All three pendulums will reach the same maximum velocity, according to the question.
What is pendulum energy?The pendulum will start swinging as the weighted end is removed since gravity will drag it downward. Kinetic energy, the force a moving item exerts, is created from potential energy. At its lowest, so when mass is traveling the quickest, an active pendulum possesses the highest kinetic energy.
Briefing:From conservation of energy;
Energy at A = Energy at B
[tex]\frac{1}{2} mv^{2}[/tex] = mg[tex]H_{max}[/tex]
[tex]H_{max}[/tex] = [tex]\frac{v^{2} }{2g}[/tex]
[tex]H_{max}[/tex] = Independent of mass
So, all pendulum will attain the highest speed.
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a 30.8-kg child swings on a rope with a length of 6.29 m that is hanging from a tree. at the bottom of the swing, the child is moving at a speed of 4.2 m/s. what is the tension in the rope?
The tension in the rope at the lower part of the swing is 388.2 N.
What is the tension in the rope?The tension in the rope at the lower part of the swing is calculated by applying the following formula.
T = W + Fc
where;
W is the weight of the childFc is the centripetal force of the swingT = mg + mac
T = m (g + ac)
T = m (g + v²/r)
where;
m is the mass of the childg is acceleration due to gravityac is the centripetal accelerationr is the radius of the circular pathThe magnitude of the tension in the ropes is calculated as;
T = 30.8 (9.8 + 4.2²/6.29)
T = 388.2 N
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as a copper wire is heated, its length increases by 0.1%. what is the change in temperature of the wire? (copper
The change in temperature of the wire is 60.2°C.
What is the change in the temperature of the copper?Near room temperature, the temperature coefficient of copper is +0.393% per degree C. It follows that the resistance will rise by 0.393% if the temperature rises by 1°C.The only way to do so would be to attach a copper plate to the wire and take its temperature in order to use an infrared thermometer to measure it (the laser only shows where you are pointing it). That would provide results almost instantly because copper is such a good heat conductor.Increasing temperature causes silicon's resistance to decrease, whereas doing so causes copper's resistance to rise. As copper warms up, the vibrations of the atoms scatter more conduction electrons.Learn more about change in the temperature refer to :
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a 50kg box is being pushed across a horizontal floor by a 100n force acting downward at a 20 degree angle from above the horizon. what is the acceleration of the box? the coefficient of friction is 0.12
The acceleration of both the box will indeed be 0.8 m/s² when the friction factor is 0.12.
What is an explain acceleration?Acceleration is the pace at which the speed and direction of a moving object change over time. Something is said to be accelerating when it commences to move quickly or slowly. Even if the voltage is constant, transportation on a circle accelerates because the angle is always shifting.
Briefing :According to the given statement we have frictional force f = µ •N
where N = normal force = mg
the given Sliding friction µ= 0.12
therefore f = 0.12 × 50 × 10 = 60 N
hence net friction = applied friction - frictional force = 100 - 60 = 40 N
also we know that Force F= ma
therefore we have acceleration formula ,
acceleration = force/mass = 40 / 50 = 0.8 m/ s²
hence the acceleration of the box is 0.8 m/s².
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an emerald has an index of refraction of 1.57. the light from a red laser of wavelength 633nm in vacuum travels within the emerald. what is the maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air?
The maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air is: 39.34.
Total Internal Reflection
[tex]M_{1}[/tex] sin(∅[tex]_{c}[/tex]) = M[tex]_{2}[/tex] Sin(90)
sin(∅[tex]_{c}[/tex])= M[tex]{2}[/tex]/M[tex]_{1}[/tex] = 1/1.57 = 0.636
∅[tex]_{c}[/tex]= 39.49
∅ = 39.34
v = c/λ
c = 1000/5.56e - 6 = 1.798 × [tex]10^{8}[/tex] m/s
v = 1.798 × [tex]10^{8}[/tex]/400e-9 = 4.496 × [tex]10^{14}[/tex] Hz
What is refraction index?
In optics, the refractive index (or refractive index) of an optical medium is a dimensionless number that indicates the ability of the medium to diffract light.
