Dynamic, $72.5^{\circ} \ \mathrm{C}$
B. Balanced, $75.8^{\circ} \ \mathrm{C}$
C. Stationary, $80.5^{\circ} \ \mathrm{C}$
D. Equilibrial, $78.3^{\circ} \ \mathrm{C}$
E. Neutral, $70.2^{\circ} \ \mathrm{C}$
F. Static, $67.1^{\circ} \ \mathrm{C}$
G. Irreversible, $85.0^{\circ} \ \mathrm{C}$
H. Reversible, $69.7^{\circ} \ \mathrm{C}$
I. Unfavorable, $63.0^{\circ} \ \mathrm{C}$
J. Favorable, $64.9^{\circ} \ \mathrm{C}$
Answer: J
Dissolve lysine in water. What should be added to bring it to its isoelectric point?

Options:
A. A sprinkle of calcium carbonate
B. A large quantity of alcohol
C. A small amount of sodium chloride
D. A small dose of sodium bicarbonate
E. A little bit of potassium hydroxide
F. A small amount of ethanol
G. A small volume of hydrogen peroxide
H. A small amount of acetone
I. A small amount of acid
J. A tiny pinch of glucose
Answer: I
The genotype of a certain organism is AaBb. After meiosis of an oocyte, an egg cell with a genome composed of Ab and three polar bodies are produced. The genetic composition of these three polar bodies is ().

Options:
A. $$
\mathrm{A b, ~ A B, ~ a b}
$$
B. $$
\mathrm{A B, ~ A B, ~ a b}
$$
C. $$
\mathrm{a b, ~ a b, ~ A b}
$$
D. $$
\mathrm{a b, ~ A B, ~ A B}
$$
E. $$
\mathrm{a b, ~ a B, ~ A B}
$$
F. $$
\mathrm{a b, ~ A b, ~ a b}
$$
G. $$
\mathrm{a B, ~ A B, ~ a B}
$$
H. $$
\mathrm{A b, ~ a B, ~ a B}
$$
I. $$
\mathrm{A B, ~ a B, ~ a b}
$$
J. $$
\mathrm{A B, ~ A b, ~ a b}
$$
Answer: H
After crossing two homozygous strains of snapdragons (Antirrhinum) with white flowers, the following results were obtained:
Strain 1 × Strain 2
↓
$\mathbf{F}_{1}$ All white flowers
$\mathbf{F}_{2}$ 131 plants with white flowers 29 plants with red flowers
Predict the results of backcrossing $\mathbf{F}_{1}$ with each of the two parent strains is().

Options:
A. $$
\begin{array} {c c c} {{1 / 4}} & {{A a b B}} & {{Red Flower}} \\ {{1 / 4}} & {{A a B B}} & {{White Flower}} \\ {{1 / 4}} & {{a a B b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a b b}} & {{White Flower}} \\ \end{array}
$$
B. $$
\begin{array} {c c c} {{1 / 4}} & {{A a B b}} & {{White Flower}} \\ {{1 / 4}} & {{A A b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a B B}} & {{Red Flower}} \\ {{1 / 4}} & {{a a b b}} & {{White Flower}} \\ \end{array}
$$
C. $$
\begin{array} {c c c} {{1 / 4}} & {{A A b b}} & {{Red Flower}} \\ {{1 / 4}} & {{A a b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a B b}} & {{White Flower}} \\ {{1 / 4}} & {{a a b b}} & {{White Flower}} \\ \end{array}
$$
D. $$
\begin{array} {c c c} {{1 / 4}} & {{A a B B}} & {{Red Flower}} \\ {{1 / 4}} & {{A a B b}} & {{White Flower}} \\ {{1 / 4}} & {{a a b B}} & {{White Flower}} \\ {{1 / 4}} & {{a a b b}} & {{Red Flower}} \\ \end{array}
$$
E. $$
\begin{array} {c c c} {{1 / 4}} & {{A a b b}} & {{White Flower}} \\ {{1 / 4}} & {{A a B B}} & {{Red Flower}} \\ {{1 / 4}} & {{a a b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a A B B}} & {{White Flower}} \\ \end{array}
$$
F. $$
\begin{array} {c c c} {{1 / 4}} & {{A A B b}} & {{White Flower}} \\ {{1 / 4}} & {{A A b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a B b}} & {{White Flower}} \\ \end{array}
$$
G. $$
\begin{array} {c c c} {{1 / 4}} & {{A a B B}} & {{White Flower}} \\ {{1 / 4}} & {{A a b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a B b}} & {{Red Flower}} \\ {{1 / 4}} & {{A A b b}} & {{White Flower}} \\ \end{array}
$$
H. $$
\begin{array} {c c c} {{1 / 4}} & {{A a B b}} & {{White Flower}} \\ {{1 / 4}} & {{A a b b}} & {{Red Flower}} \\ {{1 / 4}} & {{a a B b}} & {{White Flower}} \\ {{1 / 4}} & {{A A B B}} & {{Red Flower}} \\ \end{array}
$$
I. $$
\begin{array} {c c c} {{1 / 4}} & {{A a B b}} & {{Red Flower}} \\ {{1 / 4}} & {{A a b b}} & {{White Flower}} \\ {{1 / 4}} & {{a a b b}} & {{White Flower}} \\ {{1 / 4}} & {{a a B b}} & {{Red Flower}} \\ \end{array}
$$
J. $$
\begin{array} {c c c} {{1 / 4}} & {{A A B b}} & {{Red Flower}} \\ {{1 / 4}} & {{A a b b}} & {{White Flower}} \\ {{1 / 4}} & {{a a B b}} & {{White Flower}} \\ {{1 / 4}} & {{A a B B}} & {{Red Flower}} \\ \end{array}
$$
Answer: I
The absence of horns trait D is dominant over the presence of horns trait d, and the heterozygous combination of red hair R and white hair r results in chestnut color. If a homozygous hornless white cow mates with a horned red bull, how will the offspring of the F1 generation mating with the horned red bull parent appear in terms of traits and proportions?

Options:
A. Horned red : horned white : polled chestnut : horned chestnut = 1:1:1:1
B. Horned white : horned chestnut : polled red : polled chestnut = 1:1:1:1
C. Horned red : polled chestnut : horned white : polled red = 1:1:1:1
D. Polled white : polled chestnut : horned red : horned white = 1:1:1:1
E. Horned white : horned chestnut : polled chestnut : polled red = 1:1:1:1
F. Horned red : polled white : polled chestnut : horned chestnut = 1:1:1:1
G. Polled red : horned chestnut : polled white : horned red = 1:1:1:1
H. Polled white : horned red : polled red : horned chestnut = 1:1:1:1
I. Polled white : horned chestnut : polled red : horned white = 1:1:1:1
J. Polled red : polled chestnut : horned red : horned chestnut = 1:1:1:1
Answer: J
In chickens, white feathers are dominant over colored feathers, feathered legs are dominant over non-feathered legs, and pea combs are dominant over single combs. If purebred white-feathered, feathered-leg, pea comb chickens are crossed with colored-feathered, non-feathered-leg, single comb chickens, and the F1 generation of white-feathered, feathered-leg, pea comb chickens is selected to cross with colored-feathered, non-feathered-leg, single comb chickens to test for homozygosity, what is the proportion of this homozygosity?

