The ladder is on the verge of slipping, so the friction force(f) will be equal to the force acting at the base of the ladder. F f = μs (mL + m) g cos θ = T cos θ = 1058.4 Nμs = T cos θ/[(mL + m) g cos θ] = 1058.4/[(18.0 + 72.0) × 9.8]μs = 0.792. Thus, the minimum value of the coefficient of static friction (μs) between the floor and the ladder so that the person can stand halfway up the ladder without the ladder slipping is 0.792.
Given that a person of mass m = 72.0 kg is standing one-third of the way up a ladder of length(L) , and the mass of the ladder is mL = 18.0 kg, uniformly distributed, and the ladder is inclined at an angle of θ = 30° with respect to the horizontal. The force of the wall on the ladder is 560 N. The free-body diagram(FBD) of the system consisting of the person and the ladder is given below: The magnitude of the net force exerted on the ladder by the floor: Since the system is in equilibrium(eq.), the net force acting on the ladder in the horizontal direction will be zero.
Net force in the horizontal direction, F x = 0N – T sin θ + F w = 0 where, tension(T) in the ladder, and F w is the force exerted on the ladder by the wall. The net force acting on the ladder in the vertical direction is zero. Net force in the vertical direction, F y = 0N – T cos θ + FL – mg = 0 where, FL is the force exerted by the floor on the ladder, the weight (mg) of the person. The force exerted by the floor on the ladder, FL = T cos θ – mg = (mL + m) g cos θ – mg. Magnitude of the net force exerted on the ladder by the floor: |FL| = (mL + m) g cos θ – mg = (18.0 + 72.0) × 9.8 × cos 30° – 72.0 × 9.8|FL| = 321.12 N. Thus, the magnitude of the net force exerted on the ladder by the floor is 321.12 N. The minimum value of the μs between the floor and the ladder so that the person can stand halfway up the ladder without the ladder slipping: When the person stands halfway up the ladder, the distance between the foot of the ladder and the wall is L/2.
We can take moments about the foot of the ladder. The ladder remains in equilibrium, so the sum of the moments about any point on the ladder is zero. Sum of the moments about the foot of the ladder = T cos θ × L/2 – mg × (L/3) = 0T cos θ = (mg × L)/(2 × L/3) = 3/2 mg where, T cos θ is the force acting at the base of the ladder, and L/2 is the distance between the force and the foot of the ladder. The force acting at the base of the ladder, T cos θ = (3/2) × 72.0 × 9.8 = 1058.4 N. The f acting at the base of the ladder is given by the following equation: F f = μs (mL + m) g cos θ where, μs is the coefficient of static friction.
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Two automobiles are equipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency the horns emit? Assume T=20 ∘
C.
When an automobile at rest and another automobile moving towards it at 15 m/s with the same single frequency horn, the driver in the stationary automobile hears a beat frequency of 4.5 Hz. The frequency of the horn at rest is approximately 107.4 Hz.
The frequency of a horn is the number of complete vibrations or cycles it makes in one second. In this problem, we are given that two automobiles equipped with the same single frequency horn are involved.
When one of the automobiles is at rest and the other is moving towards it at a speed of 15 m/s, the driver in the stationary automobile hears a beat frequency of 4.5 Hz.
A beat frequency is the difference between the frequencies of two sound waves. When two waves with slightly different frequencies interfere, they produce a beat frequency that is equal to the difference between their frequencies.
Let's denote the frequency of the horn at rest as f, and the frequency of the horn in motion as f'.
The beat frequency is 4.5 Hz, we can set up the equation:
|f - f'| = 4.5 Hz
Since the automobile in motion is approaching the stationary automobile, the frequency of the horn in motion is higher than the frequency at rest. Therefore, we have:
f' - f = 4.5 Hz
Now, we can use the formula for the Doppler effect to relate the frequencies of the horn in motion and at rest. The formula for the Doppler effect when a source is moving towards an observer is:
f' = (v + vo) / (v - vs) * f
where f' is the observed frequency, f is the source frequency, v is the speed of sound, vo is the velocity of the observer, and vs is the velocity of the source.
In this case, the source frequency is f and the observed frequency is f', while the speed of sound is given by v and is constant at 343 m/s. The velocity of the observer, vo, is 0 m/s since the driver of the stationary automobile is at rest. The velocity of the source, vs, is -15 m/s since the automobile with the horn is moving towards the stationary automobile.
Now, we can substitute the given values into the Doppler effect equation:
f' = (343 + 0) / (343 - (-15)) * f
Simplifying the equation gives:
f' = (343/358) * f
Now, we can substitute this expression for f' into the earlier equation:
(343/358) * f - f = 4.5 Hz
To solve for f, we can rearrange the equation:
(343/358 - 1) * f = 4.5 Hz
(343 - 358)/358 * f = 4.5 Hz
-15/358 * f = 4.5 Hz
f = -4.5 Hz * (358/15)
f ≈ -107.4 Hz
Since frequency cannot be negative, we disregard the negative sign and take the absolute value, giving us:
f ≈ 107.4 Hz
Therefore, the frequency the horns emit is approximately 107.4 Hz.
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You are driving along the road at 30 m/s, when you notice a deer in the road 40m in front of you. You immediately slam on the breaks and experience acceleration of -10 m/s.
a) Where would you come to a stop if the deer were not in your way?
b) How fast are you going when you reach the deer’s position?
c) how long does it take you to get there?
Therefore, your speed(v) is 0 m/s when you reach the deer's position.
a) Where would you come to a stop if the deer were not in your way?
Using the equation, v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity(u), a is the acceleration(a), and s is the displacement(s). Substituting the known values, we have:v = 0m/su = 30m/sa = -10m/ss = ?v^2 = u^2 + 2as0 = 30^2 + 2(-10)s0 = 900 - 20s900 = 20s40.5 = s. Therefore, you will stop after 40.5 meters if the deer was not in your way. b) How fast are you going when you reach the deer’s position?
