Given:
The voltage in the transmission line is: V = 240000 v
The stepped-down voltage is: Vs = 40000 v
The turns of the primary coil of the transformer are: Np = 940
To find:
The turns of the secondary coil of the transformer.
Explanation:
The voltage in a transmission line is used to step down by using the transformer. Thus, the primary voltage of the transformer will be the voltage in the transmission line.
Thus, Vp = V = 240000 v
The primary voltage Vp, the secondary voltage Vs, the primary turns on the coil Np and the secondary turns on the coil Ns are related as:
\(\frac{V_p}{V_s}=\frac{N_p}{N_s}\)Rearranging the above equation, we get:
\(\begin{gathered} N_s=N_p\frac{V_s}{V_p} \\ \\ N_s=940\times\frac{40000\text{ v}}{240000\text{ v}} \\ \\ N_s=940\times\frac{4}{24} \\ \\ N_s=156.67 \\ \\ N_s\approx157 \end{gathered}\)Final answer:
The number of turns on the secondary coil of the transformer are approximately 157.
Alexis is studying how lenses work. She looks through a magnifying glass and through the peephole of a door.
Which best describes a difference between the lenses used in these two devices?
The lens in the magnifying glass can produce both real and virtual images, but the lens in the peephole can produce only real images.
The lens in the magnifying glass can produce only real images, but the lens in the peephole can produce both real and virtual images.
The lens in the magnifying glass can produce both upright and inverted images, but the lens in the peephole can produce only upright images.
The lens in the magnifying glass can produce only inverted images, but the lens in the peephole can produce inverted and upright images.
Answer:
The lens in the magnifying glass can produce both upright and inverted images, but the lens in the peephole can produce only upright images.
Explanation:
Answer: C
Explanation:
what is the acceleration of a 10 kg mass pushed by a 5 N force
Answer:
The formula is a = F m so in this case a = 5 10 = 0.5 m s 2
Explanation:
What is the real reason the skies blue
Answer:
Rayleigh scattering
Explanation:
The blue color of the sky is due to a phenomenon called Rayleigh scattering. When sunlight enters the Earth's atmosphere, the shorter blue wavelengths of light are scattered more than the other colors by the tiny molecules of nitrogen and oxygen in the air. This causes the blue light to be redirected in many different directions, making the sky appear blue to our eyes. The other colors of light are scattered as well, but to a lesser extent, which is why the sky appears blue instead of a mixture of all colors. This effect is also the reason why the sun appears more yellow, orange or red during sunrise or sunset, when its light has to travel through more of the Earth's atmosphere before reaching our eyes, causing the shorter blue wavelengths to be scattered even more, leaving behind the longer wavelengths of light.
What are some examples of motion? Include the examples you found and describe an accurate frame of reference for one example. Then, describe an inappropriate frame of reference for that example.
Walking, running, and breathing are examples of motion. For rolling of ball, the street is a frame of reference and an insect on the ball is an inappropriate frame of reference.
A frame of reference, also known as a reference frame, is a perspective used in physics to assess whether an object is moving. A frame of reference is an environment or object that is thought to be stationary. The Earth itself, despite its motion, serves as the most frequently used frame of reference.
Some examples of motion are:
Motion is a part of many of our daily activities, including walking, running, closing doors, etc.
Another illustration of motion is the passage of air into and out of our lungs.
The vehicles that transport passengers between the point of pickup and the destination have motion.
A ball is rolling down the street that it is moving.
For a ball rolling down the street, the street is an appropriate frame of reference as it is rest as compared to the ball.
For the same example, the insect sitting on the rolling ball is a part of the rolling ball.
Therefore, the insect is an inappropriate frame of reference for the motion of the ball rolling down the street.
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Why do you think the pylon in Figure 24 is designed the way it is, and not in the way shown in Figure 25?
They are specifically made tο be ideal fοr cοnducting live electrical lines because οf their electrical insulatiοn and mechanical tοughness. A structure called an electric pylοn οf hοt-rοlled steel bevels οr gusset plates.
What kinds οf patterns are used tο create electrical pylοns?Other materials, such as cοncrete and wοοd, may alsο be utilised in additiοn tο steel. Transmissiοn tοwers can be divided intο fοur main categοries: suspensiοn, terminal, tensiοn, οr transpοsitiοn.
Whο was the electrical pylοn's designer?This Central Electricity Bοard held a cοmpetitiοn in 1927, and the winning entry was chοsen by the classical designer Sir Reginald Blοοmfield. He settled οn an A-frame structure with latticewοrk that was οffered by the American cοmpany Milliken Brοthers and is still in use tοday.