Options:
A. 1/18
B. 1/30
C. 1/27
D. 1/32
E. 1/16
F. 1/24
G. 1/26
H. 1/14
I. 1/22
J. 1/20
Answer: C
A type of cucumber (Echballium elaterium) has two sexes, dioecious. Its sex is not determined by sex chromosomes, but rather depends on two pairs of alleles: $M$ determines male fertility, $m$ determines male sterility; $F$ determines female sterility, $f$ determines male fertility. In nature, approximately 50% of this plant's individuals are male and 50% are female. Occasionally, monoecious types appear, but they are extremely rare. Monoecious individuals have both male and female reproductive organs on the same plant. What is the genotype of the female plant?

Options:
A. $$MF/mF$$
B. $$mF/mF$$
C. $$MF/mf$$
D. $$mF/mf$$
E. $$Mf/mf$$
F. $$Mf/MF$$
G. $$MF/MF$$
H. $$mF/Mf$$
I. $$mf/mf$$
Answer: I
The recombination rate between the two linked genes wz (waxy) and sh (shrunken) located on chromosome 9 of maize is 36%. What is the probability of at least one crossover occurring between these two genes in cells undergoing meiosis?

Options:
A. 0.78
B. 0.58
C. 0.66
D. 0.68
E. 0.82
F. 0.54
G. 0.74
H. 0.64
I. 0.72
J. 0.70
Answer: I
In the following hybrid combinations, the offspring exhibit only one phenotype ().

Options:
A. $EeFF\times EEFf$
B. $EEff\times eeFF$
C. $EEEf\times Eeff$
D. $EeFf\times EEFf$
E. $eeFF\times EEFf$
F. $eeFf\times EeFF$
G. $Eeff\times EEFf$
H. $EeFf\times eeFF$
I. $EEFF\times eeFf$
J. $EEff\times EeFf$
Answer: A
The red eyes (W) in Drosophila are dominant over white eyes (w), with the gene located on the X chromosome. Crossing a red-eyed female fruit fly with a white-eyed father and a white-eyed male fruit fly results in offspring consisting of 25% red-eyed female fruit flies, 25% red-eyed male fruit flies, 25% white-eyed female fruit flies, and 25% white-eyed male fruit flies. The genotypes of the parent fruit flies are ().

Options:
A. $$
\mathbf{X}^{w} \mathbf{X}^{w} \times\mathbf{X}^{w} \mathbf{Y}
$$
B. $$
\mathbf{X}^{w} \mathbf{X}^{w} \times\mathbf{X}^{W} \mathbf{Y}
$$
C. $$
\mathbf{X}^{w} \mathbf{X}^{W} \times\mathbf{X}^{W} \mathbf{Y}
$$
D. $$
\mathbf{X}^{W} \mathbf{X}^{W} \times\mathbf{X}^{W} \mathbf{Y}
$$
E. $$
\mathbf{X}^{W} \mathbf{X}^{w} \times\mathbf{X}^{w} \mathbf{Y}
$$
F. $$
\mathbf{X}^{W} \mathbf{X}^{w} \times\mathbf{X}^{W} \mathbf{Y}
$$
G. $$
\mathbf{X}^{W} \mathbf{X}^{W} \times\mathbf{X}^{w} \mathbf{Y}
$$
H. $$
\mathbf{X}^{w} \mathbf{X}^{W} \times\mathbf{X}^{w} \mathbf{Y}
$$
Answer: A
If a bomber dives at an angle of $\theta=45^{\circ}$ with a diving speed of $u=1000\mathbf{km/h}$ and an altitude of $h=1800\mathbf{m}$, how far ahead of the target should the bomber release the bomb, at angle $\delta$, in order to hit the target?

Options:
A. $5^{\circ}$
B. $1^{\circ}$
C. $8^{\circ}$
D. $7^{\circ}$
E. $6^{\circ}$
F. $10^{\circ}$
G. $4^{\circ}$
H. $3^{\circ}$
I. $9^{\circ}$
J. $2^{\circ}$
Answer: A
The car is traveling at a speed of $v_0=64\text{ km/h}$ when it notices a red light at an intersection $460m$ ahead. The red light lasts for $15s$, and the green light lasts for $30s$. If the driver wants to pass through the intersection just as the green light appears, determine the car's acceleration and its speed when it passes the intersection at $460m$.

Options:
A. $a=1.70\mathrm{m/s^{2}},\quad v=41.5\mathrm{m/s}$
B. $a=1.60\mathrm{m/s^{2}},\quad v=40.0\mathrm{m/s}$
C. $a=2.00\mathrm{m/s^{2}},\quad v=45.0\mathrm{m/s}$
D. $a=1.65\mathrm{m/s^{2}},\quad v=47.5\mathrm{m/s}$
E. $a=1.90\mathrm{m/s^{2}},\quad v=48.0\mathrm{m/s}$
F. $a=1.75\mathrm{m/s^{2}},\quad v=42.5\mathrm{m/s}$
G. $a=1.72\mathrm{m/s^{2}},\quad v=43.6\mathrm{m/s}$
H. $a=1.95\mathrm{m/s^{2}},\quad v=49.0\mathrm{m/s}$
I. $a=1.85\mathrm{m/s^{2}},\quad v=46.0\mathrm{m/s}$
J. $a=1.80\mathrm{m/s^{2}},\quad v=44.0\mathrm{m/s}$
Answer: G
The missile is launched from point $O$, and its trajectory in the vertical plane is shown in Figure 1-19. The tracking station at point $O$ can record the instantaneous polar coordinates of the missile, $r$ and $\theta$, and approximately gives their functional relationships as $r=2t-\frac{t^2}{40}$, $\theta^{2}=1600-t^{2}$, where $r$ is measured in kilometers, $\theta$ in degrees, and $t$ in seconds. Find the velocity and acceleration of the missile when $t=30s$.

Options:
A. $1.000km/s$
$0.5km/s^{2}$
B. $0.300km/s$
$0.7km/s^{2}$
C. $0.894km/s$
$0.1km/s^{2}$
D. $0.600km/s$
$0.9km/s^{2}$
E. $1.200km/s$
$0.2km/s^{2}$
F. $1.100km/s$
$0.8km/s^{2}$
G. $0.750km/s$
$0.3km/s^{2}$
H. $0.450km/s$
$0.4km/s^{2}$
I. $1.050km/s$
$0.1km/s^{2}$
J. $0.800km/s$
$0.6km/s^{2}$
Answer: C
Planes $A$, $B$, and $C$ are flying in adjacent airspaces along straight flight paths. Currently, plane $A$ observes the velocities of planes $B$ and $C$ as $v_{B / A}=4i-6j+8k$ and $v_{C / A}=2i+8j+12k$, respectively. Find the velocity of plane $B$ relative to plane $C$, $v_{B / C}$.