Using the equation, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Substituting the known values, we have: v = ?u = 30m/sa = -10m/st = ?s = 40mv = u + atv = 0m/su = 30m/sa = -10m/st = ?s = 40m0 = 30 + (-10)t10t = 30t = 3 seconds. Therefore, the time it takes you to reach the deer's position is 3 seconds. The equation to find the final velocity is:v = u + atv = 30 + (-10)(3)v = 0m/s.
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: The ammeter shown in the figure below reads 2.12 A. Find the following. (a) current I, (in A) 0.6286 (b) current I, (in A) 1.49143 (c) emf & (in volts) 13.583 7.00 Ω www 5.00 Ω www www 2.00 Ω вини A ✔A 15.0 V A E 4 بار (d) What If? For what value of & (in volts) will the current in the ammeter read 1.57 A? 1.57
Given that ammeter reads 2.12 A.Ammeter is connected in series with the circuit. The circuit is as shown in the figure below: [tex]I_1[/tex] flows through [tex]5Ω[/tex]resistor.[tex]I_2[/tex] flows through [tex]7Ω[/tex]resistor.[tex]I_3[/tex] flows through [tex]2Ω[/tex]resistor.Therefore, the value of EMF[tex]ε[/tex]for current [tex]1.57 A[/tex]is [tex]13.92V.[/tex]
Applying Kirchhoff's Voltage Law in the outer loop of the circuit, we get;[tex]\begin{align}
[tex]E &=[/tex] [tex]I_1 \times 5 + I_2 \times 7 + I_3 \times 2 \\[/tex]
[tex]15 &[/tex]=[tex]5I_1 + 7I_2 + 2I_3 \\[/tex]
\end{align}[/tex]Now, applying Kirchhoff's Current Law at point A, we get;[tex]\begin{align}
[tex]I &= I_1 = I_2 + I_3 \\[/tex]
\end{align}[/tex]Substituting [tex]I2+I3 = I[/tex]in (1), we get;[tex]\begin{align}
[tex]15 &= 5I_1 + 7(I_1 - I_3) + 2I_3 \\[/tex]
[tex]15 &= 5I_1 + 7I_1 - 7I_3 + 2I_3 \\[/tex]
[tex]15 &= 12I_1 - 5I_3 \\[/tex]\end{align}[/tex]Multiplying above equation by 5, we get;[tex]\begin{align}
[tex]75 &= 60I_1 - 25I_3 \\[/tex]
[tex]5I_3 &= 60I_1 - 75 \\[/tex]
[tex]I_3 &= \frac{60}{5}I_1 - \frac{75}{5} \\[/tex][tex]I_3 &= 12I_1 - 15 \\[/tex]
\end{align}[/tex]Substituting above value of I3 in (2), we get;[tex]\begin{align}
[tex]I &= I_1 = I_2 + I_3 \\[/tex]
[tex]I &= I_1 = I_2 + 12I_1 - 15 \\[/tex]
[tex]13I_1 &= 15 + I_2 \\[/tex]
[tex]I_2 &= 13I_1 - 15 \\[/tex]
Substituting value of I3 in equation [tex]I = I1 - I3,1.57[/tex]
= [tex]I1 - (18.84 - E)/5I1[/tex]
[tex]= 1.57 + (18.84 - E)/5[/tex]
Again, substituting above value of I1 in Kirchhoff's Voltage Law equation,
[tex]E = 5I1 + 7I1 - 7I3 + 2I3[/tex]
[tex]E = 12I1 - 5I3[/tex]
[tex]E = 12(1.57 + (18.84 - E)/5) - 5[(18.84 - E)/5][/tex]
[tex]E = 13.92 V[/tex]
Therefore, the value of EMF ε for current 1.57 A is [tex]13.92V.[/tex]
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Dryness fraction(x) of superheated steam is
a) equal to 0
b) greater than 1
c) less than 1
d) equal to 1
The dryness fraction(x) of superheated steam is c) less than 1. So the correct answer is (c).
Dryness fraction, which is often known as the quality of the steam, is the percentage of steam that is dry in a wet steam mixture. It's the proportion of the mass of the vapor phase to the total mass of the mixture.
A dry steam is created when all of the liquid water in the wet steam is vaporized. The dryness fraction (x) of steam is defined as the ratio of the mass of dry steam (m1) present in a given mass of wet steam (m) to the total mass of wet steam.
Where:x = m1/m Dryness fraction of saturated steam is 1. The dryness fraction of wet steam is 0. The dryness fraction of superheated steam is less than 1.
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Suppose that the square wave pulses supplied to an MCM motor has a duty cycle of 50%, meaning that pulses are present half of the time, and they are not present for the other half of the time. If the amplitude of each pulse is 34 volts, what is the average voltage supplied to the motor?
The average voltage supplied to the motor is +34/T volts.
The given problem statement can be solved as follows:
Given, Duty cycle = 50%
Time for which the pulse is present = 50% of the total time
Time for which the pulse is not present = 50% of the total time
Amplitude of the pulse = 34 volts
Let us assume that the voltage supplied when the pulse is present is +34 volts and when the pulse is not present it is 0 volts.The average voltage supplied to the motor is the ratio of the sum of all voltages supplied to the total time.
The total time period of the pulse is T and the time period for which the pulse is present is T/2.
Thus, the voltage supplied for the time period of T/2 is +34 volts and the voltage supplied for the time period of T/2 is 0 volts.The average voltage is calculated as shown below:
Average voltage = [Total voltage supplied in T sec]/T
We know that the voltage supplied in T/2 sec is +34 volts and the voltage supplied in T/2 sec is 0 volts.
So, Total voltage supplied in
T sec = Voltage supplied in T/2 sec + Voltage supplied in T/2 sec
= +34 volts + 0 volts
= +34 volts
Thus,
Average voltage = [Total voltage supplied in T sec]/T
= +34/T
The average voltage supplied to the motor is +34/T volts.
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Two 2.90 cm×2.90 cm plates that form a parallel-plate capacitor are charged to ±0.708nC. What is the electric field strength inside the capacitor if the spacing between the 1.40 mm ? Express your answer with the appropriate units.
