when the temperature is kept constant, to increase the volume of the gas, you will decrease the pressure (Option D)
How do I increase the volume at constant temperature?The volume of a gas at constant temperature is explained by the Boyle's law equation which is states as follow:
The volume of a fixed mass of gas is inversely proportional to the pressure at conctant temperature. Mathematically, it is expressed as follow:
P ∝ = 1/V
P = K / V
P₁V₁ = P₂V₂
Where
P₁ and P₂ are initial and new pressure V₁ and V₂ are initial and new volume
From the above formula, we can see that volume and pressure exist in inverse proportionality. This means that when the volume increases, the pressure will decrease and also, when the volume decreases, the presure will increase.
With the above information, we can conclude that the correct answer to the question is: You would decrease the pressure (Option D)
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An object begins at position x = 0 and moves one-dimensionally along the x-axis witļi a velocity v
expressed as a function of time t according to the graph above. At what time does the object pass
through x = 0 again?
Answer:
The answer is "between 20 s and 30 s".
Explanation:
Calculating the value of positive displacement:
\(\ (x_{+ve}) = \frac{1}{2} \times 15 \times 20 \\\\\)
\(= \frac{1}{2} \times 300 \\\\= 150 \\\\\)
Calculating the value of negative displacement upon the time t:
\((x_{-ve}) = \frac{1}{2} \times 5 \times 20- 20(t-20) \\\\\)
\(= \frac{1}{2} \times 100- 20t+ 400 \\\\= 50- 20t+ 400 \\\\\)
\(\to X= X_{+ve} + X_{-ve} \\\\\)
\(\to 150 - 50 -20t+400 =0\\\\\to 100 -20t+400 =0 \\\\\to 500 -20t =0\\\\\to 20t =500 \\\\\to t=\frac{500}{20}\\\\\to t=\frac{50}{2}\\\\\to t= 25\)
That's why its value lie in "between 20 s and 30 s".
with an armature resistance of 0.03 2 and a field resistance of
41.67 2. The motor has compensating windings, so armature
reaction can be ignored. Mechanical and core losses may be
assumed to be negligible for the purposes of this problem. The
motor is assumed to be driving a load with a line current of 126 A
and an initial speed of 1103 r/min. To simplify the problem,
assume that the amount of armature current drawn by the motor
remains constant.
A. If the machine's magnetization curve is shown in Figure 8-9, what is the motor's
speed if the field resistance is raised to 50 ?
B. Calculate and plot the speed of this motor as a function of the field resistance RF
assuming a constant-current load.
R₁ = 0.03 2
EA
IA
IF
IL
RF + Radj
LF
+
250 V
A. The motor's speed is approximately 1086 r/min if the field resistance is raised to 50 Ω.
B. The speed of this motor as a function of the field resistance RF is approximately 1086 r/min
A. According to the magnetization curve shown in Figure 8-9, the motor's speed can be calculated by using the following equation:
EA = kϕN, where EA is the back EMF, k is a constant, ϕ is the magnetic flux, and N is the motor speed.
Since the amount of armature current remains constant, the back EMF is also constant.
Therefore, the magnetic flux must also be constant. The magnetic flux is proportional to the field current IF, which can be calculated using Ohm's law:
IF = (250 V - EA)/(RF + R₁)
At the initial field resistance of 41.67 Ω, the field current is IF = (250 V - EA)/(41.67 Ω + 0.03 Ω) = (250 V - EA)/41.70 Ω.
If the field resistance is raised to 50 Ω, then the new field current is IF = (250 V - EA)/(50 Ω + 0.03 Ω) = (250 V - EA)/50.03 Ω.
Since the magnetic flux is constant, we can set the two expressions for IF equal to each other and solve for N:
kϕN/IF1 = kϕN/IF2
N = (IF2/IF1)N1 = (250 V - EA)/(50.03 Ω + 0.03 Ω) * 1103 r/min ≈ 1086 r/min
Therefore, the motor's speed is approximately 1086 r/min if the field resistance is raised to 50 Ω.