The index of refraction determines how much a light path bends or refracts as it enters a material. This is described by Snell's law of refraction n1 sin θ1 = n2 sin θ2. where θ1 and θ2 are the angles of incidence and refraction, respectively, for a ray that crosses the interface between two media with indices of refraction n1 and n2. The index of refraction also determines the amount of light reflected upon reaching an interface, the critical angle for total internal reflection, its intensity (Fresnel equation), and Brewster's angle.
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Stars emit different wavelengths of visible light due to their different temperatures. How does this phenomenon support the particle model of light?.
The particle model of light states that light is composed of discrete particles called photons.
What is photon?
The electromagnetic force is carried by a photon, an elementary particle which is a quantum of a electromagnetic field and includes electromagnetic radiation like light and radio waves. Due to their lack of mass, photons always travel at the speed of light in a vacuum, which is 299792458 m/s (or 186,282 mi/s). The photon is a member of the boson family. Photons exhibit wave-particle duality, with their behaviour exhibiting characteristics of both waves and particles. Like other subatomic particles, photons have been best explained by quantum mechanics. In the first two decades of the twentieth century, Albert Einstein developed the modern photon theory, building on the work of Max Planck.
The varying wavelengths of visible light emitted by stars are evidence of the particle nature of light, since different temperatures of stars result in different amounts of energy being released in the form of photons, which each have a different frequency and energy level. This phenomenon supports the particle model of light because it demonstrates that light is composed of distinct particles with different energies.
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Houston, we have a problem
You are members of the crew of Earth’s first community development ship. On your way to the planet Proxima Centauri B your ship was damaged. You are not going to be able to land your ship on the planet as anticipated. You will have to take precautions when constructing your lander to arrive safely on the surface. Before you begin construction on your lander you will need to determine the gravitational acceleration between your ship and the planet.
Data:
Your spacecraft is equipped with advanced sensing equipment and you have measured the following information based on your current situation.
You are currently in a stable orbit 9 000 000 m from the center of planet Proxima Centauri B.
According to the calculations done by NASA, Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.
Based on fuel consumption and expected material aboard the ship, your colony ship lander has a mass of approximately 1.1x105 kg.
1. Using Newton's Law of Universal Gravitation, determine what the force of gravity on your ship at that orbit be using the early measurements. Please show all work.
2.Using Newton’s second law determine the acceleration of your lander due to gravity. Please show your work.
3.Upon arrival, you measure the actual force of gravity to be 6x105 N,which is different from your calculated value in question 1. Identify a specific possible causes that would account for the difference in expected vs. actual values, and why they would affect the calculation.
1. The force of gravity on the ship at that orbit be using the early measurements be 5.435 × 10^5 N..
2. The acceleration of your lander due to gravity be 4.94 m/s^2..
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Given that:
Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.
colony ship lander has a mass of approximately 1.1x10^5 kg.
stable orbit radius of 9000000 m from the center of planet Proxima Centauri B.
1. Using Newton's Law of Universal Gravitation, the force of gravity on the ship at that orbit be using the early measurements = GMm/r²
= (6.67 × 10⁻¹¹)×(6x10^24)(1.1x10^5)/(9000000)² N
= 5.435 × 10^5 N.
2. the acceleration of your lander due to gravity: a = F/m
= 5.435 × 10^5 N/ 1.1x10^5 kg.
= 4.94 m/s^2.
3.The possible causes that would account for the difference in expected vs. actual values are:
mass distribution of the planet may not be uniform. So, the center of mass of the planet does not locate at the geometrical center.Path of orbiting does not circular, it may be elliptical.Learn more about force here:
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find the resistance of a portable lantern that uses a 24 v power supply and draws a current of 0.80 a.
a portable lamp with a 30 ohm resistance, 0.80 a current demand, and a 24 v power source
What portable lantern has the most light?The Super Bright LED Recharge Portable Scene Light II of Streamligh has 10,000 lumens, which is the most lumens we've found in an LED lantern.
What LED has the highest possible brightness?E39 bulb, 300 watts: The brightest bulb currently available. It has a high efficiency of 130 lumens per watt and produces over 40,000 lumens. The 1000 watt HID, HPS, Metal Halide, or CFL fixture can be replaced with this one, which also delivers 360-degree lighting.e
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what is the speed of a point on the earth's surface located at 2/5 of the length of the arc between the equator and the pole, measured from equator? (hint: what is the radius of the circle in which the point moves?)