Options:
A. $$
0 i-1 4 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
B. $$
4 i-1 4 \, \boldsymbol{j}+1 0 \boldsymbol{k}
$$
C. $$
2 i-1 9 \, \boldsymbol{j}+1 0 \boldsymbol{k}
$$
D. $$
1 i+1 4 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
E. $$
4 i-1 3 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
F. $$
3 i-1 4 \, \boldsymbol{j}+3 0 \boldsymbol{k}
$$
G. $$
5 i+2 4 \, \boldsymbol{j}-1 0 \boldsymbol{k}
$$
H. $$
2 i-1 4 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
I. $$
1 i-1 8 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
J. $$
3 i-1 0 \, \boldsymbol{j}+2 0 \boldsymbol{k}
$$
Answer: H
A wall that is 6 meters high is subjected to water pressure over its entire vertical surface. Where is the center of water pressure on the wall ?

Options:
A. It lies $0.5 \ \mathrm{m}$ underwater
B. It lies $6 \ \mathrm{m}$ above base
C. It is $4 \ \mathrm{m}$ underwater
D. It is $5.5 \ \mathrm{m}$ underwater
E. It lies $5 \ \mathrm{m}$ above base
F. It is $2.5 \ \mathrm{m}$ underwater
G. It lies $1 \ \mathrm{m}$ below surface
H. It is $3.5 \ \mathrm{m}$ underwater
I. It is $2 \ \mathrm{m}$ underwater
J. It is $3 \ \mathrm{m}$ underwater
Answer: C
In a certain steam power plant, for every $1 MW$ of energy added to the boiler, $0.58 MW$ of energy must be discharged from the condenser, while the water pump consumes $0.02 MW$ of work. Determine the turbine's output power and the thermal efficiency of the power plant.

Options:
A. $$
0.45 \mathrm{MW}
$$
$$
0. 4 0
$$
B. $$
0.44 \mathrm{MW}
$$
$$
0. 4 2
$$
C. $$
0.40 \mathrm{MW}
$$
$$
0. 3 9
$$
D. $$
0.46 \mathrm{MW}
$$
$$
0. 4 3
$$
E. $$
0.42 \mathrm{MW}
$$
$$
0. 4 4
$$
F. $$
0.50 \mathrm{MW}
$$
$$
0. 4 7
$$
G. $$
0.41 \mathrm{MW}
$$
$$
0. 3 7
$$
H. $$
0.47 \mathrm{MW}
$$
$$
0. 4 5
$$
I. $$
0.43 \mathrm{MW}
$$
$$
0. 3 8
$$
J. $$
0.48 \mathrm{MW}
$$
$$
0. 4 1
$$
Answer: B
In the summer, to avoid direct sunlight, keep doors and windows closed and use an electric fan for cooling. Assuming the initial temperature in the room is 28°C and the pressure is 0.1 MPa, the power of the electric fan is 0.06 kW, and the heat transmitted by direct sunlight is 0.1 kW. If there are three people inside the room, each emitting heat to the environment at a rate of 418.7 kJ per hour, and the heat loss through the walls is 1800 kJ/h, find the hourly increase in temperature of the air in a room with an area of 15 m² and a height of 3.0 m is(). It is known that the relationship between the thermodynamic energy of air and temperature is given by:
$$
\Delta u = 0.72 \{\Delta T\}_{\mathrm{k}} \, \mathrm{kJ} / \mathrm{kg}
$$

Options:
A. $$
1.10 \mathrm{K}
$$
B. $$
0.89 \mathrm{K}
$$
C. $$
1.04 \mathrm{K}
$$
D. $$
0.92 \mathrm{K}
$$
E. $$
0.67 \mathrm{K}
$$
F. $$
0.78 \mathrm{K}
$$
G. $$
0.97 \mathrm{K}
$$
H. $$
1.15 \mathrm{K}
$$
I. $$
0.75 \mathrm{K}
$$
J. $$
0.86 \mathrm{K}
$$
Answer: J
In a certain steam power plant, the boiler supplies steam to a steam turbine at a rate of 40t/h. The pressure gauge at the inlet reads 9 MPa, and the specific enthalpy of the steam is 3441 kJ/kg. The vacuum gauge at the steam turbine outlet reads 0.0974 MPa, and the specific enthalpy of the outlet steam is 2248 kJ/kg. The heat dissipation to the environment by the turbine is $6.81 \times 10^{5} \, \mathrm{kJ/h}$. Find: How the power output of the steam turbine is affected when the inlet steam velocity is 70 m/s and the outlet velocity is 140 m/s.

Options:
A. $$
12500kW
$$
B. $$
11000kW
$$
C. $$
12985kW
$$
D. $$
13000kW
$$
E. $$
13456kW
$$
F. $$
14567kW
$$
G. $$
12000kW
$$
H. $$
11890kW
$$
I. $$
13500kW
$$
J. $$
11234kW
$$
Answer: C
Two men, each weighing $80 \mathrm{kg}$, eat the same food every day and complete the same work. However, $\mathbf{A}$ walks to and from work for 60 minutes each day, while $\mathbf{B}$ drives a car for 20 minutes each day for commuting and spends the other 40 minutes watching TV. Try to determine the weight difference between the two individuals after 100 workdays.

Options:
A. $$
3.89kg
$$
B. $$
6.18kg
$$
C. $$
6.67kg
$$
D. $$
2.47kg
$$
E. $$
1.43kg
$$
F. $$
4.04kg
$$
G. $$
3.02kg
$$
H. $$
5.56kg
$$
I. $$
5.02kg
$$
J. $$
7.31kg
$$
Answer: F
In a sealed container with a volume of $V=0.5 \mathrm{m}^{3}$, there is oxygen at 27°C and 0.6 MPa. After heating, the temperature rises to 327°C, based on constant specific heat capacity.

Options:
A. $$
768.45kJ
$$
B. $$
881.60kJ
$$
C. $$
808.27kJ
$$
D. $$
754.32kJ
$$
E. $$
843.19kJ
$$
F. $$
652.58kJ
$$
G. $$
912.45kJ
$$
H. $$
820.92kJ
$$
I. $$
799.84kJ
$$
J. $$
735.77kJ
$$
Answer: C
In the cylinder-piston system, there are 3 $\mathbf{kg}$ of $O_{2}$ at a pressure of 1 MPa and a temperature of 27 C. The gas in the cylinder is heated to 327 C, and at this point, the pressure is 1500 kPa. Due to the external spring on the piston, the pressure and volume in the cylinder change linearly. If the specific heat capacity of $O_{2}$ can be taken as a constant, $c_{\nu}=0.658 \ {\bf kJ} / ( {\bf kg} \cdot{\bf K} ), R_{\nu}=0.260 \ {\bf kJ} / ( {\bf kg} \cdot{\bf K} )$. Determine the heat transfer during the process.