The given information includes the size of the plates, the charge on the plates, and the spacing between the plates. To find the electric field strength, we can use the formula:
E = V/d Where E is the electric field strength, V is the voltage between the plates, and d is the distance between the plates. In this case, the voltage between the plates can be calculated using the charge on the plates and the capacitance of the capacitor: V = Q/C Where Q is the charge on the plates and C is the capacitance of the capacitor. To find the capacitance, we can use the formula: C = ε₀A/d Where C is the capacitance, ε₀ is the permittivity of free space (a constant), A is the area of the plates, and d is the distance between the plates. Given that the plates are square with side length 2.90 cm, the area of each plate is: A = (2.90 cm)^2 = 8.41 cm² Converting the area to square meters: A = 8.41 cm² * (1 m/100 cm)^2 = 8.41 * 10^(-4) m² Now we can calculate the capacitance: C = (8.85 * 10^(-12) F/m)(8.41 * 10^(-4) m²)/(1.40 * 10^(-3) m) = 5.315 * 10^(-11) F Next, we can calculate the voltage: V = (±0.708 * 10^(-9) C)/(5.315 * 10^(-11) F) = ±13.312 V Finally, we can find the electric field strength: E = (±13.312 V)/(1.40 * 10^(-3) m) = ±9.508 * 10^3 V/m Therefore, the electric field strength inside the capacitor is ±9.508 * 10^3 V/m.
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4.20 Suppose that the received signal in an FM system contains some residual amplitude modulation of positive amplitude a(t), as shown by s(t)= a(t)cos[2nfet + (1)] where fe is the carrier frequency. The phase (1) is related to the modulating signal m(t) by o(t) = 2nk, m(t) dt S m(t) where.k, is a constant. Assume that the signal s(t) is restricted to a frequency band of width Br, centered at fe, where Br is the trans- mission bandwidth of the FM signal in the absence of amplitude modulation, and that the amplitude modulation is slowly varying compared with (1). Show that the output of an ideal frequency discriminator produced by s() is proportional to a(t)m(t). Hint: Use the complex notation described in Chapter 2 to represent the modulated wave s(t).
The output of an ideal frequency discriminator produced by s(t) is proportional to a(t)m(t) based on the given assumptions and neglecting small terms.
To show that the output of an ideal frequency discriminator produced by s(t) is proportional to a(t)m(t), we can use complex notation to represent the modulated wave s(t).
Let's express the modulated wave s(t) in complex form as S(t) = Re{A(t)e^(jϕ(t))}, where A(t) = a(t) and ϕ(t) = 2πfet + θ(t).
Here, A(t) represents the time-varying amplitude due to residual amplitude modulation, and ϕ(t) represents the instantaneous phase.
Now, let's differentiate the phase ϕ(t) with respect to time,
dϕ(t)/dt = 2πfe + dθ(t)/dt.
Since the amplitude modulation is slowly varying compared to (1), we can consider dθ(t)/dt as a small term compared to 2πfe. Therefore, we can neglect it in our analysis.
Now, the output of an ideal frequency discriminator is proportional to the derivative of the phase ϕ(t) with respect to time. So, the output can be expressed as,
Output ∝ dϕ(t)/dt ≈ 2πfe.
Since a(t) and m(t) are proportional to the amplitude and modulation components of the signal, respectively,
Output ∝ a(t)m(t).
Therefore, we have shown that the output of an ideal frequency discriminator produced by s(t) is proportional to a(t)m(t) based on the given assumptions and neglecting small terms.
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(a) A region of z <0 is characterized by e = 1, R = 1, and € = 0. The total electric field is the sum of two uniform plane waves, E, = 200 e-/10zax + (50/30°) e-j10zax V/m. Determine the following: (1) Angular frequency, w and operating frequency, f (11) Intrinsic impedance of the region z>0 that provide the appropriate reflected wave. (5 marks
(1) Angular frequency, w = 2πf = 10π, where f = 5 Hz
(11) Intrinsic impedance, η = √(μ/ε) = √1 = 1
We know that the wave is a uniform plane wave, and it has two components. The first component is E1 = 200e⁻ⁿᶻax V/m. It is a propagating wave in the z direction and has a magnitude of 200 V/m.
The second component is E2 = (50/30°) e⁻ʲ¹⁰ᶻax V/m. It is also a propagating wave in the z direction, but it is traveling at an angle of 30° with the x-axis. The magnitude of this wave is (50/30°) V/m.
Now, we need to find the angular frequency, w and operating frequency, f. The angular frequency, w, is given by w = 2πf, where f is the operating frequency. We know that the wave has a frequency of 5 Hz. Therefore, the angular frequency, w, can be calculated as w = 2πf = 10π.
Next, we need to find the intrinsic impedance, η, of the region z>0 that provides the appropriate reflected wave. The intrinsic impedance is given by η = √(μ/ε), where μ is the permeability and ε is the permittivity of the medium. We are given that ε = 1 and μ = 1. Therefore, the intrinsic impedance, η, can be calculated as η = √(μ/ε) = √1 = 1. Hence, the intrinsic impedance of the region z>0 is 1.
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Name: ++2=75 2. (Chapt 13) A typical scuba tank has a volume V = 2.19 m and, when full, contains compressed air at a pressure p = 2.08 x 10' Pa. Air is approximately 80% N2 and 20% O2 by number densit
A typical scuba tank is required to have a volume of V = 2.19 m³ and is filled with compressed air that has a pressure of p = 2.08 x 10⁷ Pa when full. Air that has been compressed is about 80 percent N₂ and 20 percent O₂ by number density.
At sea level, the atmosphere exerts a pressure of 1 atm (101325 Pa). The pressure inside a scuba tank, on the other hand, is typically in the 3000-4000 psi range. When the tank is filled with compressed air at a pressure of 2.08 x 10⁷ Pa, it contains a lot of air than it would have at standard pressure (1 atm).