The speed of the given point on earth's surface is 428 m/s
Speed of point on earth's surface:A point located 1/4 of the length of the arc between the equator and the pole has an angle:
(1/4) × 90° = 22.5°
Since the arc angle of the line joining the equator and the pole is 90°
So the angle between the line joining the center and the given point, and the line joining center and the pole is Φ = 90° - 22.5° = 67.5°
Now,
Sin Φ = (radius of the point)/(radius of the earth)
Sin 67.5 = radius of the point/(6.37 × 10⁶)
Radius of the point:
r = 6.37 × 10⁶ × 0.9239 = 5.885 × 10⁶ m
Speed of the point on the globe is v = 2πr/(24 hours)
2πr = 2π × 5.885 × 10⁶ = 3.6977 × 10⁷ m
So the speed of the point is :
v = 3.6977 × 10⁷/24
v = 1.541 × 10⁶ m/h
v = 428 m/s
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what is the magnetic field at a distance x from the center of the axis of a circular loop of a radius r carrying current i ?
The magnetic field at a distance x from the center of the axis of a circular loop of a radius r carrying current is µI/2R
Think about a loop that is R in diameter and I in current. The axis of the loop OX is located in the plane of the paper, while the Y-Z plane of the coil is perpendicular to the plane of the paper. Consider breaking up the circular loop into a large number of current elements, I*dl
Then, the Magnetic field due to the whole current loop will be:
B = µI[tex]R^{2}[/tex]/2[tex]2(x^{2} +R^{2} )^{3/2}[/tex]
When x =0, we get the correct results for the field at the center of a current loop.
B = µI/2R
When x exceeds R by a significant amount, the magnetic field diminishes as [tex]1/x^{3}[/tex]
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if the charge on q1 is doubled, assuming that charge of q2 and the distance of r stay the same, what will happen to the force between the two charges? (3 points)
If the charge on q1 is doubled the force becomes 4 times its initial value.
The charge of each object has a direct impact on electrostatic force. Therefore, the force will increases if the charge of one object is doubled.
The square of the distance between the two charges has an inverse relationship with the force's size. As a result, when the gap between two charges is doubled, the attraction or repulsion weakens and drops to one-fourth of its initial strength.
Since, we know
F = (k×q1×q2)/r²
When the charges are doubled, we have :
F' = (k × 2q1 × 2q2)/r²
F' = 4 (k×q1×q2)/r²
Thus,
F' = 4F
Hence, the force becomes 4 times its initial value.
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if a particle undergoes shm with amplitude 0.23 m , what is the total distance it travels in one period?
The total distance is 0.92 m
How to calculate total distance it travels in one period ?In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium position. It is equivalent to the vibration path's half-length.
A particle can move up to 0.23 meters from its resting position if it experiences simple harmonic motion with an amplitude of 0.23 meters.
It moved twice as far from its beginning place to its original position during one period, then returned after travelling a further twice as far distance.
Given ,
A total distance of
2*amplitude + 2*amplitude
= 2*0.23 + 2*0.23
= 0.42 + 0.46
= 0.92 meters
Therefore the total distance is 0.92 m
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what is the longest wavelength of light (in nm) for which all three metals will emit photoelectrons?
The longest wavelength at which a metal will emit an electron is 520 nm.
wavelength and frequency explanationsWave length is determined by the wavelength, which is also the separation between two wave crests and troughs. The amount of vibrations that pass through a certain region in a second is referred to as "frequency," and it is expressed in cycles per second (Hz) (Hertz). The link between wavelength and frequency is discussed in this article.
What is the wavelength?The distance between identical points (adjacent crests) in adjacent cycles determines how far a waveform signal has traveled in space or over a wire. In wireless systems, this length is frequently specified in meters (m), centimeters (cm), or millimeters (mm) (mm).
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by what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency? express your answer using three significant figures.