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Complete question:
the use of solar energy should be increase in the context of Nepal.justify the statement
Answer:
The solar potential in Nepal is 50,000 terawatt-hours per year, which is 100 times larger than Nepal's hydro resource and 7,000 times larger than Nepal's current electricity consumption. Solar can easily meet all future energy needs in Nepal. Solar energy is cheaper than fossil fuels, nuclear and hydro.
For the following distance vs time graph
Answer:
3
5
4
Explanation:
x = (8=(9+9)
(9+9) = 4, 5, 3
Tuning a guitar string, you play a pure 330 Hz note using a tuning device, and pluck the string. The combined notes produce a beat frequency of 5 Hz. You then play a pure 350 Hz note and pluck the string, finding a beat frequency of 25 Hz. What is the frequency of the string note?
Answer:
The frequency is \(F = 325 Hz\)
Explanation:
From the question we are told that
The frequency for the first note is \(F_1 = 330 Hz\)
The beat frequency of the first note is \(f_b = 5 \ Hz\)
The frequency for the second note is \(F_2 = 350 \ H_z\)
The beat frequency of the first note is \(f_a = 25 \ Hz\)
Generally beat frequency is mathematically represented as
\(F_{beat} = | F_a - F_b |\)
Where \(F_a \ and \ F_b\) are frequencies of two sound source
Now in the case of this question
For the first note
\(f_b = F_1 - F \ \ \ \ \ ...(1)\)
Where F is the frequency of the string note
For the second note
\(f_a = F_2 - F \ \ \ \ \ ...(2)\)
Adding equation 1 from 2
\(f_b + f_a = F_1 + F_2 + ( - F) + (-F) )\)
\(f_b + f_a = F_1 + F_2 -2F\)
substituting values
\(5 +25 = 330 + 350 -2F\)
=> \(F = 325 Hz\)
Packages having a mass of 6 kgkg slide down a smooth chute and land horizontally with a speed of 3 m/sm/s on the surface of a conveyor belt. If the coefficient of kinetic friction between the belt and a package is
Answer:
t = 1.02 s
Explanation:
The computation of the time required is shown below:
The package speed for belt is
= 3 - 1
= 2 m/s
Moreover, the decelerative force would be acted on the block i.e u.m.g
So, the decelerative produced
= 0.2 × 9.81
= 1.962 m/s^2
And, final velocity = 0
v = u - at
here
V = 0 = final velocity
u = 2 m/s
so,
0 = 2 - 1.962 × t
t = 1.02 s
A 6 kg blue ball rolls across the ground and collides with a stationary 1 kg red ball.
Before the collision the blue ball moved right with a speed of 4 m/s, and after the
collision it moved left with a speed of 1 m/s. If the red ball was not moving before the
collision, how fast is it moving after the collision?
The final velocity of the red ball is 18 m/s.
What is momentum?The term momentum has to do with the product of the mass and the velocity of an object We know that the momentum is always conserved in accordance with the Newton third law. Also it is clear that the momentum before collision is equal to the total momentum after collision and we are going to apply this principle here.
Then;
Mass of the blue ball = 6 kg
Mass of the red ball = 1 kg
Initial velocity of the blue ball = 4 m/s
Initial velocity of the red ball = 0 m/s
Final velocity of the red ball = ??
Final velocity of the blue ball = 1 m/s
We now have;
(6 * 4) + (1 * 0) = (1 * v) + (6 * 1)
24 = v + 6
v = 24 - 6
v = 18 m/s
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Push: Explain Newton's Third Law
Explain how a rocket taking off can be an example of Newton's Third Law of Motion.
Every action have equal and opposite reaction. for example when we fire bullet from a gun, the gun will recoil back and bullet moves forward. In case of rocket, rocket is fired, thrust is reaction of force applied by the gas on the floor.
A push or a pull that an object experiences as a result of interacting with another item is known as a force. Interactions result in forces! As was covered in Lesson 2, certain forces are the result of contact interactions (reaction, frictional, tensional, and applied forces are examples of contact forces), whilst other forces (gravitational, electrical, and magnetic forces) are the consequence of action-at-a-distance interactions. Newton postulated that whenever objects A and B interact, they exert forces on one another. You put a downward force on the chair when you sit on it, and the chair responds by exerting an upward force on your body. This contact creates two forces: one force on the chair and one force on your body.
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(round to 3 significant figures pls) A block of iron at 415 degrees C is put into a 0.625 kg tub of water at 15.0 degrees C. They come to equilibrium at 100 degrees C, and 0.144 kg of the water boils off to steam. What was the mass of the iron block?