Options:
A. $$
720.5 \mathrm{kJ}
$$
B. $$
629.4 \mathrm{kJ}
$$
C. $$
650.2 \mathrm{kJ}
$$
D. $$
670.0 \mathrm{kJ}
$$
E. $$
689.7 \mathrm{kJ}
$$
F. $$
698.1 \mathrm{kJ}
$$
G. $$
701.9 \mathrm{kJ}
$$
H. $$
740.8 \mathrm{kJ}
$$
I. $$
712.3 \mathrm{kJ}
$$
J. $$
755.6 \mathrm{kJ}
$$
Answer: E
There is 2.3 kg of CO, with an initial state of $T_{1}=477 \mathrm{~K}$, $p_{1}=0.32 \mathrm{~MPa}$. It undergoes a reversible constant volume heating process to a final temperature of $T_{2}=600 \mathrm{~K}$. Assuming CO is an ideal gas, find $\Delta U$, $\Delta H$, and $\Delta S$. Determine the work done and heat transfer during the process. The specific heat capacity varies and should be calculated according to the properties of the gas.

Options:
A. $$
317.50kJ
$$
B. $$
299.30kJ
$$
C. $$
178.80kJ
$$
D. $$
265.40kJ
$$
E. $$
352.15kJ
$$
F. $$
148.37kJ
$$
G. $$
158.45kJ
$$
H. $$
209.94kJ
$$
I. $$
198.60kJ
$$
J. $$
190.72kJ
$$
Answer: H
In a certain cylinder, the initial parameters of the air are $p_{1}=8 \mathrm{~MPa,}\; t_{1}=1300°C$. After undergoing a reversible polytropic process, the final state is $p_{2}=0.4 \mathrm{~MPa,}\; t_{2}=400 \mathrm{~}^{\circ} \mathrm{C}$. The gas constant of the air is $R_{g}=0.287\ \mathbf{kJ} / (\mathbf{kg} \cdot\mathbf{K})$. Try to calculate the amount of heat absorbed according to the following method: the specific heat capacity is a linear function of temperature $\left\{c_{\nu} \right\}_{\mathrm{wit (kg\ K)}}=0.7088+0.000186 \left\{t \right\}_{\mathrm{^{\circ}c}}$.

Options:
A. $$
8.1kJ/kg
$$
B. $$
5.5kJ/kg
$$
C. $$
9.3kJ/kg
$$
D. $$
5.9kJ/kg
$$
E. $$
8.5kJ/kg
$$
F. $$
7.2kJ/kg
$$
G. $$
6.2kJ/kg
$$
H. $$
4.7kJ/kg
$$
I. $$
6.9kJ/kg
$$
J. $$
7.8kJ/kg
$$
Answer: I
Before firing the air pistol, the air pressure inside the barrel is 250 kPa, the temperature is 27°C, and the volume is $1 \, \text{cm}^3$. The bullet, locked by the trigger, acts like a piston sealing the compressed air. When the trigger is pulled, the bullet is released. If the air pressure inside the barrel is 100 kPa and the temperature is 235 K when the bullet exits, determine the volume of the air at that moment, the work done by the air during the process, and the entropy production per unit mass of air.

Options:
A. $$
16.3 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
B. $$
13.5 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
C. $$
17.7 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
D. $$
20.1 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
E. $$
15.8 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
F. $$
19.2 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
G. $$
14.7 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
H. $$
21.3 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
I. $$
18.5 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
J. $$
22.6 \mathrm{J} / ( \mathrm{k g} \cdot\mathrm{K} )
$$
Answer: C
The exhaust gas pressure from the internal combustion engine is 0.2 MPa, with a temperature of $550 ^{\circ}\mathrm{C}$, and a flow velocity of $110 \mathrm{m/s}$. If it is introduced into a converging nozzle, try to determine the error caused by neglecting the inlet flow velocity when the back pressure is 0.1 MPa.

Options:
A. $$
0.36 \%
$$
B. $$
1.25 \%
$$
C. $$
1.64 \%
$$
D. $$
0.54 \%
$$
E. $$
0.18 \%
$$
F. $$
0.92 \%
$$
G. $$
1.05 \%
$$
H. $$
3.12 \%
$$
I. $$
0.82 \%
$$
J. $$
2.45 \%
$$
Answer: A
Using a single-cylinder piston compressor to prepare compressed air at 0.8 MPa, it is known that the cylinder diameter is $D=300 \, \mathrm{mm}$, the piston stroke is $S=200 \, \mathrm{mm}$, and the clearance volume ratio is 0.05. The shaft speed is 400 r/min, and the intake air parameters of the compressor are $p_{1}=0.1 \, \mathrm{MPa}$ and $t_{1}=20^{\circ} \mathrm{C}$. The polytropic index of the compression process is $n=1.25$. If the isothermal efficiency of the compressor is $\eta_{\mathrm{c}, T}=0.77$, try to calculate the compressor output (in $\mathbf{kg/h}$) and the power required by the prime mover to drive the compressor (assuming external friction losses of the compressor are negligible).

Options:
A. $$
16.0 kW
$$
B. $$
22.0 kW
$$
C. $$
25.0 kW
$$
D. $$
18.5 kW
$$
E. $$
15.0 kW
$$
F. $$
21.5 kW
$$
G. $$
19.0 kW
$$
H. $$
17.5 kW
$$
I. $$
20.0 kW
$$
J. $$
23.5 kW
$$
Answer: I
A horizontal shell and tube condenser has heat exchange steel tubes with a diameter of $\phi$ 25mm×2mm and a length of 3m. Water at 17°C flows inside the tubes with a velocity of 0.7 m/s, exiting at a temperature of 37°C. Saturated hydrocarbon vapor at a temperature of 72°C condenses outside the tubes with a flow rate of 1.25 kg/s, and the latent heat of condensation for the hydrocarbon vapor is 315 kJ/kg. It is known that the heat transfer film coefficient for condensing vapor $\alpha_0$ is 800 W·m$^{-2}$·°C$^{-1}$, the heat resistance on the inside of the tube is 40% of that on the outside, and the fouling resistance is 70% of the heat resistance on the inside of the tube. Heat conduction through the tube walls and heat loss are ignored during calculations. The specific heat capacity of water at constant pressure is 4.18 kJ/kg·°C. What is the heat transfer area per pass of the heat exchanger using the outer surface as the basis?

Options:
A. $5.39m^{2}$
B. $5.82m^{2}$
C. $3.14m^{2}$
D. $3.56m^{2}$
E. $6.13m^{2}$
F. $7.49m^{2}$
G. $2.89m^{2}$
H. $6.57m^{2}$
I. $4.71m^{2}$
J. $4.25m^{2}$
Answer: I
Place a simple second-order liquid-phase reaction in both a Plug Flow Reactor (PFR) and a Continuous Stirred Tank Reactor (CSTR). If the initial volumetric flow rate $q_\mathrm{V.o}$ and the initial concentration $c_\mathrm{\Lambda\omega}$ are approximately the same, and the final conversion rate is 50%. What is the volume efficiency of the CSTR (Vp/Vc)?