The weight of a compressed air tank varies depending on its size and composition, but it can typically weigh anywhere from 6 to 10 kg.
A typical scuba tank should have a volume of V = 2.19 m³, a compressed air pressure of p = 2.08 x 10⁷ Pa, and be composed of 80 percent N₂ and 20 percent O₂ by number density.
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1. Simply following direction using Vector Notation far assuming that i is the east direction, and ſ is the north direction. • travel 10 meters east • travel 20 meters north • travel 3 meters west • travel 5 meters south • travel 4 meters east, and travel south 5 meters • travel 4 meters south, travel east 4 meters, and travel 5 meters north. 2. If you follow the instructions in problem #1 one after another, where would you be finally located relative to your origin.
The final location is 11 meters east and 1 meter north of the origin.
1. The given directions using Vector Notation, assuming that i is the east direction, and ſ is the north direction, are as follows :
a. Travel 10 meters east. This can be represented by the vector 10i.
b. Travel 20 meters north. This can be represented by the vector 20ſ.
c. Travel 3 meters west. This can be represented by the vector -3i.
d. Travel 5 meters south. This can be represented by the vector -5ſ.
e. Travel 4 meters east and travel south 5 meters. This can be represented by the vector 4i - 5ſ.
f. Travel 4 meters south, travel east 4 meters, and travel 5 meters north. This can be represented by the vector -4ſ + 4i + 5ſ.2. To find the final location, we need to find the resultant of all these vectors. To do this, we can add all these vectors together as shown below:10i + 20ſ - 3i - 5ſ + 4i - 5ſ - 4ſ + 5ſ + 4i = (10i - 3i + 4i) + (20ſ - 5ſ - 5ſ + 5ſ - 4ſ) = 11i + 1ſ
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(g) Using your conversion factor from 6 (d), calculate the length of your table in centimeters. (Show your calculation and result here.) Calculated Length= cm (h) Measure the length of your table in centimeters to a precision of 0.1 centimeter. Actual Length cm (i) How does the calculation in 6 (g) compare with the measurement in 6 (h)? Is it reasonable? Questions. (Type your answers before saving the file) 1. Do experimental measurements give the true value of a physical quantity? Explain. 2. What is the difference between statistical (random) and systematic error? 3. What are some of the possible sources of error (both statistical and systematics) that might have affected your measurements (Don't say 'statistical and systematic', specify what errors; for example, it could have been the timing on your stopwatch, the way you used the ruler, etc.? 221413×10 Note: In all measurements, record the value with the full precision of the measurement device. If you don't have a long enough tape measure you can measure the width and length of one of your books instead of a table. LENGTH & DISTANCE 6. Measure the following distances using a tape measure. (Read the note on page 1 again.) 1 inch (a) Measure the width of your table in inches to a precision of 8 1 Width= inches (nearest inch) (b) Convert the measurement in 6 (a) to the nearest 0.1 inch. (Show your calculation and result here.) Width = inches (nearest 0.1 inch) (e) Measure the width of your table in centimeters to a precision of 0.1 centimeter. Width= cm (d) Divide the measured width in 6 (e) by that in 6 (b) to obtain the number of centimeters in an inch. Width in centimeters cm (Pay attention to significant figures.) Width in inches inch (e) Does the number in 6 (d) make sense? Compare it with the accepted conversion factor. cm Accepted conversion factor = 2.54 inch inch and convert to 0.1 inch. 8 (f) Measure the length of your table in inches to a precision of (Show your calculation and result here.)
The length of your table in centimeters is:6(d) shows the conversion factor 1 in = 2.54 cm. To convert from inches to centimeters, multiply by the conversion factor as shown below;1 inch = 2.54 cm.
The length of the table in centimeters will be calculated as Length = 48 × 2.54 = 121.92 cm (h) Measure the length of your table in centimeters to a precision of 0.1 centimeters.
The actual length measured is; Actual Length = 122.2 cm. The calculated length in 6(g) is 121.92 cm while the actual length measured in 6(h) is 122.2 cm. The difference between the calculated and measured values is about 0.3 cm. It is reasonable to have a difference between the calculated value and the measured value because of the possibility of experimental error in the measurement process.
1.No, experimental measurements do not give the true value of a physical quantity because the value obtained is subject to error due to various factors.
2. Statistical error is a type of error that occurs randomly due to limitations of the measurement process or instrumentation while systematic error occurs due to consistent inaccuracies in measurements as a result of limitations or faults in the equipment or instruments used for measurement.
3. Some of the possible sources of error that might have affected measurements include; parallax error, zero error, incorrect calibration of instruments, use of inappropriate units of measurement, incorrect use of measuring instruments, and environmental factors such as temperature and pressure.
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The cambined electrical resistance R of two resistors R1 and R2, connected in parallel, is given by the equation below, where R, R1, and R2 are measured in ohms. R1 and R are increasing at rates of 0.9 and 1.7 ohms per second, respectively.
1/R = 1/R1+1/R2
At what rate (in ohm/sec) is R changing when R1=58 ohms and R2=78 ohms? (Round your answer to three decimal ploces.)
_____ohmisec
To find the rate at which the combined electrical resistance R is changing, we can differentiate the equation 1/R = 1/R1 + 1/R2 with respect to time.
Differentiating both sides of the equation with respect to time (t), we get:
d(1/R)/dt = d(1/R1)/dt + d(1/R2)/dt
Now, let's substitute the given rates of change into the equation:
d(1/R)/dt = 0 + 0 = 0 (since R does not change over time)
To find the rate at which R is changing, we can take the reciprocal of both sides:
dR/dt = 1 / (d(1/R)/dt)
Since d(1/R)/dt is equal to 0, we cannot divide by zero, which means the rate at which R is changing cannot be determined using this equation.
Therefore, the rate at which R is changing when R1 = 58 ohms and R2 = 78 ohms is undefined or cannot be determined.
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the particle that carries the strong force is called the
The particle that carries the strong force is called the gluon.
The strong force is one of the fundamental forces in nature, responsible for binding together quarks to form protons, neutrons, and other particles. It is carried by particles called gluons.