Temperature of iron (Ti) = 415 °C Temperature of water (Tw) = 15.0 °CTemperature at equilibrium (Te) = 100 °CMass of water (m) = 0.625 kgMass of steam evaporated (ms) = 0.144 kgHeat lost by iron (Q1) = Heat gained by water (Q2) + Heat required to evaporate steam .
Heat lost by iron = (mass of iron (m) x specific heat capacity of iron (c) x change in temperature of iron (ΔT1))Heat gained by water = (mass of water (m) x specific heat capacity of water (c) x change in temperature of water (ΔT2))Heat required to evaporate steam = (mass of steam (ms) x specific latent heat of vaporization of water (L))Now, using the above formula we can calculate the mass of the iron block as:
Q3m x c x ΔT1 = m x c x ΔT2 + ms x L
Let's calculate the value of Q1 first.
Q1 = m x c x ΔT1m = Q1 / (c x ΔT1)
We know that
c = 450 J/kg °C and ΔT1 = Ti - Te = 415 - 100 = 315°CQ1 = m x c x ΔT1= m x 450 J/kg
°C x 315°C= 141750 m Jm = Q1 / (c x ΔT1)= 141750 / (450 x 315)= 1.002 kg
Now, let's calculate the value of Q3.Q3 = ms x L= 0.144 kg x 2.26 x 10^6 J/kg= 325440 J
Now, let's calculate the value of Q2
.Q2 = m x c x ΔT2m = (Q2 + Q3) / (c x ΔT2)
We know that ΔT2 = Te - Tw = 100 - 15 = 85°CQ2 = m x c x ΔT2= 0.625 kg x 4186 J/kg °C x 85°C= 276981.25 JNow, let's calculate the mass of the iron block.m =
(Q2 + Q3) / (c x ΔT2)= (276981.25 + 325440) / (450 x 85)= 1.003 kg
Hence, the mass of the iron block is 1.003 kg rounded off to 3 significant figures.
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Cobalt-60 (Co) is often used as a radiation source in medicine. It has a half-life of 5.25 years. 4.1. Explain what is meant by the underlined sections in the statement above. [5] Using her knowledge and understanding of nuclear physics, a student was asked to answer the following problem about cobalt-60: How long after a new sample is delivered will its activity have decreased (a) to about one-eighth its original value? (b) to about one-third its original value? Give your answers to two significant figures. The student was also provided with the following information: The activity is proportional to the number of undecayed atoms (AN/At = AN) 4.2. Explain what is meant by the information above provided to the student. [5]
From the question;
1) It takes 15.75 years to decrease to 1/8
2) It takes 8.36 years to decrease to 1/3
What is half life?
Half-life is the length of time it takes for a chemical to degrade or go through a particular process. It frequently refers to the length of time it takes for half of a radioactive substance to decay into a stable form in the context of radioactive decay.
We know that;
\(N/No = (1/2)^t/t1/2\)
No = initial amount
N = amount at time t
t = Time taken
t1/2 = half life
\(1/8 = (1/2)^t/5.252^-3 = 2^-t/5.25\)
t = 15.75 years
Again;
\(1/3 = (1/2)^t/5.25\)
ln0.33 = t/5.25ln0.5
t = ln0.33/ln0.5 * 5.25
t = 8.36 years
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213.49 in standard form is
Answer:
21349/ 100
Explanation:
Why is it better to use the metric system, rather than the English system, in scientific measurement?
A. The English system uses one unit for each category of measurement.
B. The metric system uses one unit for each category of measurement.
C. The English system uses consistent fractions that are multiples of 10.
D. The metric system utilizes a variety of number conversions.
A. The English system uses one unit for each category of measurement.
Answer:
A
Explanation:
Is a parked car potential or kinetic ?
Answer:
Potential energy is the energy that is stored in an object. ... When you park your car at the top of a hill, your car has potential energy because the gravity is pulling your car to move downward; if your car's parking brake fails, your vehicle may roll down the hill because of the force of gravity.
Kinetic energy is the energy an object has due to its
Kinetic energy is the energy an object has due to its Motion.
Kinetic energy is a characteristic of a moving particle. It is a type of energy that a matter or particle possesses due to its motion.
It is expressed:
\(K_E = \frac{1}{2}mv^2\)
Where m is the mass of the particle and v is velocity.
Hence, Kinetic energy is the energy an object has due to its Motion.
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A baseball is popped straight up into the air and has a hang-time of 6.25 S.