Options:
A. 1.2
B. 1.5
C. 0.8
D. 0.7
E. 1.0
F. 2.3
G. 0.3
H. 0.6
I. 0.5
J. 0.9
Answer: I
Given that the dry-bulb temperature of moist air is 40°C, the relative humidity is 60%, and the total pressure is 101.3 $kPa$. What is the dew point?

Options:
A. $4.10kPa$
B. $5.26kPa$
C. $4.38kPa$
D. $5.67kPa$
E. $4.91kPa$
F. $6.45kPa$
G. $4.42kPa$
H. $3.74kPa$
I. $3.89kPa$
J. $5.03kPa$
Answer: G
Two weights, one 10N and the other 5N, are suspended at different positions on the same rope, with the heavier one hanging lower and the lighter one hanging higher. Assuming the top of the rope is fixed, what is the tension in the rope?

Options:
A. $$
6 \mathrm{~ N},1 4 \mathrm{~ N}
$$
B. $$
1 0 \mathrm{~ N},1 5 \mathrm{~ N}
$$
C. $$
7 \mathrm{~ N},1 3 \mathrm{~ N}
$$
D. $$
0 \mathrm{~ N},2 0 \mathrm{~ N}
$$
E. $$
5 \mathrm{~ N},1 0 \mathrm{~ N}
$$
F. $$
5 \mathrm{~ N},1 5 \mathrm{~ N}
$$
G. $$
10 \mathrm{~ N},5 \mathrm{~ N}
$$
H. $$
1 0 \mathrm{~ N},2 0 \mathrm{~ N}
$$
I. $$
8 \mathrm{~ N},1 7 \mathrm{~ N}
$$
J. $$
7 \mathrm{~ N},1 0 \mathrm{~ N}
$$
Answer: B
The small wheel with a radius of $r = 50$ mm rolls steadily along the inclined plane. The material in contact is steel, and the rolling friction coefficient is $k = 0.05$ mm. What is the inclination angle $\alpha$ of this inclined plane ? ( Since the angle $\alpha$ is very small, it can be considered that $\alpha = \tan \alpha$ . )

Options:
A. $$
5'30"
$$
B. $$
2'45"
$$
C. $$
5'05"
$$
D. $$
1'58"
$$
E. $$
3'50"
$$
F. $$
3'26"
$$
G. $$
4'15"
$$
H. $$
3'10"
$$
I. $$
4'00"
$$
J. $$
2'30"
$$
Answer: F
The train is traveling at a speed of 72 km/h. During braking, the train has an acceleration of $0.4 \ \mathrm{m/s^{2}}$ in the direction opposite to its velocity.
What are the braking time and braking distance of the train ?

Options:
A. $$48 s, 520 m$$
B. $$55 s, 490 m$$
C. $$47 s, 540 m$$
D. $$54 s, 460 m$$
E. $$50 s, 500 m$$
F. $$49 s, 530 m$$
G. $$46 s, 550 m$$
H. $$53 s, 470 m$$
I. $$52 s, 480 m$$
J. $$45 s, 560 m$$
Answer: E
A rod $AB$ of length 0.2 m undergoes planar motion. The accelerations of points $A$ and $B$ are both perpendicular to $AB$, pointing in opposite directions, with magnitudes equal to $2 \ \mathrm{m} / \mathrm{s}^{2}$. What are the angular velocity, the angular acceleration of the rod, and the acceleration of the midpoint $C$ ?

Options:
A. $$1, \, 1 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 2$$
B. $$0, \, 2 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 0$$
C. $$3, \, 2 5 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 0$$
D. $$2, \, 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 1$$
E. $$0, \, 7 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 2$$
F. $$3, \, 4 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 1$$
G. $$1, \, 5 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 3$$
H. $$5, \, 6 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 0$$
I. $$2, \, 1 5 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 1$$
J. $$4, \, 3 0 \, \, \mathrm{r a d} / \mathrm{s}^{2}, 2$$
Answer: B
It is known that the air resistance is $R=k \sigma v^{2}$, where $\boldsymbol{v}$ is the velocity of motion, $\sigma$ is the projected area of the object in the direction of vertical motion, and $k$ is a coefficient related to the shape of the object. For a sphere, this coefficient is $0.24 \mathrm{~N} \cdot \mathrm{s}^{2} / \mathrm{m}^{4}$. What is the maximum falling speed of a sphere with a mass of 10 $\mathbf{kg}$ and a radius of $r=8$ cm ?

Options:
A. $$1 6 2. 9 \ \mathrm{m / s}$$
B. $$1 5 8. 4 \ \mathrm{m / s}$$
C. $$1 4 9. 7 \ \mathrm{m / s}$$
D. $$1 6 9. 0 \ \mathrm{m / s}$$
E. $$1 4 2. 5 \ \mathrm{m / s}$$
F. $$1 2 0. 4 \ \mathrm{m / s}$$
G. $$1 2 6. 8 \ \mathrm{m / s}$$
H. $$1 5 3. 1 \ \mathrm{m / s}$$
I. $$1 3 0. 2 \ \mathrm{m / s}$$
J. $$1 3 5. 6 \ \mathrm{m / s}$$
Answer: E
The speed of the meteorite at infinity is equal to 10 km/s. What is its speed when entering the Earth's atmosphere ?

Options:
A. $$\approx5 0 \mathrm{~ k m / s}$$
B. $$\approx3 5 \mathrm{~ k m / s}$$
C. $$\approx3 0 \mathrm{~ k m / s}$$
D. $$\approx2 5 \mathrm{~ k m / s}$$
E. $$\approx4 0 \mathrm{~ k m / s}$$
F. $$\approx4 5 \mathrm{~ k m / s}$$
G. $$\approx1 5 \mathrm{~ k m / s}$$
H. $$\approx6 0 \mathrm{~ k m / s}$$
I. $$\approx2 0 \mathrm{~ k m / s}$$
J. $$\approx5 5 \mathrm{~ k m / s}$$
Answer: G
Cup-type micro-manometer, cup diameter $\mathbf{D}=50 \mathbf{mm}$, connecting tube diameter $d=5 \mathrm{mm}$, specific weight of kerosene $\gamma_{2}=8142 \mathbf{N} / \mathbf{m}^{3}$, specific weight of ethanol $\gamma_{1}=8535 \mathrm{N} / \mathrm{m}^{3}$, when $p_{1}=p_{2}$ the interface between kerosene and ethanol is at 0-0. Now, given $h=280 \mathrm{mm}$, What is the $p_{1}-p_{2}$?