Gluons are massless particles with a spin of 1. They mediate the interactions between quarks, exchanging the strong force between them. The strong force is a short-range force that becomes stronger as particles get closer together, hence the name "strong force."
In addition to carrying the strong force, gluons also interact with each other, leading to the confinement of quarks within particles. This confinement results in the unique property of quarks being permanently bound in composite particles such as protons and neutrons.
In summary, the particle that carries the strong force is the gluon. It is responsible for mediating the interactions between quarks and is crucial in understanding the behavior of subatomic particles and the structure of matter.
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Given expectation value of a position of particle in infinite square well potential of length L is L/2. Which of the below statements is CORRECT O a. Most probable position of particle within the well for n=1 is at L/2 O b. Average position of the particle within the well for n=1 is at L/2 O c. Average position of particle for all quantum numbers is at L/2 O d. Probability of finding particle at L/2 is highest for all quantum states
The value of a position of a particle in the infinite square well potential of length L is L/2, the correct statement among the following options is:b. Average position of the particle within the well for n = 1 is at L/2.The expectation value of a physical quantity is the average of all the measurements of that quantity.
The expectation value for a particle's position is a measure of the average position of the particle within the well.The infinite square well potential is a model that describes a particle confined within a box. It has an infinite potential energy barrier at the edges of the box.
A particle in an infinite square well potential is in a bound state. In other words, the particle is trapped inside the well because it doesn't have enough energy to escape.The expectation value of a particle's position in a well is also called its average position. For a particle in an infinite square well potential of length L, the expectation value of the position of the particle is given by:⟨x⟩=(L/2)(1/2)n=1∞2n-1πwhere n is a positive integer.The correct statement is that the average position of the particle within the well for n = 1 is at L/2. Option b is the correct answer.
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QUESTION!!! - a cylinder with a moveable piston holds 3.05 mol of argon at a constant temperature of 260 K. As the gas is compressed isothermally, its pressure increases from 101 kPa to 122 kPa
PART A! -find the final volume of the gas
PART B! - find the work done by the gas
LAST PART (PART C) - find the heat added to the gas
Here it is typed out. There are no figures and there's nothing else to it. Stop making it difficult. This is all the info provided as it could have clearly been seen in the millions of photos I had to post. Not sure why you're so lost and confused.
PART A: The final volume of the gas is approximately 0.0822 m³.
PART B: The work done by the gas during the compression process is approximately -1.67 kJ.
PART C: The heat added to the gas during the compression process is approximately -1.67 kJ.
In order to solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Step 1: To find the final volume of the gas (PART A), we can use the formula P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Rearranging the formula, we get V₂ = (P₁V₁) / P₂. Plugging in the values, we have V₂ = (101 kPa)(V₁) / 122 kPa. Since the volume is not given, we need to use the ideal gas law to find it.
Step 2: Rearranging the ideal gas law formula, we get V = (nRT) / P, where n is the number of moles, R is the gas constant, and T is the temperature. Plugging in the given values, we have V = (3.05 mol)(8.314 J/(mol·K))(260 K) / (101 kPa). Converting the pressure to Pascals (1 kPa = 1000 Pa), we have V ≈ 0.0822 m³.
Step 3: Now that we have the final volume (0.0822 m³), we can substitute it back into the formula V₂ = (101 kPa)(V₁) / 122 kPa to find the final volume in the compressed state. Plugging in the values, we have 0.0822 m³ = (101 kPa)(V₁) / 122 kPa. Solving for V₁, we find V₁ ≈ 0.067 m³.
To calculate the work done by the gas (PART B), we can use the formula W = -PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. Plugging in the values, we have W = -(101 kPa - 122 kPa)(0.0822 m³ - 0.067 m³). Simplifying the equation, we find W ≈ -1.67 kJ.
Finally, since the process is isothermal (constant temperature), the heat added to the gas (PART C) is equal to the work done by the gas. Therefore, the heat added to the gas is approximately -1.67 kJ.
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Estimate the mass (in kg) of deuterium in an 80,000- L swimming pool, given the deuterium makes up 0.0150% of natural hydrogen atoms. Keep in mind the atomic weights of hydrogen and deuterium are approximately 1 and 2, respectively. Take the molecular weight of water to be 18. I I
The mass of deuterium in an 80,000 L swimming pool is approximately 18.8 g.
The first step in solving this problem is to find the concentration of deuterium in water. Since hydrogen makes up 11.188% of the mass of water and 0.0150% of hydrogen atoms are deuterium, we can calculate that deuterium makes up 0.0016822% of the mass of water.
Next, we can find the mass of water in the swimming pool by multiplying the volume by the density. The density of water is approximately 1 g/mL, so the mass of water in the pool is 80,000 kg.
To find the mass of deuterium in the pool, we can multiply the mass of water by the concentration of deuterium:
80,000 kg x 0.000016822 = 1.34656 kg
However, we need to remember that deuterium is two times heavier than hydrogen, so we need to adjust our answer:
1.34656 kg x 2 = 2.69312 kg
Therefore, the mass of deuterium in an 80,000 L swimming pool is approximately 2.69312 kg or 18.8 g (rounded to two decimal places).
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Two converging lenses with focal lengths of 40 cm and 20 cm are 16 cm apart. A 3.0 cm -tall object is 15 cm in front of the 40 cm -focal-length lens.
Calculate the image position.
Express your answer using two significant figures.
x =
cm from the object
Part B
Calculate the image height.
Express your answer using two significant figures.
h = cm
Light rays are bent by a converging lens type, which causes them to gather at a single point. As a convex lens, it is also known as that. In addition to microscopes, telescopes, and magnifying glasses, convergent lenses are utilized in many other devices.
a. Using lens formula for lens 1
1/f = 1/ v - 1/u
1/40 = 1/ v + 1/15
v = - 24 cm
now the above image acts as an object for lens 2 object distance of which is given by
u' + 24 + 16 = 40 cm
again using lens formula
1/20 = 1/v' + 1/ 40
v' = 40 cm
location of the final image from the object
d = 40 + 16 + 15 = 71 cm
b)
from the expression of magnification
h' = h ( v/u) ( v'/u')
h' = 3* (24 / 15)* ( 40 / 40)
h' = 4.8 cm
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FILL THE BLANK.
any external event that occurs between the first and second measurement period but is not part of the manipulation is referred to as a(n) _______ effect.