B. The speed of the motor as a function of the field resistance RF can be plotted using the same equation used in part A:
N = (250 V - EA)/(RF + R₁ + Radj) * 1103 r/min
where Radj is the resistance of any additional resistance in the circuit. Since the load current is constant, the current through the motor is also constant, so EA is also constant.
Therefore, the speed is inversely proportional to the total resistance in the circuit, which includes the field resistance RF, armature resistance R₁, and any additional resistance Radj.
A plot of the speed as a function of the field resistance is shown in Figure 8-10. As the field resistance increases, the speed of the motor decreases due to the increased total resistance in the circuit. This relationship is linear for this type of constant-current load.
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A Child stands on the bus Remains Still When The bus is at rest. When the bus moves forward AndeaThe bus is at rest. When the bus moves forward And then slows down, the children the Contnues moving forward at the original speed. This is an example of
Answer:
inertia
Explanation:
what is the force acting on point O? Check picture for diagram! please and thank you
The magnitude of the force acting at point O is determined as 240 N.
What is the magnitude of the force at point O?The magnitude of the force at point O is calculated by applying the principles of moment as shown below.
sum of the clockwise moment = sum of the anticlockwise moment
F₀(2 m + 2m + 2m) = 260 N (2m + 2 m ) + 200 N ( 2 m )
where;
F₀( is the force at point O6F₀ = 260 (4) + 200(2)
6F₀ = 1,440
F₀ = 1440 / 6
F₀ = 240 N
Thus, the magnitude of the force acting at point O is determined as 240 N.
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#1 . If a wire is plugged into row 1, column and another nb wire plugged into row 1 , column f, are the two wires connected ?
In a breadboard, internal connections run horizontally, that is, that all holes in the same row are internally connected. That means that if two wires are inserted in the same row, they are connected.
Answer: The two wires are connected.
53-54, Image is attached!
Answer:
2.29 s
Explanation:
This problem is a description of an elastic collision (the two objects collide and effectively become one object). The equation for an elastic collision is
\(m_1v_1+m_2v_2=m_3v_3\), where:
\(m_1v_1\) = the mass of the child (55.0 kg) times the velocity of the child (2.5\(\frac{m}{s}\))
\(m_2v_2\) = the mass of the sled (12.0 kg) times the velocity of the sled (0.0\(\frac{m}{s}\))
\(m_3v_3\) = the combined mass of the child and the sled (67.0 kg) times the combined velocity of the child and the sled (\(v_3\))
First, rearrange the problem to solve for \(v_3\):
\(\frac{m_1v_1+m_2v_2}{m_3}=v_3\)
So,
\(\frac{(55.0\ kg)(2.5\ \frac{m}{s})+(12.0\ kg)(0.0\ \frac{m}{s})}{67.0\ kg}=v_3\\\frac{137.5\frac{kg*m}{s}}{67.0\ kg}=v_3\\2.05\frac{m}{s}=v_3\)
The force of friction for this problem is given as 60 N. To stop the child and the sled, the force of friction must be equal and opposite to the force of the child and sled. According to Newton's first law, force equals mass times acceleration (F=ma). So, an equation to solve this portion of the problem can be given as -60 N=ma, where m=67.0 kg. So,
\(-60\ N=(67.0\ kg)a\\\frac{-60\ \frac{kg*m}{s^2}}{67.0\ kg}=a\\-0.90\frac{m}{s^2}\)
Acceleration can then be used in kinematic equation #1 (\(v_f=v_i+at\)) to solve for time. Rearrange the equation and let
\(v_f=0.0\frac{m}{s}\\v_i=2.05\frac{m}{s}\\a=-0.90\frac{m}{s^2}\)
So,
\(\frac{v_f-v_i}{a}=t\\\frac{0.0\frac{m}{s}-2.05\frac{m}{s}}{-0.90\frac{m}{s^2}}=t\\\frac{-2.05\frac{m}{s}}{-0.90\frac{m}{s^2}}=t\\2.29\ s=t\)
Describe the relationship between frequency and wavelength of the visible light spectrum?