The factor through which the constant would have to change is given as 0.00412
How to solve for the oscillation frequencyThe moment of inertia is expressed as I = mr²
mass and volume has the relationship that is written as:
m = pV
m α V
mass is directly proportional to volume
m∝r³
m ∝ (1/3)³ = 1 / 27
the moment of inertia can be decreased by: 1 / 27 * (1 / 3)²
= 1 / 243
a. The angular frequency is gotten by
√1 / I
[tex]\sqrt{\frac{1}{1/243} }[/tex]
= 243
The factor through which the torsion constant would have to be reduced is given as 1 / 243
= 0.00412
There was a decrease of 0.00412
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Your boss at the Cut-Rate Cuckoo Clock Company asks you whatwould happen to the frequency of the angular SHM of the balancewheel if it had the same density and the same coil spring (thus thesame torsion constant), but all the balance wheel dimensions weremade one-third as great to save material.
By what factor would the torsion constant need to be changedto make the smaller balance wheel oscillate at the originalfrequency?
a 10 kilogram rock is dropped off the top of a 20 meter tall building. what is the kinetic energy of the rock right before it impacts the ground?
The kinetic energy of the rock right before it impacts the ground is 2940J.
Solution:
[tex]E_{P} = m_{gh}[/tex]
10 KG * 9.8m/s² * 30 m
[tex]E_{p}[/tex] = 2940 J
A falling ball has kinetic energy due to its motion. Therefore, the potential energy stored in the ball in its elevated position is converted into kinetic energy when the ball falls. When an object is in free fall, its potential energy is converted into kinetic energy.
When an object hits the ground its kinetic energy is converted into heat and sound energy. When an object falls, its potential energy decreases, and its kinetic energy increases. A decrease in potential energy is exactly the same as an increase in kinetic energy.
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the following measurements from yaw marks left at the scene of an accident were taken by law enforcement officers. using a 31-ft length chord, the middle ordinate measured approximately 3 ft. the drag factor for the road surface is 1.02. a. determine the radius of the yaw mark to the nearest tenth of a foot. fill in the blank 1 41.5 b. determine the minimum speed that the car was going when the skid occurred to the nearest tenth.
The minimum speed of the car is 11.1634 mph and the radius of the yaw mark is 11.2 ft.
Yaw marks are always curved. They are, initiated by a steering input. They're what's left from a tire that is still rolling but is simultaneously sliding laterally.
The radius of the yaw mark to the nearest tenth of a foot = r
The minimum speed = s
Length of the chord = c = 31 ft
Middle ordinate = m = 3 ft
Drag factor = f = 1.02
The formula for determining radius from a chord and middle ordinate is =
= r² = (c² / 8 x m) + (m / 2)
= r² = (31² / 8 x 3) + (3 / 2)
= r² = 41.541
= r = 11.2 ft
(b) Now minimum speed = s
= s = √(15 X f X r)
= s = √ (15 X 1.02 X 11.2)
= s = 11.1634 mph
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The following images show five planets in our solar system. Rank these planets from left to right based on their average surface (or cloud-top) temperature, from highest to lowest. (Not to scale.)
Highest -- Mercury, Earth, Mars, Jupiter, Neptune -- Lowest
Notice that, for these five planets, temperature correlates with distance from the Sun: the closer to the Sun, the hotter the planet. Remember, however, that this is not always the case, because a planet’s temperature also depends on its reflectivity and on the strength of its greenhouse effect (if any). For example, the greenhouse effect gives Venus a higher average temperature than Mercury, even though Venus is nearly twice as far from the Sun.
Loftiest to smallest temperature
Mercury
Earth
Mars
Jupiter
Neptune
What's the average face temperature?
Planetary face temperatures range from over 400 °C on Mercury and Venus to below-200 °C on distant globes. The factors that determine temperature are the complex balance of heat entered and lost.
Thus, for these five globes, temperature correlates with distance from the Sun. The near to the sun, the hotter the earth. Note, still, that this isn't always the case, as the earth's temperature also depends on its reflectance and the strength of the greenhouse effect( if present). For illustration, although Venus is nearly doubly as far from the Sun, the average temperature on Venus is advanced than on Mercury due to the greenhouse effect.
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consider a tall, skinny pine tree, initially upright, that falls over in a forest. as it is falling, its base remains in contact with the ground and does not move from side to side. what sort of path does the tree's center of mass follow as it falls?
The tree will fall along quarter circular path by virtue of centre of mass.
