starting from rest, a 95-kg firefighter slides down a fire pole. the average frictional force exerted on him by the pole has a magnitude of 805 n, and his speed at the bottom of the pole is 3.7 m/s. how far did he slide down the pole?
Answers
To solve this problem, we will use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. We can break this down into the following steps:
1. Calculate the firefighter's final kinetic energy.
2. Calculate the work done by the frictional force.
3. Use the work-energy principle to find the distance the firefighter slid down the pole.
Step 1: Calculate the final kinetic energy.
Final kinetic energy (KE) = (1/2) * mass * final speed^2
KE = (1/2) * 95 kg * (3.7 m/s)^2
KE = 648.575 J (joules)
Step 2: Calculate the work done by the frictional force.
Since the frictional force opposes the motion, the work done by friction will be negative. Thus,
Work (W) = - Frictional force * distance
Step 3: Use the work-energy principle to find the distance.
According to the work-energy principle, the work done is equal to the change in kinetic energy. Since the firefighter starts from rest, his initial kinetic energy is 0 J. Therefore, the change in kinetic energy is equal to the final kinetic energy (648.575 J).
W = change in KE
-805 N * distance = 648.575 J
Now, solve for the distance:
distance = 648.575 J / 805 N
distance ≈ 0.805 m
The firefighter slid down approximately 0.805 meters down the fire pole.
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Related Questions
The object has a tangential acceleration only if the disk has an angular acceleration.
Answers
The statement is true. The tangential acceleration of an object on a rotating disk is directly related to the angular acceleration of the disk.
When the disk undergoes angular acceleration, there is a change in the tangential velocity of any object on the disk. This change in velocity results in a tangential acceleration. However, if the disk is not undergoing angular acceleration, there will be no change in the tangential velocity of the object, and therefore no tangential acceleration.
Angular acceleration is the rate at which the angular velocity of a rotating object changes over time. It is a measure of how quickly an object is changing its rotational speed. Mathematically, angular acceleration is defined as the time derivative of angular velocity:
α = dω/dt
where:
α is the angular acceleration (measured in radians per second squared)ω is the angular velocity (measured in radians per second)t is time (measured in seconds)Visit here to learn more about radians brainly.com/question/27025090
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A convex spherical surface with radius r separates a medium of n=2 and air. As an object is moved along optical axis in the air and far away from surface the image of the object becomes _________
(a) real and is r/2 from surface
(b) virtual and 2r from surface
(c) real and 2r from surface
(d) virtual and r/2 from surface
(e) none of the above
Answers
The correct answer is (d) virtual and r/2 from surface.
As the object moves along the optical axis and gets farther away from the spherical surface, the image formed by the surface will move closer to the surface. At a certain point, when the object is at infinity, the image will be formed at the focal point of the spherical surface, which is located at a distance of r/2 from the surface for a convex surface.
Since the image is formed behind the spherical surface, it is virtual. And since the image is located at a distance of r/2 from the surface, the correct option is (d) virtual and r/2 from surface.
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A 221-gram ball is thrown at a speed of 36.7 m/s from the top of a 39.8-m high cliff. Determine the impact speed of the ball when it strikes the ground. Assume negligible air resistance.
Answers
Given:
The mass of the ball is
\(\begin{gathered} m=221\text{ g} \\ =0.221\text{ kg} \end{gathered}\)The initial height of the ball is
\(h=39.8\text{ m}\)The initial speed of the ball is
\(v_i=36.7\text{ m/s}\)To find:
the impact speed of the ball when it strikes the ground
Explanation:
The initial potential energy of the ball is
\(\begin{gathered} (PE)_i=mgh \\ =0.221\times9.8\times39.8 \\ =86.2\text{ J} \end{gathered}\)The initial kinetic energy is
\(\begin{gathered} (KE)_i=\frac{1}{2}mv_i^2 \\ =\frac{1}{2}\times0.221\times(36.7)^2 \\ =148.8\text{ J} \end{gathered}\)The final energy of the ball is fully kinetic energy. Let the final impact speed of the ball is
\(v_f\)We can write, using the energy conservation principle that
\(\begin{gathered} (PE)_i+(KE)_i=\frac{1}{2}mv_f^2 \\ 86.2+148.8=\frac{1}{2}\times0.221\times v_f^2 \\ v_f^2=2\times\frac{86.2+148.8}{0.221} \\ v_f=46.1\text{ m/s} \end{gathered}\)Hence, the final impact speed of the ball is 46.1 m/s.