An astronaut brings a cube from the Earth to the Moon.
What is true about the inertial mass and weight of the cube?
Note that the gravitational acceleration on the Moon is about 1.6m/s^2
A) The inertial mass increases but the weight decreases.
B) Both the inertial mass and weight decrease.
C) The inertial mass decreases but the weight increases.
D) The inertial mass remains constant but the weight decreases.
Answer:
Answer D. Inertial mass constant, weight decreases.
Explanation:
Khan Academy
You are pulling a wagon with a mass10kg and it’s moving forward at a constant rate. Your friend gets into the wagon and it’s slows down. What can you do to get the wagon moving faster?
Explanation:
Without changing the constant speed, your friend can empty the contents of the wagon, or decrease the overall rate, or the terrain the wagon is traveling on, all of these would increase the wagon's speed. Also, you could try applying a heavier pulling force, like using a horse instead of yourself, or you and a horse to get going faster.
Hope this helps!
a bucket filled with water feels lighter while it is inside water
It will be harder to move about.
1.Luca is a member of a game development team that recently released a new game. They are now developing visual upgrades such as additional vehicle models and character skins. Which of the following terms refers to these upgrades?
A. Season System
B. DLC
C. Licensing
D. Monetization
2.Jodie and her development team are creating DLC for their video game. They will soon release new levels and content packs that unlock challenges in the gameplay. What type of DLC are Jodie and her team creating?
A. Season System
B. Visual Updates
C. Game Exposition
D. Licensing
3.Donell has created a new DLC for his video game. Which of the following should Donell consider when determining the price of his DLC?
A. Color of the new skins
B. Competition and expectations
C. Copyright Licensing
D. Soundtrack
4.Gia is releasing new content packs based on a seasons system. How frequently will she likely release new content for her video game?
A. Every six months
B. Every year
C. every month
D. every three months
5.Judah is looking to monetize the development process of his recently-released video game by selling external content. Which of the following is an example of external content?
A. behind-the-scenes video
B. in-game challenges
C. visual updates
D. game expansion packs
6.Katelin is creating new custom skins for the characters in her recently released video game, in addition to cosmetic items such as glasses, wigs, clothing, and hats. What type of DLC is Katelin creating?
A. Game expansion
B. monetization
C. visual updates
D. mobile
7.Mohammad has experienced everything that a video game has to offer. He has reached the highest level and has defeated all of the challenges. What type of DLC is he most likely to purchase?
A. game expansion
B. visual updates
C. license
D. monetization
8.Jayden is a member of a game development team praised for the visual artistry of their characters and game environment. Which of the following is an example of external content that Jayden and the team could monetize?
A. Soundtrack
B. novel
C. concept art books
D. in-game visual upgrades
9.Bret and his development team released a new video game a few months ago. After strong sales initially, it is now not selling well at full price. What should Bret and his team do to ensure a boost in profits so that they can begin their next game project?
A. Create DLC
B. increase the price of the game
C. confirm their licensing agreements
D. hold a temporary sale on popular marketplaces
10.Which of the following should a game development team do before they consider releasing their game music in other forms?
A. check licensing agreements
B. create a digital art book
C. create DLC
D. add unique visual upgrades
11.Myra is transitioning from being an independent developer to starting a game development company. How should Myra release herself from direct legal liability?
A. register a business license
B. report income on taxes
C. open a new bank account
D. separate her personal finances from the business finances
12.Masami’s newly-released video game has received much praise for its distinctive audio. Which of the following types of external content should Masami monetize?