Options:
A. 161.3 $\mathbf{N} / \mathbf{m}^{3}$
B. 157.5 $\mathbf{N} / \mathbf{m}^{3}$
C. 156.7 $\mathbf{N} / \mathbf{m}^{3}$
D. 153.4 $\mathbf{N} / \mathbf{m}^{3}$
E. 149.5 $\mathbf{N} / \mathbf{m}^{3}$
F. 162.8 $\mathbf{N} / \mathbf{m}^{3}$
G. 158.3 $\mathbf{N} / \mathbf{m}^{3}$
H. 150.9 $\mathbf{N} / \mathbf{m}^{3}$
I. 160.1 $\mathbf{N} / \mathbf{m}^{3}$
J. 154.2 $\mathbf{N} / \mathbf{m}^{3}$
Answer: C
In an originally stationary, unbounded, incompressible, ideal fluid domain, there is a spherical boundary moving with a radius $R_{s}=R_{b}(t)$. Given that the pressure at infinity on the horizontal plane passing through the center of the sphere is $p_{∞}$, and the fluid density is $\rho$, what is the pressure distribution in the flow field?

Options:
A. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}+\frac{R_{b}\dot{R}_{b}^{2}-R_{b}^3\ddot{R}_{b}}{R^2}-\frac{1}{2}\frac{R_{b}^{4}\dot{R}_{b}}{R^{4}}-gR\mathrm{cos}\theta\mathrm{cos} \alpha$
B. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}-\frac{R_{b}\dot{R}_{b}^{3}+R_{b}^{2}\ddot{R}_{b}}{R^{3}}+\frac{1}{2}\frac{R_{b}^{5}\dot{R}_{b}}{R^{5}}+gR\mathrm{sin}\theta\mathrm{sin} \beta$
C. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}+\frac{R_{b}^{3}\dot{R}_{b}^{2}+R\ddot{R}_{b}}{R^{3}}-\frac{1}{2}\frac{R_{b}^{4}}{R^{2}}-gR\mathrm{sin}\epsilon\mathrm{cos} \beta$
D. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}+\frac{R\dot{R}_{b}^{2}-2R_{b}^{2}\ddot{R}_{b}}{R^{2}}+\frac{1}{2}\frac{R_{b}^{3}\dot{R}_{b}^{3}}{R^{5}}-gR\mathrm{cos}\theta\mathrm{sin} \delta$
E. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}-\frac{2R_{b}\dot{R}_{b}+R_{b}^{2}\ddot{R}_{b}}{R^{2}}+\frac{1}{2}\frac{R_{b}^{3}\dot{R}_{b}^{2}}{R^3}+gR\mathrm{cos}\theta\mathrm{cos} \epsilon$
F. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}+\frac{2R_{b}\dot{R}_{b}^{2}+R_{b}^{2}\ddot{R}_{b}}{R}-\frac{1}{2}\frac{R_{b}^{4}\dot{R}_{b}^{2}}{R^{4}}-gR\mathrm{sin}\theta\mathrm{cos} \epsilon$
G. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}-\frac{R_{b}^{2}\dot{R}_{b}^{2}+R_{b}\ddot{R}_{b}}{R^3}+\frac{1}{2}\frac{R_{b}^{5}\ddot{R}_{b}^{3}}{R^{6}}-gR\mathrm{sin}\theta\mathrm{sin} \delta$
H. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}-\frac{2R_{b}^{2}\dot{R}_{b}+R\ddot{R}_{b}}{R^{4}}+\frac{1}{2}\frac{R_{b}^{6}\dot{R}_{b}^{2}}{R^{5}}+gR\mathrm{cos}\epsilon\mathrm{sin} \theta$
I. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}-\frac{R_{b}\dot{R}_{b}^{2}-R_{b}^{2}\ddot{R}_{b}}{R}+\frac{1}{2}\frac{R_{b}^{4}\dot{R}_{b}^{3}}{R^{3}}+gR\mathrm{sin}\theta\mathrm{sin} \gamma$
J. $\quad\frac{p}{\rho}=\frac{p_{\infty}}{\rho}+\frac{2R_{b}\ddot{R}_{b}+R\dot{R}_{b}^{2}}{R}-\frac{1}{2}\frac{R_{b}^{4}\ddot{R}_{b}^{2}}{R^{6}}-gR\mathrm{sin}\epsilon\mathrm{cos} \theta$
Answer: F
The air flows steadily within a variable cross-section duct. At the known cross-sectional area of 0.01314 $m^{2}$, the temperature $T_{\mathfrak{a}}$ is 38°C, $\dot{p}=41,37 \mathrm{kN/m^{2}}, \ \ \dot{m}=1 \mathrm{kg/s}$. The Mach number of the flow at this cross-section is ().

Options:
A. 0.455
B. 0.613
C. 0.578
D. 0.697
E. 0.489
F. 0.750
G. 0.638
H. 0.532
I. 0.521
J. 0.874
Answer: A
The water flows through a horizontally placed galvanized steel pipe, with $l=300 \mathrm{m}, \; \; d=150 \mathrm{mm}, \; \; \nu=1.14 \mathrm{mm}^{2}/s$, $Q=50 \mathrm{l/s}$. the friction head loss is ().

Options:
A. 25.7m
B. 19.6m
C. 20.5m
D. 22.2m
E. 15.4m
F. 16.8m
G. 14.7m
H. 12.3m
I. 18.1m
J. 23.9m
Answer: F
At an altitude of 1 km, a balloon with a diameter of $d = 1 \mathrm{m}$ is tethered by a rope, which makes an angle of 60° with the ground. Disregarding the weight of the balloon, what is the wind speed $V_{\infty}$?

Options:
A. 4.40m/s
B. 4.20m/s
C. 4.30m/s
D. 4.14m/s
E. 4.25m/s
F. 4.00m/s
G. 3.95m/s
H. 3.80m/s
I. 3.90m/s
J. 4.35m/s
Answer: D
The airplane flies at a high altitude with a speed of 400 m/s, where the temperature T is 228 K and the pressure p is 30.2 kN/m². Now, a scaled-down model, 20 times smaller, is used for a simulation experiment in the wind tunnel. It is known that the air temperature T in the wind tunnel is 288 K, and the dynamic viscosity coefficient $\mu \approx \frac{T^{1.5}}{T+117}$. The pressure in the wind tunnel is ().

Options:
A. 900kN/m²
B. 1200kN/m²
C. 700kN/m²
D. 1400kN/m²
E. 1000kN/m²
F. 1300kN/m²
G. 500kN/m²
H. 1100kN/m²
I. 600kN/m²
J. 820kN/m²
Answer: J
For a certain oil, at 20°C, the refractive index is 3.2°E, and at 70°C, the refractive index is 1.6°E. Its viscosity-temperature index $\lambda$ is ().

Options:
A. $$
\lambda=0.06{°C}^{-1}
$$
B. $$
\lambda=0.07{°C}^{-1}
$$
C. $$
\lambda=0.04{°C}^{-1}
$$
D. $$
\lambda=0.02{°C}^{-1}
$$
E. $$
\lambda=0.10{°C}^{-1}
$$
F. $$
\lambda=0.00{°C}^{-1}
$$
G. $$
\lambda=0.08{°C}^{-1}
$$
H. $$
\lambda=0.01{°C}^{-1}
$$
I. $$
\lambda=0.03{°C}^{-1}
$$
J. $$
\lambda=0.05{°C}^{-1}
$$
Answer: D
When using a water pipeline with a diameter of 60 cm at the pump station, the head loss along the pipe is 27 m. To reduce the head loss, another pipe of the same length is added in parallel, and the head loss after parallel connection is reduced to 9.6 m. Assuming the friction coefficients along both pipes are the same and the total flow remains unchanged in both scenarios, what is the diameter of the newly added pipe?