Physics defines the center of mass as the location where the weighted position of a body's mass in relation to other points is equal to zero, creating a point of balance. Any distribution of mass within an object is possible. In essence, it is a hypothetical position defined in the laws of physics themselves in relation to any object at all, or even a system of objects based on the distribution of masses. The body can now be forced to experience some linear acceleration without experiencing any angular acceleration. Only rotation's effects are visible when a body is rotated through its center of mass.The tree's center of mass will be affected by the weight of the entire tree because the base is fixed in place at its initial location.To know more center of mass -
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Barium-131 is used in the detection of bone tumors. The half-life of barium-131 is approximately 12 days. How long will it take for the radiation level of barium-131 to drop to 1/4 of its original level?.
It will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.
We know that radioactive reactions are 1st order reactions.
Given half life of Barium-131 is approximately 12 days.
So to drop to 1/4 of it's original level it will take more 12 days i.e. one more half life.
Total days are : 12+12=24 days
So it will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.
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how many times larger in diameter of the smallest jovian planet than the diameter of the largest terrestrial planet
The diameter of the smallest jovian planet is 3.96 times larger than the diameter of the largest terrestrial planet.
What are the jovian and terrestrial planets?The jovian planets or also called giant gaseous planets are those that are far away in the solar system, which includes Jupiter, Saturn, Uranus, and Neptune, while terrestrial rocky planets include Mercury, Venus, the Earth planet and Mars.
Therefore, with this data, we can see that the jovian and terrestrial planets are different based on the composition of their surfaces and also due to the distance to the Sun.
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a student of mass 50kg decides to go on the ride. the coefficient of static friction between the student and wall is 0.8. if the diameter of the ride is 10m, what is the maximum period of the ride's rotation that will keep the student pinned to the wall once the floor drops?
Ride's rotation that will keep the student pinned to the wall once the floor drops is 3.97 sec.
What is rotation?rotation is a type of trasfermation that takes each point in a figure and rotates its a certain number.
Mass of student = 50 kg
Coefficient of static friction \mu = 0.8 μ=0.8
Ride diameter d = 10 m d=10m
Ride radius r = \frac{d}{2} = 5 m r= 2d
=5m
Acceleration due to gravity g = 10 m/s^2 g=10m/s
2
Maximum period of ride's rotation =
Formula: \text{ Maximum period } = \500{\text{ Circumference }}{\10m/s{ Velocity }} Maximum period =
Velocity
Circumference
Step 1: Calculating the static frictional force and normal force
This frictional force will be equal to the student's weight to
find out what minimum static frictional force is required
Hence, maximum period of ride's rotation P = 3.97 P=3.97 sec
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when doing a chin-uo, a student lifts her 50.0 kg body a distance of .3 meters in 2 seconds. what is the power delivered by the student's biceps?
The Power provided by the student's biceps is 7.5 J/s.
What is power?The amount of energy transferred or converted per unit time is referred to as power. The watt is the unit of power in the International System of Units, equal to one joule per second. Power is sometimes referred to as activity in older works. A scalar quantity is power.The rate at which work is completed is referred to as power. Rate means per unit of time in this context. Power is calculated by dividing the amount of work done by the amount of time it took to complete the work.Given,
Mass = 50kg
Distance = 0.3 meters
Time = 2 seconds
W = fd
P = W/(t₂ - t₁)
To find work
W = (50kg)(0.3m)
W = 15J
To find power.
P = 15J / 2 - 0
P = 15J / 2
P = 7.5 J/s
Therefor the power is 7.5J/s
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which of the following was originally classified as a nebula? a. orion nebula b. hercules globular star cluster c. andromeda galaxy d. ring nebula e. pluto
The examples that were originally classified as a nebula are Orion nebula, Hercules globular star cluster, Andromeda galaxy, and Ring nebula; option A, B, C, and D.
What is a nebula?A nebula is a giant cloud of dust and gas that is found in space. More than one nebula is collectively called nebulae. The gases present in a nebla are usually hydrogen and helium.
Some nebulae are made from the gas and dust that are released by the explosion of a dying star, for example in a supernova.
Some other nebulae are the sites for the formation of new stars.