A. digital art book
B. soundtrack
C. behind-the-scenes video
D. novel based on the main character
13.Which of the following terms refers to how team members interact with each other?
A. innovation
B. encouragement
C. group dynamics
D. onboarding
14.Khalid is starting a game development business of his own. Which of the following is a legal requirement?
A. to report income on yearly taxes
B. to open a personal bank account
C. to open a business bank account
D. to hire a team of developers
15.Moriah is the team leader of a new game development team. Which of the following does Moriah do to introduce the team members to each other and encourage open communication in the workplace?
A. group dynamics
B. onboarding activities
C. communication
D. motivation
Answer: B. DLC
B. Visual Updates
B. Competition and expectations
D. Every three months
D. Game expansion packs
C. Visual updates
A. Game expansion
C. Concept art books
A. Create DLC
A. Check licensing agreements
D. Separate her personal finances from the business finances
B. Soundtrack
C. Group dynamics
C. To open a business bank account
B. Onboarding activities
Explanation: :)
The phenomenon of magnetism is best understood in terms ofA) the existence of magnetic poles.B)the magnetic fields associated with the movement of charged particles.C)gravitational forces between nuclei and orbital electrons.D) electrical fluid
Answer:
A) the existence of magnetic poles.Explanation:
Magnetism is defined as the ability of a magnet to attract magnetic substance to itself. Such magnet has the ability of being magnetized. A magnet is known to possess poles which are the north poles and south poles. The presence of this poles is what makes them possess the properties of a magnet. An ordinary steel bar doesn't have the properties of a magnet unless it is magnetized and when you are trying to magnetize a steel bar, you are invariably introducing the magnetic poles.
According to the law of magnetism, like poles repel but unlike poles attract. From the above explanation, it can be concluded that the phenomenon of magnetism is best understood interns of existence of magnetic poles. This poles are called the north and the south poles.
name a suitable thermometer for steady temperature of 1000 degree Celsius?
Answer: A platinum resistance thermometer
Explanation:
It is a versatile instrument for temperature measurement in the range from — 200° to 1000°C. It is used both for precision measurements of the highest accuracy and for routine industrial work.
Answer:
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45:56
Which of these is an example of acceleration?
a bicyclist turning around a corner
a car traveling south with its cruise control set
a bus traveling north at 25m/s
a helicopter waiting to take off
Answer:
A car traveling south with its cruise control set
Explanation:
Turning could cause anything to slow down but going forward could mean that anything could go faster.
A square wire loop with 2.00 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in Figure . The loop contains an ideal battery with emf E = 20.0V. If the magnitude of the field varies with time according to B=0.0420â0.870t,with B in teslas and t in seconds, what are (a)the net emf in the circuit and (b) the direction of the (net) current around the loop?
If the surface is parallel to the field, there will be no angle and the magnetic flux will just be B A B A BA.
A wire loop is turned around an axis that is perpendicular to a uniform magnetic field. Each time a current is induced in the loop, its direction is reversed. an illustration of the magnetic flux produced by two distinct orientations of a flat test area to a magnetic field. A charged particle will revolve on a circular path if it is projected perpendicular to a uniform magnetic field, and its kinetic energy won't change because the magnetic force isn't doing any work. Since a particle's direction varies over a circular path, momentum likewise alters.
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You have isolated a highly lethal toxin from an octopus that you have reason to believe binds with high affinity to the pore opening of a voltage-gated sodium channel. To determine the effect of toxin binding, you perform a patch clamp experiment. Based on the following results, what do you conclude is the effect of the toxin on channel function (downward deflections indicate channel opening)?
Based on the results we conclude that the toxin delays channel closing.
What is toxin?A toxin is a naturally occurring organic poison created by the metabolic processes of living cells or organisms. In particular, toxins exist as proteins or proteins that have been conjugated. Organic chemist Ludwig Brieger (1849–1919)[4] coined the term "toxin," which is derived from the word "toxic."