Two wires carrying equal currents lie in the plane of the screen with currents to the right. These horizontal wires are connected to a battery with wires that are vertical and can be ignored in this problem. The length the wires is
I=1.67 m, the distance between the wires is d=1.846×10^−3 m, and the current is i=19.20 A. In this problem, only consider field due to the horizontal parts of the wires, and assume that the field due to these wires is approximately equal to that of an infinite straight wire. What is the magnitude of the force on the top wire? Give your answer in Newtons to three significant figures.
Answers
Two wires carrying equal currents lie in the plane of the screen with currents to the right. These horizontal wires are connected to a battery with wires that are vertical and the magnitude of the force on the top wire 20.8017 × 10⁻⁴ T
How is it calculated?Given is ,
μ₀ = 4π × 10 ⁻⁷
d = 1.846 × 10⁻³ m
i = 19.20 A
The magnitude field at distance d due to bottom wire is given by,
B = μ₀ i / 2πd
B = (4π × 10 ⁻⁷× 19.20) / (2 × 3.14 × 1.846 × 10⁻³)
B = (2 × 10 ⁻⁷ × 19.20) / (1.846 × 10⁻³)
B = (38.4 × 10 ⁻⁷) / (1.846 × 10⁻³)
B = 20.80173348 × 10⁻⁴
B = 20.8017 × 10⁻⁴ T
Hence , the magnitude of the force on the top wire is 20.8017 × 10⁻⁴ T
What is the magnitude of force?Force is a vector quantity, so it has magnitude and direction. A force magnitude is a number that expresses the strength of a force.Example: Suppose the force is = 10 N towards the east."East" is the direction and "10" is the strength of the force.Quantities are basically "values" or "magnitudes" of physical quantities so it is always ar scalar quantity.Can learn more about magnitude of force from
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Three screens are placed exactly one behind the other. The light of the torch falls on all the three screens. One of the screen is a bathroom mirror which one?
Answers
Answer:
Explanation:
Three screens are placed one behind the other and light falls on all of them from a torch . In this case a mirror can be only the last screen . In case of first or second screen being a mirror , light would not have reached the last screen because the nature of mirror is to reflect the light back.
Hence , the only possibility is that , the last screen is mirror.
un auto recorre 212 km en un tiempo de 3.1 h.Calcular su rapidez en m/s
Answers
Para hacerlo a m/s un método muy práctico es sólo dividir entre 3.6, por cuestiones de conversiones, lo puedes comprobar.
212 km/hr /3.6 = 58 m/s
Comprobación :
V= d / t
V= 212 m / 18000 seg <---- nota que aquí los segundos son de las 3.1hrs
V= 58 m/seg
Ag Express your answer as a signed integer. View Available Hint(s) the oxidation state of Ag =
Answers
The oxidation state of Ag or the charge on Ag is +1.
The oxidation state of an element is the charge the element would have if all its bonds were covalent. In the case of Ag, it forms an ionic bond with one oxygen atom, Ag+O- => AgO.
The oxygen atom has an oxidation state of -2 and the Ag is +1. To determine the oxidation state, one must understand the ionic charges of the elements in the compound.
The charge of the compound must be equal to zero, so since the oxygen has a charge of -2, the Ag must have a charge of +1. If the compound had more than one of the same element, the oxidation state would be the average of the oxidation states of the atoms.
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explain three major advantages of ccds over other imaging techniques is that they:
Answers
Charge-coupled devices (CCDs) are electronic imaging sensors that are widely used in digital cameras, telescopes, and other imaging devices. Some of the major advantages of CCDs over other imaging techniques include:
High sensitivity: CCDs are highly sensitive to light, allowing them to capture clear and detailed images even in low-light conditions. This makes them ideal for applications such as astrophotography and microscopy, where light levels are often very low.
Low noise: CCDs produce very little electronic noise, which means that images captured using CCDs tend to be very clean and free of unwanted artifacts. This makes CCDs particularly well-suited for scientific imaging applications, where accuracy and precision are critical.
High resolution: CCDs can capture images with very high spatial resolution, allowing them to resolve fine details in images. This makes them ideal for applications such as digital microscopy, where the ability to capture and analyze fine details is essential.
Overall, CCDs offer a powerful combination of high sensitivity, low noise, and high resolution that makes them well-suited for a wide range of imaging applications, from scientific research to artistic photography.
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A spring has an unstretched length of 0.2 m. A 0.2 kg mass hanging from the spring stretches it to an equilibrium length of 0.3 m. Suppose the mass is pulled down to where the spring’s length is 0.5 m. When it is released, it begins
to oscillate. What is the amplitude of the oscillation?