The four types of nebulae are:
Emission Nebula e.g. Omega NebulaReflection Nebula - e.g. Iris NebulaDark Nebula - e.g Horsehead NebulaPlanetary Nebula - e.g. Ring NebulaLearn more about nebula at: https://brainly.com/question/1162533
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a suitcase is hanging straight down from your hand as you ride an escalator. your hand exerts a force on the suitcase, and this force does work. this work is
The work is positive when you ride up the escalator and negative when you ride down the escalator.
What is work?
Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance traveled for a constant force directed in the same direction as the motion.
So, work done is positive when you ride up the escalator and negative when you ride down the escalator.
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Which description is true for the following situation? As you are taking a shower, water vapor in the humidified air strikes the mirror and turns into a water droplet.
Alright, the answer is A.
Endothermic means that the source requires absorption of heat. Exothermic means that the source is accompanied by the release of heat.
B and D are incorrect, as they mean the opposite of the term associated.
So between A and C, when you lose heat in water vapor, the water VAPOR turns into regular water. Therefore:
A is correct.
(Logically, anyways.)
Let me know if this helped.
if a harmonic oscillator were acted upon by minor dissipative forces, how would the amplitude of the oscillations change as time goes on?
The amplitude of the oscillations change as time goes on is the more rigid (or less compressible) the medium, the faster the speed of sound.
What is meant by amplitude ?In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium location. It is equivalent to the vibration path's half-length.
Distance between the wave's resting position and its highest displacement is known as amplitude. The number of waves that pass by a specific location each second is known as its frequency. Period: the amount of time needed for a wave cycle to complete.
Sound waves' relative strength, which we experience as loudness or volume, is known as amplitude. Decibels (dB), which stand for sound pressure level or intensity, are used to measure amplitude.
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which component within an absorption refrigeration system requires heat transfer from a high temperature aource
Generator component within an absorption refrigeration system requires heat transfer from a high temperature source.
The evaporator "buckets" or collects heat from the chilled area. Low pressure causes the "bucket" to undergo a state shift (latent heat transfer) as it takes in heat. The "bucket" of low pressure and heat is then transported to the compressor by the evaporator. The component of the refrigeration system that actually cools things down is called the evaporator. The evaporator is situated in the region to be cooled because its purpose is to absorb heat into the refrigeration system (from where you don't want it to).
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The position vs. time graph shows how far away I am from the table while cooking breakfast. Which parts of the journey show where I am:
The velocity of an object is represented by the slope of a location graph. Thus, the slope's value at a given instant corresponds to the object's velocity at that precise moment.
What does a graph of position vs time reveal?
Position in relation to the starting point is plotted on the y-axis of a position vs. time graph, while time is plotted on the x-axis to represent motion. The gradient of a position vs. time graph serves as a representation of the velocity. The slope gets steeper as the motion changes more quickly.
Where is the time graph located?
The Position Time Graph: What Is It?
The Position-Time graph is the graph on which the time t and the instantaneous position x of a particle are shown.
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what is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (we can neglect the volume of the capillary tubing connecting the bulbs.)\
The calculated pressure is 40 atm. An area of the Earth's atmosphere that has a very high or low pressure in comparison to the air surrounding it is referred to as a pressure system.
The distance between air molecules is all that is meant by the term pressure. High pressure is created when the air is compressed and tightly confined. Low pressure occurs when the air is dispersed. Boyle's law states that if T is constant, then so is the PV.
∴P \s1
V 1 + P 2 + P 3 + P 4 =P 4 V 4
P 4 stands for total pressure, and V 4 stands for total volume.
The total capacity of all the containers is now V 4 = V 1 + V 2 + V 3 = 1+1 + 0.5 = 2.5L.
Now, after plugging all the data into equation (1), we get 3001+2401+4400.5=X2.5 X= 2.5 760 =304mm, where 760mm is 1atm. The conversion from 304mm to 760 304 = 0.4 atm
Therefore, x=0.4 atm.
100x=40atm
The complete question is- Consider the arrangement of bulbs shown in the drawing. Each of three bulbs contains a gas at pressure shown. What is pressure of system when all stopcocks are opened. Assuming that temperature remain constant. (Neglect the volume of capollary tubing connecting bulbs)
A-440 torr
B-200 torr
C-360 torr
D-320 torr
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suppose that the frequency f of the current in an ac circuit goes to zero (which means that the current becomes a direct current). which circuit element would not permit charge to flow in the circuit?