Toxins can be small molecules, peptides, or proteins that can cause disease when they come into contact with or are absorbed by body tissues and interact with biological macromolecules like enzymes or cellular receptors. Toxins range widely in their toxicity, from typically minor (like a bee sting) to potentially fatal even at very low doses (such as botulinum toxin)
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Replace the incandescent bulb with the Voltage meter and return loop # to 3. What happens when you move the bar magnet back-n-forth through the loop? Does this appear to be creating a Direct Current or an Alternating Current? How do you know?
If we replace the incandescent bulb with a voltage meter and return the loop to its original configuration, then moving the bar magnet back and forth through the loop will induce an electrical current in the loop, as described by Faraday's law of electromagnetic induction.
What is magnet?A magnet is a material or object that produces a magnetic field, which is a force that can attract or repel certain other materials, such as iron or steel. The magnetic field is created by the motion of electric charges within the magnet, which align in such a way that they produce a net magnetic field. Magnets can be made from a variety of materials, including iron, cobalt, nickel, and certain alloys. They come in many different shapes and sizes, including bars, discs, horseshoes, and rings.
Here,
The type of current that is generated depends on the direction and rate of the magnet's motion. If the magnet is moved back and forth with a constant speed and in a straight line, the current induced in the loop will be an alternating current (AC), because the direction of the current will reverse every time the magnet changes direction. This can be observed by the voltage meter reading a voltage that periodically changes in direction.
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(b)
The total power input to the leaf blower is 750 W.
The useful power output of the leaf blower is 360 W.
Calculate the efficiency of the leat blower.
The efficiency of the leaf blow is 48%.
How can we find the efficiency of the leaf blower?E = m×c×ФHere, E = Energy transferred
m = Mass
Ф = Temperature change
efficiency = (Useful energy out / Total energy in ) × 100efficiency = (Useful power out / Total power in ) × 100E = P × tHere, E = Energy transferred
P = Power
t = time
v = f ×∧Here, v = speed
f = frequency
∧ = wavelength
Substitute into the time equation,Efficiency = (Useful power out / Total power in ) = 360/750 = 0.48
Convert it to percentage = 0.48 × 100 = 48%So, the efficiency of the leaf blower is 48%.
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E
Please select the word from the list that best fits the definition
freezing point of carbon dioxide
A. Meter
B. Liter
C. Kilogram
D. Kelvin
Two charges are repelling each other with a force magnitude F. If each charge doubled and the distance between the charges became four times the original distance, determine the new magnitude of the force. (1/2)F 4F 2F 16 F (1/4)F
Answer:
(1/4)F
Explanation:
Let F be the force on charges q and q' separated by a distance, d
F = kqq'/d²
Now, if q and q' are doubled, our new charges are 2q and 2q' respectively and, if the distnace is increased by four times, then our new distance is 4d. So our new force F' = k (2q)(2q')/(4d)²
= 4kqq'/16d²
= kqq'/4d²
= F/4
So, the magnitude of our new force is F/4
Question 9 of 27
While working out, a man performed 500 J of work in 8 seconds. What was
his power?
The power of man performing 500 J of work in 8 seconds is 62.5 J/s.
Power can be defined as the pace at which work is completed in a given amount of time.
Horsepower is sometimes used to describe the power of motor vehicles and other machinery.
The pace at which work is done on an item is defined as its power. Power is a temporal quantity.
Which is connected to how quickly a project is completed.
The power formula is shown below.
Power = Energy / Time
Power = E / T
Because the standard metric unit for labour is the Joule and the standard metric unit for time is the second, the standard metric unit for power is a Joule / second, defined as a Watt and abbreviated W.
Here we have given Energy as 500 J and Time as 8 second.
Power = Energy / Time
Power = 500 / 8 Joule / sec
Power = 250 / 4 Joule / sec
Power = 125 / 2 Joule / sec
Power = 62.5 Joule / sec or 62.5 watt
Power came out to be 62.5 J/s when the man performed 500 Joule of work in 8 seconds.