Answers
But there could be some other people that think differently
find the wavelength of the three longest-wavelength lines of the lyman series.
Answers
The Lyman series is a series of lines in the emission spectrum of hydrogen that corresponds to transitions from higher energy levels to the n = 1 level. The formula for the wavelengths of the lines in the Lyman series is given by:
1/λ = R (1 - 1/n^2)
Where λ is the wavelength of the line, R is the Rydberg constant (1.097 × 10^7 m^-1), and n is an integer greater than 1 that corresponds to the energy level of the electron before the transition.
To find the three longest-wavelength lines in the Lyman series, we need to plug in values of n and solve for λ, and then arrange the wavelengths in decreasing order.
When n = 2:
1/λ = R (1 - 1/2^2) = 3R/4
λ = 4/3R = 121.6 nm
When n = 3:
1/λ = R (1 - 1/3^2) = 8R/9
λ = 9/8R = 102.6 nm
When n = 4:
1/λ = R (1 - 1/4^2) = 15R/16
λ = 16/15R = 97.3 nm
Therefore, the three longest-wavelength lines in the Lyman series have wavelengths of 121.6 nm, 102.6 nm, and 97.3 nm, in decreasing order.
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Explain the difference between the point of origin and the point of convergence. Which is shown in the image below?
Answers
The point of origin is the three dimensional location while the point of convergence is the area containing intersections.
Blood pattern analysisBlood pattern analysis is usually used by the forensic specialists to determine the facts surrounding an investigation using physical nature of blood stains.
There are different types of blood analysis but the one that was displayed in the picture is the impact spatter patterns which contains a point of origin and point of convergence.
The point of origin is the three-dimensional location from which blood spatter originated while the point of convergence is the area containing the intersections generated by lines drawn through the long axes of individual stains that indicates in two dimensions the location of the blood source.
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What determines the radiation that an electromagnetic wave emits?
a. its speed
b. its visibility
c. its amplitude
d. its wavelength
PLEASE HELP!!!!
Answers
The electromagnetic waves are determined by the wavelength. Hence, the correct option is D.
What are electromagnetic waves?Electromagnetic waves are made up of vibrating electric and magnetic fields. The electric and magnetic fields are mutually perpendicular to each other. EM waves are transverse in nature.
Electromagnetic waves can travel through the vacuum in the form of radiation. The EM waves travel with the speed of light 3×10⁸ m/s. EM waves have no mass and charge. These waves can carry energy in space.
The behavior of electromagnetic waves depends on its frequency and wavelength. EM waves are classified into 7 types based on its frequency and wavelength. They are classified from radio waves to Gamma rays.
Frequency is inversely proportional to wavelength, f = c / λ. Higher frequencies have shorter wavelength and lower frequencies have longer wavelength.
Thus, the wavelength determines the radiation that an electromagnetic waves. Hence, the option D is correct.
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how much water should be taken up by a plant when the air around it is completely saturated with water - 100 percent humidity.
Answers
The amount of water that a plant should take up when the air around it is completely saturated with water, i.e. 100 percent humidity, is the maximum amount of water the plant is capable of taking up from the environment. This is because there is no water left in the air for the plant to absorb.
What is humidity?Humidity refers to the amount of moisture present in the air. The humidity in the air is an important factor for the growth of plants. Humidity refers to the amount of moisture present in the air. The humidity in the air is an important factor for the growth of plants. In addition, the amount of water vapor present in the air determines how much water a plant can take up. As a result, humidity can play an important role in plant water uptake.
When the air around the plant is completely saturated with water, it means that the air has reached its maximum capacity for water vapor. The relative humidity, in this case, is 100%. When the air is completely saturated with water, it becomes difficult for the plant to take up any more water from the environment, as there is no water left in the air to absorb.
Therefore, the amount of water that a plant can take up is limited by the amount of water vapor present in the air.
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Explain this phase diagram by relating what you know about temperature, states of matter and
pressure.
Answers
Answer:
See explanation
Explanation:
The vertical axis corresponds to the pressure of a substance, while the horizontal axis corresponds to the temperature. The solid is the substance which contains particles of strong intermolecular force and compaction, typically ionic at a certain temperature, the liquid is the substance which contains relatively compact molecules, however lacks a particular arrangement. The gaseous substance is caused by particles with weak intermolecular forces, causing particle movement and collision with no arrangement whatsoever. The triple point as shown in the diagram, is the phrase on a diagram where each substance: solid, liquid and gas coexist. The critical point is the phase at which the/a substance is indistinguishable between liquid and gaseous states. A substance or elements state is highly dependent on its environment and it’s temperature, of which ultimately affects its kinetic energy within its particles. This is what the graph portrays and represents.