A capacitor, because it has the greatest reactance at frequency f = 0 Hz.
A capacitor is a device that stores electrical energy in an electric field through the accumulation of electrical charges on two nearby surfaces insulated from each other. It has two terminals and is a passive electrical component. Charges flow through the capacitor when it is supplied with electricity, but this flow is blocked by the insulation between the metal plates. Since the capacitor's electrode plates are separated by an insulator (air or dielectric), no direct current can flow unless the insulator decays. In other words, a capacitor blocks direct current. When we connect a capacitor across an AC power source, it starts charging and discharging continuously due to the continuous change in the supply voltage. Capacitors do not store charge. Capacitors actually store a charge imbalance.
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Thermodynamics deals with the macroscopic properties ofmaterials. Scientists can make quantitative predictions about thesemacroscopic properties by thinking on a microscopic scale. Kinetictheory and statistical mechanics provide a way to relate molecularmodels to thermodynamics. Predicting the heat capacities of gasesat a constant volume from the number of degrees of freedom of a gasmolecule is one example of the predictive power of molecularmodels.
The molar specific heat C_v of a gas at a constant volume is thequantity of energy required to raise the temperature T of one mole of gas by one degree while thevolume remains the same. Mathematically,
C_{\rm v}= \frac{1}{n}\,\frac{dU}{dT},
where n is the number of moles of gas, dU is the change in internal energy, anddT is the change in temperature.
Kinetic theory tells us that the temperature of a gas isdirectly proportional to the total kinetic energy of the moleculesin the gas. The equipartition theorem says that each degree offreedom of a molecule has an average kinetic energy equal to\frac{1}{2}k_{\rm B}T, wherek_B is Boltzmann's constant1.38 \times 10^{-23} \rm {J/K}. Whensummed over the entire gas, this gives \frac{1}{2}nRT, where R=8.314\;{\rm \frac{J}{mol\cdot K}}is the ideal gas constant, for each molecular degree offreedom.
Part A
Using the equipartition theorem, determine the molar specific heat,C_v, of a gas in which eachmolecule has s degrees of freedom.
Express your answer in terms ofR and s.
Part B
Given the molar specific heat C_v of a gas at constant volume, you candetermine the number of degrees of freedom s that are energetically accessible.
For example, at room temperature cis-2-butene,\rm C_4 H_8, has molar specific heatC_v=70.6\;{\rm \frac{J}{mol \cdot K}}. How many degrees of freedom of cis-2-butene areenergetically accessible?
Express your answer numerically tothe nearest integer.
Mathematically, the answer to the following question's a part is: [tex]C_{v} = \frac{Rs}{2}[/tex] and b part is: s=17.
a) Using the equipartition theorem,
U = [tex]\frac{1}{2} k_{b} T[/tex]
= [tex]\frac{1}{2} n_{R} T[/tex]
Degree of freedom for 's'
= [tex]\frac{1}{2} sn R T[/tex]
Then, molar specific heat [tex]C_{v} = \frac{1}{n} \frac{dU}{dT}[/tex]
Mentioning it in terms of R and s;
[tex]C_{v} = \frac{1}{n} \frac{dU}{dT} (\frac{1}{2} sn RT)[/tex]
[tex]C_{v} = \frac{Rs}{2}[/tex]
b) As per question,
[tex]C_{v}[/tex] = 70.6 J/mol.K and R = 8.314 J/mol.K
Using the formula, [tex]C_{v} = \frac{Rs}{2}[/tex]
70.6 J/mol.K = [tex]\frac{(8.314 J/mol.K) X s}{2}[/tex]
taking 2 on the left side by moving it from the division
70.6 J/mol.K x 2 = 8.314 J/mol.K x s
= [tex]\frac{70.6 J/mol.K X 2}{8.314 J/mol.K}[/tex]
s = 16.983 then we round it off to the nearest figure
We get, s = 17
Each degree of freedom that only appears quadratically in the total energy has an average energy of 1/2 kBT in thermal equilibrium, which increases the system's heat capacity by 1/2 kB, according to the equipartition theorem, also known as the law of equipartition, the equipartition of energy, or simply equipartition. The classical physics presumption that this concept holds true in all situation is refuted by the quantum theory.
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