So we can conclude that the power in the Energy transmitted per unit of time, and can be find out by dividing Energy by time. In our case the Power came out to be 62.5 Joule / Second.
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A 30 kg chair initially at rest on a horizontal floor requires a 160 N horizontal force to set it in motion. Once the chair is in motion, a 125 N horizontal force keeps it moving at a constant velocity. The acceleration of gravity is 9.81 m/s 2 . a) What is the coefficient of static friction between the chair and the floor? 017 (part 2 of 2) 10.0 points b) What is the coefficient of kinetic friction between the chair and the floor?
(a). The chair's dynamic friction factor with the floor is = 0.602.
(b). The chair's as well as the floor's kinetic friction factor is = 0.475.
What is a simple definition of velocity?The metre per second (m/s) is the accepted unit of velocity magnitude (also known as speed).
Briefing:a)Let's practice using Newton's second law. In the reference system, the x axis is perpendicular to the axis and parallel to the floor.
Y Axis
N-W = 0
N = W
X axis
F-fr = ma
The formula for the friction force is
fr = μN
The acceleration is zero where the movement starts.
Let's replace
F = μ (mg) = 0
F = μ mg
μ = F / mg
μ = 160/30 9.81
μ = 0.602
b) The formula is the same in this instance, but the friction is kinetic.
μ = F2 / mg
μ = 125/30 9.81
μ = 0.475
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find the velocity v of the block as a function of time. express your answer in terms of some or all of the variables: k , m , a , and t .
The velocity of the block as a function of time is \(v(t) = - A \sqrt{\frac{k}{m}} (\: sin \: \sqrt{\frac{k}{m}} t)\)
Look at the attachment to see the picture of the block. The block is attached to a spring and placed on a frictionless surface. Simple harmonic motion applies to the system. The equation of the position as a function of time for the system
x(t) = A cos ωt
A = the amplitudet = the time interval ω = the angular frequencyx = the positionThere is the force of the spring in the system, according to Newton's second law
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Can the potential of a non uniform charged sphere be the same as that of a point charge? Explain in details
No. The potential of a non-uniform charged sphere cannot be the same as that of a point charge.
Non-uniform charged sphere as a point chargeThe potential at any point in space is determined by the distribution of charge within the system, and a non-uniform charged sphere has a different charge distribution than a point charge.
A point charge has all of its charges concentrated at a single point, while a non-uniform charged sphere has charge distributed throughout its volume.
As a result, the electric field and potential will be different for these two systems, even if they have the same total charge. Therefore, the potential of a non-uniform charged sphere cannot be the same as that of a point charge.
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The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons
The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)
Why the electron number cannot be used instead?The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.
This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.
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A non-ideal battery has a 6.0-V emf and an internal resistance of 0.6 l. Determine the terminal voltage (in volts) when the current drawn from the battery is 1.0 A
What capacitance is needed to store 3μC of charge at a voltage of 120V?
Answer:
C = 0.025F
Explanation:
Charge =q=3×\(10^{-6}\)C
Voltage=V=120V
Q=CV
C=Q/V
=3×\(10^{-6}\)/120
=1/40×\(10^{-6}\)
C = 0.025F
C=2.5 \(10^{-4}\)C 0r 25 ×\(10^{-3}\)F
c. is what percent of 125?
Answer:
Step 1: We make the assumption that 125 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=125$.
Step 4: In the same vein, $x\%=125$.
Step 5: This gives us a pair of simple equations:
$100\%=125(1)$.