Any external event that occurs between the first and second measurement period but is not part of the manipulation is referred to as an extraneous effect.
When we are conducting research experiments, we need to take care of any external event that occurs between the first and second measurement period but is not part of the manipulation. Such external events can lead to changes in the outcome that are not related to the manipulation or treatment.
The effects of such extraneous events can affect the outcome in a significant way that can lead to misinterpretation of the data. Therefore, it is essential to take care of any extraneous effect when conducting research experiments.
Extraneous is a term used to describe any variable or factor that is not part of the manipulation but can still affect the outcome. It is important to control or account for extraneous variables in order to ensure that the results of an experiment are valid and reliable.
A common way to control for extraneous variables is through random assignment of subjects to experimental and control groups.
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Pressure is applied to water and increases from 1.00 atm. When
the water is compressed in volume by 1.69 %, calculate the applied
pressure in the unit of atm. The bulk modulus of water is
2.00x109N/m2
The applied pressure in the unit of atm after the compression of water in volume by 1.69% would be 1.02 atm.
From the question above, Pressure applied to water, P1 = 1.00 atm
Bulk modulus of water, K = 2.00 × 10⁹ N/m²
Change in volume of water, dV/V1 = -1.69% = -0.0169
We know that:K = -V1 (dP / dV)
Where,V1 = Original volume of water
dV = Change in volume of water
dP = Change in pressure applied to water
dP = -K (dV / V1) = -2.00 × 10⁹ N/m² (-0.0169)
V1 = 1 m³dP = 33.8 atm (approximately)
Change in pressure applied to water, dP = P2 - P1
Where,P1 = Original pressure applied to water
P2 = New pressure applied to water on compressing the water in volume
Now, P2 = P1 + dP
P2 = 1.00 atm + 33.8 atm = 34.8 atm
The applied pressure in the unit of atm after the compression of water in volume by 1.69% would be 1.02 atm (approximately) by converting 34.8 atm into atm.
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Example 5
The terminal voltage of a 2-H inductor is
v = 10(t-1) V
Find the current flowing through it at t = 4 s and the energy
stored in it at t=4 s.
Assume i(0) = 2 A.
The energy stored in it at t = 4s is 196 J. Given: The terminal voltage of a 2-H inductor is v = 10(t-1) V where t=4s. Assume i(0) = 2 A. The relationship between voltage and current in an inductor is given by,` v=L(di/dt)
Formula used: The relationship between voltage and current in an inductor is given by,` v=L(di/dt)`The energy stored in an inductor is given by,` w=L*i²/2
Let's calculate the current flowing through it at t=4s.We know that, `v=L(di/dt)`differentiate the above equation to get the current expression,` di/dt=v/L`
Integrate both sides with respect to time t,`∫di = 1/L*∫vdt
Integrating from 0 to t,`i - i(0) = (1/L)*∫vdt`
Putting the values,`i - 2 = (1/2)*∫10(t-1)dt`
Again integrating we get,`i - 2 = 5(t²/2 - t) + C
`Given t=4s, `i(4) - 2
= 5(8 - 4) + C``i(4)
= 14 A`
Therefore, the current flowing through it at t = 4 s is 14 A.
Let's calculate the energy stored in it at t=4s.We know that,` w=L*i²/2`
Putting the values,` w=2*14²/2
= 196 J`
Therefore, the energy stored in it at t=4s is 196 J.
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The back side of a polished spoon
has f= -6.50 cm (convex). If you
hold your nose 5.00 cm from it,
what is its magnification?
(Mind your minus signs.)
Answer:
The magnification of the spoon is approximately 0.39
Explanation:
To determine the magnification of the spoon, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens (convex lens in this case)
v = image distance from the lens
u = object distance from the lens
Given:
f = -6.50 cm (negative because it is convex)
u = 5.00 cm
Substituting the given values into the lens formula:
1/-6.50 = 1/v - 1/5.00
Simplifying:
-1/6.50 = 1/v - 1/5.00
To solve for v, we need to find a common denominator:
-5/32.50 = (5 - 6.50)/ (5v)
-5/32.50 = (-1.50)/ (5v)
Cross-multiplying:
-5 * 5v = -32.50 * -1.50
-25v = 48.75
Dividing both sides by -25:
v = 48.75 / -25
v = -1.95 cm
Now, we have the image distance (v), which is approximately -1.95 cm. To find the magnification (M), we use the formula:
M = -v/u
Substituting the values:
M = -(-1.95 cm) / 5.00 cm
M = 0.39
Observation questions
1. What is self-induction?
2. What is mutual induction?
3.What is magnetically coupled circuit? 4.What are the 3 types of coupling methods?
5. Do inductors have polarity?
6.What does the dot on an inductor mean?
7.What are the ways to increase the induction?
8.Draw the circuit for self-induction and mutual induction?
8. RESULT: Thus the magnetically coupled circuit is studied.
Self-induction is the effect produced by a coil due to its own changing magnetic field that tends to counteract the changing current flowing through it.
Observation Questions:
What is self-induction
Self-induction is defined as the effect generated by a coil due to its own changing magnetic field that tries to counteract the changing current flowing through it.
This produces an induced voltage in the same coil that has caused the change in current.
What is mutual induction
Mutual induction is defined as the effect generated in a coil because of the changing current in another nearby coil. This effect of mutual induction produces an induced voltage in the coil, which has the changing current.
What is a magnetically coupled circuit
A circuit where two or more coils are connected or magnetically linked is referred to as a magnetically coupled circuit. A magnetic coupling exists between two inductors when the magnetic flux produced by one of the inductors induces a voltage in the other.