Determine the height to which the ball rises before it reaches its peak. (Hint: the
time to rise to the peak is one-half the total hang-time.)
Answer:
To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.
The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.
The height to which the ball rises can be calculated using the formula:
height = v * t - (1/2) * g * t^2
Substituting in the values we know, we get:
height = v * 3.125 s - (1/2) * g * (3.125 s)^2
To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.
Explanation:
Answer:
Approximately \(47.9\; {\rm m}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance on the baseball is negligible.)
Explanation:
If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly \((1/2)\) the time it is in the air. In this example, that will be \(t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}\).
When the baseball is at maximum height, the velocity of the baseball will be \(0\). Let \(v_{f}\) denote the velocity of the baseball after a period of \(t\). After \(t = 3.125\; {\rm s}\), the baseball would reach maximum height with a velocity of \(v_{f} = 0\; {\rm m\cdot s^{-1}}\).
Since air resistance is negligible, the acceleration on the baseball will be constantly \(a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})\).
Let \(v_{i}\) denote the initial velocity of this baseball. The SUVAT equation \(v_{f} = v_{i} + a\, t\) relates these quantities. Rearrange this equation and solve for initial velocity \(v_{i}\):
\(\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}\).
The displacement of an object is the change in the position. Let \(x\) denote the displacement of the baseball when its velocity changed from \(v_{i} = 0\; {\rm m\cdot s^{-1}}\) (at starting point) to \(v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}\) (at max height) in \(t = 3.125\; {\rm s}\). Apply the equation \(x = (1/2)\, (v_{i} + v_{t}) \, t\) to find the displacement of this baseball:
\(\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}\).
In other words, the position of the baseball changed by approximately \(47.9\; {\rm m}\) from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately \(47.9\; {\rm m}\!\).
A phone with a mass of 0.2 kg is dropped from a height of 30 m what is it’s speed when it hits the ground?the acceleration of gravity is 9.8ms
Answer:
24.2 m/s
Explanation:
Mass is irrelevant in this situation....
Displacement: ( to find time)
x = xo + vo t - 1/2 at^2
30= 0 + 0 - 1/2 (9.8)t^2
t = 2.47 seconds
Velocity:
vf = a t = 9.8 (2.473) = 24.2 m/s
write down the value of
920 kg in g
Answer:
920000
Explanation:
Each kg contains 1,000 grams
True/False
1. The Law of Superposition states that older rocks are on the top, younger rocks are on the botom.
Answer:
yeah
Explanation:
Geology. a basic law of geochronology, stating that in any undisturbed sequence of rocks deposited in layers, the youngest layer is on top and the oldest on bottom, each layer being younger than the one beneath it and older than the one above it.
Answer:
Found this answer off of google, "Geology. a basic law of geochronology, stating that in any undisturbed sequence of rocks deposited in layers, the youngest layer is on top and the oldest on bottom, each layer being younger than the one beneath it and older than the one above it."
Hope this helps, have a great day and stay safe!
Also Happy Halloween! :) :D :3
On a warm summer day, a large mass of air (atmospheric pressure 1.01×105Pa) is heated by the ground to a temperature of 25.0 ∘C and then begins to rise through the cooler surrounding air. Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×104 Pa. Assume that air is an ideal gas, with γ=1.40. (This rate of cooling for dry, rising air, corresponding to roughly 1 ∘C per 100 m of altitude, is called the dry adiabatic lapse rate.)
The temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.
Using the ideal gas law, we can write: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature. Since the mass of air is not changing, we can write: PV = constant.
Applying this to the situation where the air mass rises to a level where the pressure is 8.70×10⁴ Pa, we get:
(1.01×10⁵ Pa)×V = (nR/T1)×T1(8.70×10⁴ Pa)×V = (nR/T2)×T2Dividing the second equation by the first and using the fact that γ=Cp/Cv=1.40 for air, we get:
(T2/T1) = [(P2/P1)^(γ-1)/γ] = [(8.70×10⁴ Pa)/(1.01×10⁵ Pa)]^(1.4/1.4) = 0.813Solving for T2, we get:
T2 = T1×(P2/P1)^(γ-1)/γ = (25+273) K×0.813 ≈ 287.3 K ≈ 14.3°CThus, the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.
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Maria read on an internet blog that infrared light is dangerous to humans. According to the blog, infrared light exposure is responsivle for a number of detrimental effects in humans. Which of these can actually be caused by exposure to infrared light?
a-overheating
b-skin cancer
c-radiation sickness
d-memory less
Of the options listed, the only effect that can be caused by exposure to infrared light is overheating (option a).