Options:
A. 64.37m
B. 70.92m
C. 72.81m
D. 67.58m
E. 65.74m
F. 69.36m
G. 71.59m
H. 68.44m
I. 63.49m
J. 66.13m
Answer: D
If the electric charge $q$ is divided into $n$ point charges each with a charge of $\frac{q}{n}$, how much work is done by an external force to move these $n$ point charges from infinity to a metal sphere with radius $R$ and charge $Q$?

Options:
A. $$
\frac{3k q Q}{R} + \frac{k q^{2}}{nR} \left(1 - \frac{1}{n^3}\right)
$$
B. $$
\frac{k q Q}{4R} + \frac{k q^{2}}{R} \left(1 + \frac{2}{n^2}\right)
$$
C. $$
\frac{k q Q}{R} - \frac{k q^{2}}{5n} \left(1 - \frac{2}{R}\right)
$$
D. $$
\frac{2k q Q}{R} + \frac{k q^{2} R^2}{2n} \left(1 - n\right)
$$
E. $$
\frac{k q Q}{2R} + \frac{k q^2 R}{n} \left(1 + \frac{1}{n}\right)
$$
F. $$
\frac{n k q Q}{R^2} + \frac{k q^{2}}{6n} \left(1 + \frac{1}{R}\right)
$$
G. $$
\frac{k q Q} {R}+\frac{k q^{2}} {2 R} ( 1-\frac{1} {n} )
$$
H. $$
\frac{k q Q R}{n} + \frac{k q^{2}}{4R} \left(1 - \frac{2}{n}\right)
$$
I. $$
\frac{4k q Q}{5R} + \frac{k q^{2}}{R} \left(1 - \frac{1}{2n}\right)
$$
J. $$
\frac{k q Q}{n} + \frac{k q^{2}}{3R} \left(1 - \frac{1}{3n}\right)
$$
Answer: G
The average molecular weight of air is known to be $\mu_{\mathrm{air}}=29$, and the mass of the hydrogen balloon shell can be neglected. To make a hydrogen balloon with a lifting force of $F_{\mathrm{up}}=2000 \ \mathrm{N}$ under standard atmospheric pressure, the hydrogen is obtained by electrolyzing a sulfuric acid solution. If the current through the electrolyte is $I=100 \ \mathrm{A}$, how long does it take to produce this amount of hydrogen?

Options:
A. $4.13 \times 10^{5} \mathrm{s}$
B. $7.30 \times 10^{5} \mathrm{s}$
C. $2.50 \times 10^{6} \mathrm{s}$
D. $8.75 \times 10^{7} \mathrm{s}$
E. $5.20 \times 10^{6} \mathrm{s}$
F. $3.25 \times 10^{7} \mathrm{s}$
G. $6.95 \times 10^{6} \mathrm{s}$
H. $9.80 \times 10^{5} \mathrm{s}$
I. $1.46 \times 10^{7} \mathrm{s}$
J. $2.00 \times 10^{8} \mathrm{s}$
Answer: I
The effective value of the AC power voltage is $U = 120 \text{ V}$, with a frequency of $f = 50 \text{ Hz}$. If the ignition voltage and the extinguishing voltage of a neon lamp are both $U_{0} = 84 \text{ V}$, how much time is the neon lamp lit during each half-cycle?

Options:
A. $\frac{1}{140} \mathrm{s}$
B. $\frac{1}{130} \mathrm{s}$
C. $\frac{1}{120} \mathrm{s}$
D. $\frac{1}{180} \mathrm{s}$
E. $\frac{1}{100} \mathrm{s}$
F. $\frac{1}{220} \mathrm{s}$
G. $\frac{1}{200} \mathrm{s}$
H. $\frac{1}{160} \mathrm{s}$
I. $\frac{1}{150} \mathrm{s}$
J. $\frac{1}{190} \mathrm{s}$
Answer: I
Artificial satellites are gradually deflected from their original orbit due to the pressure from sunlight. Suppose an artificial satellite has a mass of $m = 100 \, \text{kg}$ and is a sphere with a radius of $r = 1.0 \, \text{m}$. Of the sunlight hitting it, 50% is reflected and 50% is absorbed. The solar constant is known to be $1.35 \times 10^3 \, \text{W/m}^2$ (the solar constant is the power of solar radiation received per square meter at Earth's orbit perpendicular to the sunlight). What is the pressure exerted on this satellite by sunlight and the resulting acceleration?

Options:
A. $$
4. 5 \times1 0^{-6} \mathrm{N} ,\ 4. 5 \times1 0^{-8} \mathrm{~m / s^{2}}
$$
B. $$
4. 2 \times1 0^{-5} \mathrm{N} ,\ 4. 2 \times1 0^{-7} \mathrm{~m / s^{2}}
$$
C. $$
2. 2 \times1 0^{-6} \mathrm{N} ,\ 2. 2 \times1 0^{-8} \mathrm{~m / s^{2}}
$$
D. $$
3. 0 \times1 0^{-5} \mathrm{N} ,\ 3. 0 \times1 0^{-7} \mathrm{~m / s^{2}}
$$
E. $$
3. 5 \times1 0^{-6} \mathrm{N} ,\ 3. 5 \times1 0^{-8} \mathrm{~m / s^{2}}
$$
F. $$
1. 0 \times1 0^{-5} \mathrm{N} ,\ 1. 0 \times1 0^{-7} \mathrm{~m / s^{2}}
$$
G. $$
1. 1 \times1 0^{-6} \mathrm{N} ,\ 1. 1 \times1 0^{-8} \mathrm{~m / s^{2}}
$$
H. $$
2. 9 \times1 0^{-5} \mathrm{N} ,\ 2. 9 \times1 0^{-8} \mathrm{~m / s^{2}}
$$
I. $$
1. 5 \times1 0^{-5} \mathrm{N} ,\ 1. 5 \times1 0^{-7} \mathrm{~m / s^{2}}
$$
J. $$
2. 1 \times1 0^{-5} \mathrm{N} ,\ 2. 1 \times1 0^{-7} \mathrm{~m / s^{2}}
$$
Answer: J
In the air, there is a monochromatic plane electromagnetic wave with a frequency of $1.0 \times 10^{8} \, \text{Hz}$, and the root mean square value of the displacement current density is $1.0 \times 10^{-5} \, \text{A/m}^{2}$. What are the amplitudes of the electric field strength and magnetic field strength, $E_{0}$ and $H_{0}$, for this electromagnetic wave?