Hopefully I have aided you, and I apologize for the relatively late response.
suppose the electric field between two points separated by 4 meters is 14 volt/m. what is the electric potential (in volt) between the two points?
Answers
Assume that the electric field between two points that are 4 meters apart has a 14 volt/m potential. The electric potential between the two points is 460 w (in volts).
V =Er
= 67 X 13
V =871 volts
I =q/t=8/2
I=4 Amp
P=VI
230 X 2
P=460 W
A unit of electric charge must be moved from a reference point to a specific point in an electric field, and this amount of work energy is known as the electric potential. Against an electric field, the amount of work required to move a unit charge from one point to another is known as electric potential. Although any location outside the range of the electric field charge can be used, Earth is typically used as the reference point. The external effort required to move a charge from one location to another in an electric field is known as an electric potential difference, or voltage. A test charge that has an electric potential difference of +1 will experience a change in potential energy.
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In a dentist's office an X-ray of a tooth is taken using X-rays that have a frequency of 4.99 × 1018 Hz. What is the wavelength in vacuum of these X-rays?
Answers
The wavelength in vacuum of these X-rays is approximately 6.01 × 10^-11 meters. In a dentist's office, an X-ray of a tooth is taken using X-rays that have a frequency of 4.99 × 10^18 Hz. To calculate the wavelength in vacuum of these X-rays, we can use the equation:
wavelength = speed of light / frequency
The speed of light in vacuum is approximately 3 × 10^8 meters per second. Plugging in the given frequency, we get:
wavelength = (3 × 10^8 m/s) / (4.99 × 10^18 Hz)
Simplifying this expression, we get:
wavelength = 6.01 × 10^-11 meters
Therefore, the wavelength in vacuum of these X-rays is approximately 6.01 × 10^-11 meters. It's important to note that X-rays have a very short wavelength, which allows them to penetrate through tissues and bones. However, this also means that they can be harmful if not used carefully and with proper shielding.
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In which general compass traction is this hurricane moving
Answers
Answer:
It looks like its moving north.
Explanation:
Two forces of
411
N and
617
N act on an object. The angle between the forces is
46°.
Find the magnitude of the resultant and the angle that it makes
with the larger force.
Answers
Let's first resolve the two forces into their components as shown in the diagram below: The larger force (617 N) makes an angle of 46° with the horizontal axis.
Therefore, the horizontal component will be given by:
H = 617 cos 46°H = 617 × 0.69H = 425.73 N
The vertical component will be given by:V = 617 sin 46°V = 617 × 0.73V = 450.66 NOn the other hand, the smaller force (411 N) makes an angle of (90° - 46°) = 44° with the horizontal axis. Therefore, the horizontal component will be given by:H = 411 cos 44°H = 411 × 0.72H
= 296.52 N
The vertical component will be given by:V = 411 sin 44°V = 411 × 0.67V = 274.47 N The resultant horizontal component, R will be given by:R = 425.73 + 296.52R = 722.25 N The resultant vertical component, R will be given by:R = 450.66 + 274.47R = 725.13 N The magnitude of the resultant, R will be given by:R² = (722.25)² + (725.13)²R = √(522198.06)R = 722.82 N The angle that R makes with the larger force (617 N) will be given by:θ = tan⁻¹(725.13/722.25)θ = 45.23° Therefore, the magnitude of the resultant is 722.82 N and it makes an angle of 45.23° with the larger force.
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A 400-m train is moving on a straight track with a speed of 83.4 km/hr. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/hr. Assuming constant acceleration, how long did the train take to pass the crossing?
Answers
Answer:
28.9 seconds
Explanation:
Convert km/hr to m/s.
83.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 23.2 m/s
16.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 4.56 m/s
Given:
Δx = 400 m
v₀ = 23.2 m/s
v = 4.56 m/s
Find: t
Δx = ½ (v + v₀) t
400 m = ½ (4.56 m/s + 23.2 m/s) t
t = 28.9 s
Answer: The train took 28.9 seconds to pass the crossing.
We first convert km/hr to m/s.