Infrared light is a form of electromagnetic radiation that is invisible to the human eye but can be detected as heat. When exposed to high levels of infrared light, such as in close proximity to a powerful infrared source, it can lead to overheating of the body or objects. Skin cancer (option b) is not directly caused by infrared light. It is primarily associated with overexposure to ultraviolet (UV) radiation from the sun or artificial sources like tanning beds. UV radiation falls in the higher energy range of the electromagnetic spectrum, while infrared radiation has lower energy. Radiation sickness (option c) is caused by exposure to high-energy ionizing radiation, such as gamma rays or X-rays. Infrared light does not possess enough energy to cause ionization and is therefore not capable of inducing radiation sickness. Memory loss (option d) is not a known effect of exposure to infrared light. Memory loss can be attributed to various factors, such as neurological conditions, head injuries, or aging, but not specifically to infrared light exposure. In summary, while exposure to high levels of infrared light can lead to overheating, it does not cause skin cancer, radiation sickness, or memory loss.
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The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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Bending the stick stretches the chemical bonds holding the stick's atoms together, which provides a source of elastic energy.
a. True
b. False
Answer:
true
Explanation:
A sample of helium behaves as an ideal gas as it is heated at constant pressure from 283 K to 358 K. If 70 J of work is done by the gas dur- ing this process, what is the mass of the he- lium sample? The universal gas constant is 8.31451 J/mol · K. Answer in units of g.
The mass of the helium sample is approximately 0.187 g.
To solve this problem, we can use following formula:
w = nR(T2 - T1)
We can rearrange this formula to solve for n:
n = w / (R * (T2 - T1))
To find the mass of the helium sample, we can use following formula:
m = n * M
where m is the mass of the sample, n is number of moles of gas, and M is the molar mass of helium.
Substituting the given values into the first equation, we get:
70 J = n * 8.31451 J/mol*K * (358 K - 283 K)
Simplifying this equation, we get:
n = 0.0467 mol
Substituting this value into the second equation, we get:
m = 0.0467 mol * 4 g/mol = 0.187 g
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what term is used to describe the block of organs (heart, lungs, liver, kidneys and spleen) that are removed during the autopsy?
The term used to describe the block of organs that are removed during the autopsy is Thoracic organs.
The organs that are removed during autopsy include:
Thoracic organs;Cervical organs, and Abdominal organsThe thoracic cavity contains organs and tissues that function in the respirator, cardiovascular, nervous and digestive system.
These thoracic organs include the following;
heart, lungs, liver, kidneys and spleen.Thus, we can conclude that the term used to describe the block of organs that are removed during the autopsy is Thoracic organs.
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Where is the near point of an eye for which a spectacle lens of power +2 D is prescribed for reading purpose?
The near point of a human eye is about a distance of 25 cm.
The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.
This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.
The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.
In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.
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Which correctly describes latent heat?
A. The heat of molecules that are under pressure
B. The heat held inside of ice crystals colder than -2°C
C. The heat absorbed or lost by a substance while it's changing state
D. The heat used to change the temperature of a liquid
Option C. The heat absorbed or lost by a substance while it's changing state correctly describes latent heat
Latent heat is the heat absorbed or lost by a substance while it is changing state.
The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.
For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.
Latent heat is not associated with a temperature change; rather, it's associated with a change of state.
For instance, the temperature of water remains at 100°C while boiling.
When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.
When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.
Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.
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A boy starts at rest and slides down a frictionless slide as in the figure below. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground a distance d as shown. Using energy methods, determine the initial height H of the boy in terms of h and d.
The initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track: H = h + d.
To determine the initial height H of the boy in terms of h and d, we can use the principle of conservation of energy. The total mechanical energy of the system remains constant throughout the motion.
At the top of the slide, the boy has gravitational potential energy given by mgh, where m is the mass of the boy, g is the acceleration due to gravity, and h is the height of the slide above the ground.
As the boy slides down the slide, there is no friction or other dissipative forces, so there is no change in mechanical energy. At the bottom of the track, the gravitational potential energy is converted entirely into kinetic energy.
Therefore, we can equate the initial potential energy to the final kinetic energy:
mgh = 1/2 m\(v^{2}\),
where v is the horizontal velocity of the boy when he leaves the track.
Since the boy leaves the track horizontally, the vertical component of his velocity is zero. Therefore, we can use the relationship between horizontal distance d and horizontal velocity v:
d = vt.
Solving these equations, we can express the initial height H in terms of h and d:
H = h + d.
So the initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track.G
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