Explanation:
Volume (m3) 1.337E+0 moles of an ideal diatomic gas undergoes a transition from a to c along the diagonal path in the figure. The temperature of the gas at point a is 900 K. During the transition, what is the change in internal energy of the gas? Submit Answer Tries 0/10 How much heat is added to the gas in going directly from a to c? Submit Answer Tries 0/10 How much heat must be added to the gas if it goes from a to c along the indirect path abc? Submit Answer Tries o/10
The change in internal energy of gas is Delta U = 1.337E+0 moles * (5/2)R * (900 K - Tc) Where Tc is the temperature of the gas at point c. the heat added to the gas in going directly from a to c is Q = 1.337E+0 moles * (5/2)R * (900 K - Tc).
To find the change in internal energy of an ideal gas during a process, you can use the equation: Delta U = n * Cv * Delta T Where Delta U is the change in internal energy, n is the number of moles of the gas, Cv is the molar specific heat capacity at constant volume, and Delta T is the change in temperature. For a diatomic gas, the molar specific heat capacity at constant volume is Cv = (5/2)R, where R is the ideal gas constant. Plugging in the given values, you get: Delta U = 1.337E+0 moles * (5/2)R * (900 K - Tc). To find the heat added to the gas in going directly from a to c, you can use the equation: Q = Delta U + Delta (PV) Where Q is the heat added to the gas, Delta U is the change in internal energy, and Delta (PV) is the change in the product of pressure and volume. For an ideal gas, the change in internal energy is equal to the heat added, so you can simply use the equation: Q = Delta U Plugging in the values, you get: Q = 1.337E+0 moles * (5/2)R * (900 K - Tc).
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Time Dilation. A group of scientists discover a new, rare isotope and are able to store a small amount of it. They determine that the isotope is unstable and half of their sample will decay in 13.0 monthsmonths . The scientists need a new laboratory to properly conduct measurements on the isotope. If laboratory is built before half the sample decays there will still be enough of the isotope available for experiments. However, it will take 21.0 monthsmonths to build the new lab. Fortunately, the scientists can quickly start construction and they have access to a spaceship that can travel at speeds approaching the speed of light c = 3.00
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Time Dilation. A group of scientists discover a new, rare isotope and are able to store a small amount of it. They determine that the isotope is unstable and half of their sample will decay in 13.0 months . The scientists need a new laboratory to properly conduct measurements on the isotope. If laboratory is built before half the sample decays there will still be enough of the isotope available for experiments. However, it will take 21.0 months to build the new lab. Fortunately, the scientists can quickly start construction and they have access to a spaceship that can travel at speeds approaching the speed of light c = 3.00 x 10⁸ m/s.
If they place their sample of the isotope on the spaceship, at what speed must it travel in order for the new laboratory to be completed on Earth by the time half of the isotope on the spaceship decays? Assume that it took one month for the scientists to actually start construction and launch the spaceship so half the sample will remain in 12.0 months but it will still take 21.0 months to build the new lab.
Answer:
the required speed is 2.4618 x 10⁸ m/s
Explanation:
Given the data in the question;
Time taken to complete a lab = 21 months
it took them one one to actually start so
Time remaining so that sample only decays by 1/2 = (13 - 1) = 12 months
we need to find at what speed the spaceship should travel so that time on earth ( = 12 months) become time on spaceship ( = 21 months)
we make use of time dilation equation;
t' = t/√( 1 - v²/c² )
where t is time in rest frame = 12 and t' is time in moving frame = 21
so we substitute
21 = 12/√( 1 - v²/c² )
21√( 1 - v²/c² ) = 12
√( 1 - v²/c² ) = 12/21
we square both side
( 1 - v²/c² ) = ( 12/21 )²
( 1 - v²/c² ) = 0.3265
v²/c² = 1 - 0.3265
v²/c² = 0.6735
v² = 0.6735 × c²
v = √0.6735 × √c²
v = 0.8206 × c
given that speed of light c = 3 x 10⁸ m/s
v = 0.8206 × 3 x 10⁸ m/s
v = 2.4618 x 10⁸ m/s
Therefore, the required speed is 2.4618 x 10⁸ m/s