83.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 23.2 m/s
16.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 4.56 m/s
Given:
Δx = 400 m
v₀ = 23.2 m/s
v = 4.56 m/s
Then we find t:
Δx = ½ (v + v₀) t
400 m = ½ (4.56 m/s + 23.2 m/s) t
t = 28.9 s
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An object has 10 J of GPR.What would be its GPE if its mass was halved?
Answers
If the mass of the object is halved, its new GPE would be 5 J. The gravitational potential energy (GPE) of an object near the surface of the Earth is given by the formula:
GPE = mgh
where:
m is the mass of the object
g is the acceleration due to gravity (9.81 m/s² near the surface of the Earth)
h is the height of the object above some reference level (usually taken to be the ground level)
The given information of the object having 10 J of gravitational potential energy (GPE) is insufficient to calculate its mass or height. As a result, we cannot use the above formula to calculate the object's GPE if its mass is halved.
However, we can take advantage of the fact that an object's GPE is directly proportional to its mass. That is, if we cut the object's mass in half, its GPE will be cut in half as well. This is mathematically expressed as:
GPE2 = (1/2) GPE1
where:
GPE1 is the object's first GPE.
GPE2 is the object's new GPE after its mass has been halved.
As a result, if the object's GPR is considered its initial GPE and its mass is halved, its new GPE is:
GPE2 = (1/2) GPR
Substituting the given value of GPR = 10 J, we get:
GPE2 = (1/2) x 10 J = 5 J
So, if the mass of the object is halved, its new GPE would be 5 J.
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What the relationship between frequency and wavelength of electromagnetic radiation? choose. If you double the wavelength of light, what happens to the energy of the photons? choose. Which has a greater energy, long wavelength red light or short wavelength uv light? choose.
Answers
Frequency is inversely proportional to the wavelength of electromagnetic radiation.
When the wavelength of light is doubled, the frequency is reduced to its original value.
Short wavelength UV (ultraviolet) light will have more energy.
What is meant by wavelength?The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal propagated in space or along a wire is defined as the wavelength.
The relationship between frequency of electromagnetic radiation and wavelength of radiation is:
ν==1/λ
Where,
ν= frequency
As a result, the frequency of electromagnetic radiation is inversely proportional to its wavelength.
The frequency is reduced to its original value when the wavelength of light is doubled.
The energy of a photon is proportional to the frequency of light.
Using Relationship,
E=hν=h c/λ
h = Planck's constant
c = speed of light
Both h and c are constants
As a result, energy will be reduced to its initial value.
The light with the shortest wavelength will have the greatest energy.
UV (ultraviolet) light with a shorter wavelength has more energy.
It is because of the previously stated relationship..
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An unknown element has 5 protons, 5 electrons, and 6 neutrons what is the atomic mass of this element
Answers
The atomic mass is the protons + the neutrons.
So your answer would be 5 + 6 = 11.
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relative to sphere at the speed of sphere Z is _ m/s
Answers
We are given that a sphere Z moves with a relative speed of 1 m/s with respect to sphere X which moves at 5 m/s. Let's draw the velocity vectors of the spheres:
Where:
\(\begin{gathered} v_x=\text{ velocity of sphere x} \\ v_z=\text{ velocity of sphere z} \end{gathered}\)From the relative velocity equation we have:
\(v_z=v_r+v_x\)Where:
\(v_r=\text{ velocity of z relative to x}\)Since we are given the relative velocity we can plug in the values to get the velocity of "z":
\(\begin{gathered} v_z=1\frac{m}{s}+5\frac{m}{s} \\ \\ v_z=6\frac{m}{s}_{} \end{gathered}\)Now, we do the same but now using the sphere Y:
Now, we use the relative velocity equation for these velocities:
\(v_z=v_r+v_y\)In this case, we have that:
\(v_r=\text{ velocity of z with respect to y}\)Now, we subtract the velocity of "y" from both sides:
\(v_z-v_y=v_r\)Substituting the values:
\(6\frac{m}{s}-2\frac{m}{s}=v_r\)Solving the operations:
\(4\frac{m}{s}=v_r\)Therefore, the velocity of "Z" relative to "Y" is 4 m/s.
A pulley with a diameter of 4 cm has a downward force of 20 N on the left side and a downward force of 30 N on the right side.What is the net torque about the axle on the pulley?
Answers
The net torque about the axle on the pulley is 20 Ncm.
The net torque about the axle on the pulley can be calculated by first determining the direction of rotation. Since there are two forces acting in opposite directions, the pulley will not rotate in either direction unless there is a net torque acting on it. Therefore, we need to find the difference between the clockwise torque and the counterclockwise torque.