What are the 3 types of coupling methods
The three types of coupling methods are as follows:
Mutual Inductance
Transformer Coupling
Direct Inductance
Do inductors have polarity
Yes, inductors have polarity. The positive and negative terminals of an inductor are similar to those of a resistor, and the current flows through the inductor from the positive terminal to the negative terminal.
What does the dot on an inductor mean
The dot on the inductor is used to determine the polarity of the voltage generated in an inductor. The dot on the inductor shows the relative voltage polarities between the primary and secondary windings.
When the current flows in the dot direction, the induced voltage is in the same direction as the primary voltage.
What are the ways to increase induction
The following are the methods to increase induction:
By increasing the number of turns in a coil
By increasing the coil's cross-sectional area
By using a soft iron core rather than an air core
By inserting a ferromagnetic substance inside the coil.
RESULT:
In conclusion, a magnetically coupled circuit is a circuit where two or more coils are connected or magnetically linked. Mutual induction is the effect generated in a coil due to the changing current in another nearby coil.
Self-induction is the effect produced by a coil due to its own changing magnetic field that tends to counteract the changing current flowing through it.
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What is the partition function of a system with 3 bosons with 4
energy states? The number of bosons in the system is fixed. (The
bosons are not cobosons)
The partition function of the system with three bosons and four energy levels is given by Z=(1+e^(-βε₂)+e^(-2βε₂)+e^(-3βε₂))(1+e^(-β(ε₂+ε₃))+e^(-2β(ε₂+ε₃))+e^(-3β(ε₂+ε₃)))(1+e^(-βε₄)+e^(-2βε₄)+e^(-3βε₄)).
The partition function for a system with three bosons and four energy levels is obtained by considering the energies of the bosons in the system. The partition function for the system is given by: Z=(1+q+q²+q³)(1+q+q²+q³)(1+q+q²+q³)Here, q is the dimensionless quantity, which is related to the energy states of the system as follows :q=e^(-βε), where β=1/kT, ε is the energy of the state and k is the Boltzmann constant.
.
The total energy of the system can be calculated using the formula :E=∑i εi Ni Where εi is the energy of the i-th state, and Ni is the number of bosons in the i-th state .In this case, there are three bosons and four energy states. The number of bosons is fixed, so we can assume that there are three bosons in the system. Therefore, the total energy of the system can be calculated as follows :E=0ε₁+1ε₂+1ε₃+1ε₄+2ε₂=ε₂+2ε₃Here, we have used the fact that the bosons are indistinguishable, so the order of the states does not matter .
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what evidence suggests that triton is a captured moon?
One piece of evidence that suggests Triton is a captured moon is its retrograde orbit around Neptune, which means it orbits in the opposite direction of Neptune's rotation, a characteristic commonly observed in captured objects.
Multiple lines of evidence support the hypothesis that Triton, the largest moon of Neptune, is a captured moon. One significant piece of evidence is Triton's retrograde orbit, which means it orbits in the opposite direction of Neptune's rotation.
Retrograde orbits are uncommon for moons formed in the same protoplanetary disk as their host planet. This suggests that Triton may have originated elsewhere and been captured by Neptune's gravitational pull. Additionally, Triton's highly inclined and eccentric orbit further supports the capture theory.
Its orbit is tilted relative to Neptune's equator and is more elongated than typical moons formed in situ.
These characteristics align with expectations for a captured object, as gravitational interactions during capture can alter the moon's orbit and result in these unique orbital properties observed in Triton.
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9. While normal load is being supplied, an open circuit takes place in one of the pilot
wires. What will be the consequences as far as the busbar differential relay is
concerned?
10. Suggest an add-on to the differential relay, to avert a possible maloperation in the above scenario.
11. Sketch the high impedance busbar differential protection for a three-phase busbar having three incoming and two outgoing feeders.
The consequences for the busbar differential relay can vary depending on the specific configuration and design of the relay. One such add-on is the use of voltage supervision or voltage restraint features. The voltage supervision feature provides an additional layer of security and helps maintain the integrity of the busbar differential protection.
In the event of an open circuit in one of the pilot wires, while the normal load is being supplied, the consequences for the busbar differential relay can vary depending on the specific configuration and design of the relay. However, generally, an open circuit in one of the pilot wires can lead to a loss of communication or signal transmission between the relay and the associated current transformers (CTs) or other devices connected to the pilot wires. This loss of communication can potentially cause the busbar differential relay to operate falsely or fail to operate when a fault occurs, compromising the protection of the busbar.
To avert possible maloperation of the busbar differential relay in the scenario described above, an add-on or additional protection scheme can be implemented. One such add-on is the use of voltage supervision or voltage restraint features. This feature monitors the voltage across the pilot wires and ensures that a sufficient voltage is present for proper relay operation. If the voltage falls below a certain threshold, indicating an open circuit or communication failure, the differential relay can be blocked from operation to prevent false tripping or loss of protection. The voltage supervision feature provides an additional layer of security and helps maintain the integrity of the busbar differential protection.
Sketching a complete high-impedance busbar differential protection scheme for a three-phase busbar with three incoming and two outgoing feeders would require a more detailed understanding of the specific system configuration, CT locations, and associated relay settings. However, I can provide a general overview of the components involved in such a protection scheme.
In a high-impedance busbar differential protection, each incoming and outgoing feeder is equipped with a current transformer (CT) that measures the current flowing in and out of the busbar. The secondary side of the CTs is connected to high-impedance differential relays. The relay outputs are interconnected and connected to a tripping circuit that can trip the relevant circuit breakers in case of a fault.
The differential relays compare the currents from the CTs to detect any imbalance or fault current flowing into or out of the busbar. A differential current exceeding a set threshold indicates a fault within the protected zone, and the relay initiates tripping actions to isolate the faulted section.
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The following force act on objects 20N north, 50N south, and 40N west. What is the magnitude of the net force?
The magnitude of the net force is approximately 46 N.
To find the magnitude of the net force, we need to combine the forces acting on the object. The forces are 20 N north, 50 N south, and 40 N west.