Options:
A. $$
E_{0}=3. 1 \times1 0^{-4}\mathrm{~V / m},\ H_{0}=5. 7 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
B. $$
E_{0}=1. 9 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=9. 2 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
C. $$
E_{0}=3. 3 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=5. 3 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
D. $$
E_{0}=2. 5 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=6. 6 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
E. $$
E_{0}=2. 9 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=4. 6 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
F. $$
E_{0}=2. 1 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=7. 0 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
G. $$
E_{0}=2. 2 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=8. 4 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
H. $$
E_{0}=2. 7 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=4. 8 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
I. $$
E_{0}=1. 7 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=6. 0 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
J. $$
E_{0}=1. 8 \times1 0^{-3}\mathrm{~V / m},\ H_{0}=7. 8 \times1 0^{-6} \mathrm{~A} / \mathrm{m}
$$
Answer: D
The resonant frequency of an $RLC$ series circuit is $\nu_{0}=\frac{1}{2 \pi} \, \frac{1}{\sqrt{LC}}$. What is the $LC$ value of its oscillating circuit if an electromagnetic wave emitted by a transmitting antenna has a frequency of 1.25 MHz?

Options:
A. $$
7. 5 8 \times1 0^{-1 6}~\mathrm{s}^{2}
$$
B. $$
8. 7 3 \times1 0^{-1 3}~\mathrm{s}^{2}
$$
C. $$
1. 2 4 \times1 0^{-1 5}~\mathrm{s}^{2}
$$
D. $$
5. 0 5 \times1 0^{-1 5}~\mathrm{s}^{2}
$$
E. $$
1. 7 8 \times1 0^{-1 3}~\mathrm{s}^{2}
$$
F. $$
1. 6 2 \times1 0^{-1 4}~\mathrm{s}^{2}
$$
G. $$
2. 4 5 \times1 0^{-1 4}~\mathrm{s}^{2}
$$
H. $$
1. 6 2 \times1 0^{-1 3}~\mathrm{s}^{2}
$$
I. $$
1. 1 2 \times1 0^{-1 4}~\mathrm{s}^{2}
$$
J. $$
3. 9 1 \times1 0^{-1 6}~\mathrm{s}^{2}
$$
Answer: F
A coil has a self-inductance of $L = 5.0 \mathrm{H}$ and a resistance of $R = 20 \Omega$. A constant voltage of $U = 100 \mathrm{V}$ is applied across its terminals. From the moment the voltage is applied, how long does it take for the energy stored in the coil from $W_{m} / 2$ to reach $0.99W_{m}$?

Options:
A. $0.60~\mathrm{s}$
B. $0.08~\mathrm{s}$
C. $0.31~\mathrm{s}$
D. $0.45~\mathrm{s}$
E. $0.15~\mathrm{s}$
F. $0.67~\mathrm{s}$
G. $0.54~\mathrm{s}$
H. $0.23~\mathrm{s}$
I. $0.75~\mathrm{s}$
J. $0.39~\mathrm{s}$
Answer: C
A solenoid is 30 cm long, with a cross-sectional diameter of 12 cm, and is closely wound with 600 turns of thin insulated wire. The interior of the solenoid is air. When a current of 1.0 A passes through the wire, what is the magnetic energy density at the center of the solenoid and along the axis at the end of the solenoid?

Options:
A. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{5 R} {l} \right)^{2}}},\ \frac{3} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2R} {l} \right)^{2}}}
$$
B. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{4 R} {l} \right)^{2}}},\ \frac{1} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}}
$$
C. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}},\ \frac{3} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2R} {l} \right)^{2}}}
$$
D. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{3 R} {l} \right)^{2}}},\ \frac{1} {4} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}}
$$
E. $$
\frac{\mu_{0} n I^{2}} {\sqrt{1+\left( \frac{2 R} {l} \right)^{2}}},\ \frac{3} {2} \frac{\mu_{0} n I^{2}} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}}
$$
F. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2 R} {l} \right)^{2}}},\ \frac{1} {3} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {2l} \right)^{2}}}
$$
G. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2 R} {l} \right)^{3}}},\ \frac{1} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2R} {l} \right)^{2}}}
$$
H. $$
\frac{\mu_{0} n I^{2}} {\sqrt{1+\left( \frac{2 R} {l} \right)^{2}}},\ \frac{1} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {2l} \right)^{2}}}
$$
I. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{2 R} {l} \right)^{2}}},\ \frac{1} {2} \frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}}
$$
J. $$
\frac{\mu_{0} n I} {\sqrt{1+\left( \frac{R} {2l} \right)^{2}}},\ \frac{1} {2} \frac{\mu_{0} n I^{2}} {\sqrt{1+\left( \frac{R} {l} \right)^{2}}}
$$
Answer: I
Superconducting materials are in a superconducting state at temperatures $T < T_{c}$ (critical temperature). If an electric current passes through them, and the magnetic field strength produced on their surface is $H > H_{c}$, the superconducting state will be destroyed. $H_{\mathrm{c}}$ is called the critical magnetic field. Experiments have determined that the relationship between $H_{\mathrm{c}}$ and temperature $T$ is
$$
H_{\mathrm{c}} = H_{0} \Big[ 1 - \Big( \frac{T}{T_{\mathrm{c}}} \Big)^{2} \Big]
$$
where $H_{0}$ is the critical magnetic field at $T = 0$. For lead, $T_{\mathrm{c}} = 7.2 \, \mathrm{K}, H_{0} = 6.39 \times 10^{4} \, \mathrm{A/m}$. Using lead to make a wire with a diameter of 1.0 mm, how much current can pass through at $T = 3.6 \, \mathrm{K}$ without destroying the superconducting state?

Options:
A. $$
5. 0 \times1 0^{2}~\mathrm{A}
$$
B. $$
7. 2 \times1 0^{2}~\mathrm{A}
$$
C. $$
6. 0 \times1 0^{2}~\mathrm{A}
$$
D. $$
8. 0 \times1 0^{2}~\mathrm{A}
$$
E. $$
1. 5 \times1 0^{2}~\mathrm{A}
$$
F. $$
2. 5 \times1 0^{2}~\mathrm{A}
$$
G. $$
4. 5 \times1 0^{2}~\mathrm{A}
$$
H. $$
3. 0 \times1 0^{2}~\mathrm{A}
$$
I. $$
3. 5 \times1 0^{2}~\mathrm{A}
$$
J. $$
2. 0 \times1 0^{2}~\mathrm{A}
$$
Answer: H
The magnetic moment of atoms and molecules is generally on the order of a Bohr magneton $\mu_{\mathrm{B}} = \frac{e \hbar}{2 m} = 9.274 \times 10^{-24} \, \mathrm{A} \cdot \mathrm{m}^{2}$. In an external magnetic field with a magnetic flux density of $B = 10 \mathrm{T}$, what is the ratio of the potential energy, when $\mu_{\mathrm{B}}$ is antiparallel to $B$, to the energy of molecular thermal motion at room temperature (on the order of $k T$)?

Options:
A. $50$
B. $55$
C. $60$
D. $35$
E. $30$
F. $20$
G. $45$
H. $40$
I. $25$
J. $15$
Answer: G