To calculate the torque, we need to use the formula: torque = force x distance. The distance is the radius of the pulley, which is half of the diameter, or 2 cm.
On the left side, the force of 20 N is pulling down and to the left, creating a clockwise torque. The distance from the axle to the force is 2 cm, so the torque is 20 N x 2 cm = 40 Ncm.
On the right side, the force of 30 N is pulling down and to the right, creating a counterclockwise torque. The distance from the axle to the force is also 2 cm, so the torque is 30 N x 2 cm = 60 Ncm.
Therefore, the net torque is the difference between these two torques: 60 Ncm - 40 Ncm = 20 Ncm.
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consider a 50 kg cylindrical barrel resting on a wooden pallet. the pressure applied on the pallet by the barrel is 260 pa. what is the radius r of the barrel
Answers
The radius of the cylindrical barrel is 0.78 m.
Circular area of the cylindrical barrel
The circular area of the cylindrical barrel is calculated as follows;
P = F/A
A = F/P
where;
F is the applied force due to its weightP is pressure applied on the palletA is area of the cylindrical barrelA = mg/P
A = (50 x 9.8) / (260)
A = 1.885 m²
Radius of the cylinderA = πr²
r² = A/π
r = √(A/π)
r = √(1.885/π)
r = 0.78 m
Thus, the radius of the cylindrical barrel is 0.78 m.
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Describe the relationship between kinetic energy and speed and give an example of how changing and object speed would affect its kinetic energy
Answers
Answer:
I'm not sure
Explanation:
I have had that question to Uchida c r go crew in to go be
The light intensity incident on a metallic surface with a work function of 1.88 eV produces photoelectrons with a maximum kinetic energy of 1.2 eV.
if the frequency of the light is doubled, what is the maximum kinetic energy of the photoelectrons?
Answer in units of eV.
Answers
Answer:
KE = KE (incidental) - KE of emitted photons
or KE = h * f - Wf
So h * f = KE + Wf = 1.2 + 1.88 = 3.08 incident energy
If you double the frequency then h * f = 6.16
KE = 6.16 - 1.2 = 4.96 eV
A toy car is moving along with 0. 50 joules of kinetic energy. If its speed is doubled, then its new kinetic energy is.
Answers
Answer:
2 Joules
Explanation:
Kinetic Energy = 1/2 of (Mass x Velocity^2)
What determines the speed of a wind?
o The difference in air pressure between air masses.
O The moisture content of air over land.
O The altitude of the warmer air mass.
The moisture content of air over water.
Answers
Answer:
Answer: The difference in air pressure between air masses.
Answer:
The difference in air pressure between air masses.
Explanation:
The difference in air pressure, just like letting the higher-pressure air out of a balloon, determines the speed of the wind.
An engine using 1 mol of an ideal gas initially at 18.1 L and 280 K performs a cycle
consisting of four steps:
1) an isothermal expansion at 280 K from
18.1 L to 34.2 L ;
2) cooling at constant volume to 151 K ;
3) an isothermal compression to its original
volume of 18.1 L; and
4) heating at constant volume to its original
temperature of 280 K .
Find its efficiency. Assume that the
heat capacity is 21 J/K and the universal gas constant is 0.08206 L · atm/mol/K =
8.314 J/mol/K.
Answers
The efficiency of the engine is 16%.
The efficiency of the engine is given by,
η = W/Q
η = (W₁ + W₂ + W₃ + W₄)/(Q₁ + Q₂ + Q₃ + Q₄)
Since, the steps 2 and 4 are held at constant volume, the work done in these steps will be zero. Also, the heat enters into the system only during the steps 1 and 4.
So, the efficiency,
η = (W₁ + W₃)/(Q₁ + Q₄)
In step 1
The work done in isothermal expansion,
W₁ = nRT ln(V₂/V₁)
During isothermal expansion, there is no change in internal energy. So, the heat energy,
Q₁ = W₁ = nRT ln(V₂/V₁)
In step 3
Work done in isothermal compression,
W₃ = nRT₂ ln(V₄/V₃)
In step 4
The heat entering into the system,
Q₄ = CvΔT = Cv(T₁ - T₂)
Therefore, efficiency,
η = [nRT₁ ln(1.88) + nRT₂ ln(1/1.88)]/[nRT₁ ln(1.88) + Cv(T₁ - T₂)]
η = (280 - 151)/[280 + (21/8.314 ln(1.88)) (280 - 151)
η = 0.16
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