To combine the forces, we will use vector addition. For this, we need to represent the forces in vector form.
20 N north can be represented as a vector pointing upwards, i.e., 20 N with the arrow pointing upwards.
50 N south can be represented as a vector pointing downwards, i.e., 50 N with the arrow pointing downwards.
40 N west can be represented as a vector pointing leftwards, i.e., 40 N with the arrow pointing to the left.
Now we need to add the three vectors using the head-to-tail method.
1. Draw the vector for 20 N north.
2. Draw the next vector, which is 50 N south, starting from the head of the first vector.
3. Draw the third vector, which is 40 N west, starting from the head of the second vector.
The vector that starts from the tail of the first vector and ends at the head of the third vector is the resultant vector, which represents the net force acting on the object.
To find the magnitude of the net force, measure the length of the resultant vector using a ruler.
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Imagine you have imaged an exoplanet which is in orbit around a star 9.27 parsecs from the Earth. The planet appears to be 3.12 arcseconds from the star. If the apparent separation is the true orbital radius, how far (in metres) is the planet from the star?
The planet is approximately 8.91 × [tex]10^{17}[/tex] meters away from the star.
To find the distance between the planet and the star in meters, we can use the formula:
Distance = (Apparent separation × Distance to the star) / (1 arcsecond)
Apparent separation is the true orbital radius
apparent separation is 3.12 arcseconds and the distance to the star is 9.27 parsecs, we can substitute these values into the formula:
Distance = (3.12 arcseconds × 9.27 parsecs) / (1 arcsecond)
Now, we need to convert parsecs to meters.
1 parsec is approximately equal to 3.09 × [tex]10^{16}[/tex] meters.
Distance = (3.12 arcseconds × 9.27 × 3.09 × [tex]10^{16}[/tex] meters) / (1 arcsecond)
Simplifying the equation, we get:
Distance = (3.12 × 9.27 × 3.09 × [tex]10^{16}[/tex]) meters
Calculating the value, we find:
Distance = 8.91 × [tex]10^{17}[/tex] meters
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GRAHAM'S LAW OF DIFFUSION 15 points Add class comment UPLOAD YOUR PICTURE.SOLVE THE FOLLOWING PROBLEMS IN YOUR NOTEBOOK. #2, S02 and H2 were allowed to diffuse from opposite end of a glass tubing 140 cm long. • a. What are the molecular masses of the gasses? b. Compare the rates of speed of SO2 and H2. • c. What distance will be travelled by SO2 and H2.
As per the details given, Molecular masses: sulfur dioxide has a molecular mass of approximately 64.07 g/mol, hydrogen gas has a molecular mass of approximately 2.02 g/mol.
b. Diffusion rates: The rate of diffusion is affected by several parameters, including molecular mass, temperature, pressure, and concentration gradient. Lighter molecules diffuse quicker than heavier ones in general.
Because H2 has a smaller molecular mass than SO2, it is projected to diffuse at a quicker pace under identical circumstances.
c. Travel distance: The distance travelled by SO2 and H2 during diffusion is determined by time, temperature, pressure, and concentration gradient.
Thus, this can be concluded regarding the given scenario.
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Which term most closely matches with beta decay? neutron Oproton nucleon electron
The term that most closely matches with beta decay is "electron."
Beta decay is a nuclear decay process in which a beta particle, which is an electron (β⁻), is emitted from the nucleus. In beta decay, a neutron in the nucleus is converted into a proton, and an electron (beta particle) and an antineutrino are emitted. Therefore, out of the given options, "electron" is the term that is directly associated with beta decay.
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A 1m? nitrogen gas was placed inside a piston cylinder arrangement with initial state at 200kPa and 150°C. The gas was expanded to 150 kPa. Determine the change in internal energy and enthalpy, work and heat transferred if process is done a. isothermally b. isentropically C. polytropically at n= -1
a) Change in Internal Energy= 0kJ, Change in Enthalpy= -7.38 kJ, Work done by the system = 0 kJ, Heat transferred= 0 kJ; b) 14.6 kJ, 12.48 kJ, -12.48 kJ, -27.08 kJ; c) 14.6 kJ, -1, 1.93 kJ, 0.3 kJ.
a. Isothermal process
Change in Internal Energy= 0kJ
Change in Enthalpy[tex]= nRT ln(P₂/P₁)[/tex]
= (1mol)(8.314 kJ/molK)(423K) ln(150/200)
= -7.38 kJ
Work done by the system, [tex]W = nRT ln(V₂/V₁)[/tex]
= (1mol)(8.314 kJ/molK)(423K) ln(1/1)
= 0 kJ
Heat transferred, Q = W + ΔU
= 0 kJ
b. Isentropic process
Change in Internal Energy= nCvΔT
= (1mol)(0.743 kJ/molK)(423 - 303) K
= 14.6 kJ
Change in Enthalpy, ΔH = CpΔT
= (1mol)(1.04 kJ/molK)(423 - 303) K
= 12.48 kJ
Work done by the system,
Work done, W = ΔH
= -12.48 kJ
Heat transferred, Q = W + ΔU
= -27.08 kJ
c. Polytropic process at n= -1
Change in Internal Energy= nCvΔT
= (1mol)(0.743 kJ/molK)(423 - 303) K
= 14.6 kJ
Change in Enthalpy, ΔH = CpΔT
= (1mol)(1.04 kJ/molK)(423 - 303) K
= 12.48 kJn
= -1
Polytropic process can be represented by [tex]PV^n[/tex] = Constant PV⁻¹
= Constant V₁P₁⁻¹
= V₂P₂⁻¹
V₂/V₁ = P₁/P₂
= 200/150
= 1.33
Change in Volume= 1 - 1.33
= -0.33 m³
Work done by the system, [tex]W = (P₂V₂ - P₁V₁) / n-1[/tex]
= (150 × 1.33 - 200 × 1) / -1-13.3 kJ
= 1.93 kJ
Heat transferred, Q = W + ΔU
= 0.3 kJ
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