Answer:
45°
Explanation:
Range is the horizontal distance travelled by an object undergoing projectile motion.
Range is given by the formula:
[tex]R=\frac{u^2sin(2\theta)}{g}[/tex]
where u = velocity, g = acceleration due to gravity and θ = angle above the horizontal.
For angle of 15°:
[tex]R=\frac{u^2sin(2*15)}{g}=\frac{0.5u^2}{g}[/tex]
We get a maximum range when sin(2θ) = 1
sin(2θ) = 1
2θ = sin⁻¹(1)
2θ = 90⁰
θ = 90°/2
θ = 45⁰
For angle of 45°:
[tex]R=\frac{u^2sin(2*45)}{g}=\frac{u^2}{g}[/tex]
my heart strike him to dead.what figure of speech is that?
Answer:
Hyperbole
Explanation:
this is an extreme exaggeration or overstatement/ magnification
It takes a minimum distance of 48.96 m to stop a car moving at 12.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 25.0 m/s.
Answer:
102 m
Explanation:
Given that It takes a minimum distance of 48.96 m to stop a car moving at 12.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 25.0 m/s.
Let the stopping distance be equal to S.
According to the definition of speed,
Speed = distance / time.
make time the subject of the formula
Time = distance / speed
then, the equivalent time is:
48.96 / 12 = S / 25
Cross multiply
12S = 48.96 x 25
12S = 1224
S = 1224 / 12
S = 102 m
Therefore, the stopping distance is 102 m
Help solve these two problems im having trouble trying to start these problems?
Answer:
25. Approximately 8.1 meters
26. North 1.31 km, and East 2.81 km
Explanation:
25.
Notice that the displacements: 6 meters east and 5.4 south create the legs of a right angle triangle. The hypotenuse of that triangle will be the distance (d) needed to cover in order to get the ball in the hole in one putt. That is:
[tex]d=\sqrt{6^2+5.4^2} =\sqrt{65.16} \approx 8.072\,\,\,m[/tex]
which can be rounded to 8.1 m.
26.
Notice that the 3.1 km at an angle of 25 degrees north of east, is the hypotenuse of a right angle triangle that has for legs the east and north components of that distance.
We can find the leg corresponding to the east displacement using the cosine function (that relates adjacent side with hypotenuse):
[tex]east\,\, comp=3.1 * cos(25^o)\approx 2.809\,\,km[/tex]
and we can calculate the north component using the sine function that relates the opposite side to the angle with the hypotenuse.
[tex]north\,\,component = 3.1 * sin(25^o) \approx 1.31 \,\,km[/tex]
Which statements about potential energy are true?
▫ Gaining potential energy is always associated with a force field.
▫ A change in position always means that an object gains potential energy.
▫ There's only one kind of potential energy.
▫ Some kinds of potential energy are related to electric forces exerted by atoms and molecules.
Answer:
the answer is 1 and 4
Explanation
Plato users
For the potential energy, statement 1 and statement 4 are correct.
The potential energy of the object the energy of the object in its steady position. When the object is at rest, the energy of the object in that condition is called potential energy.
Let us consider an electron having charge [tex]e[/tex] is moving the distance [tex]d[/tex] in uniform electric field E.
Its potential energy can be written as,
[tex]P = eEd[/tex]
Where P is the potential energy and E is the electric field.
Hence, the potential energy of the electron is associated with the electric field.
The electric force can be written as,
[tex]F =eE[/tex]
Where [tex]F[/tex] is the electric force, [tex]E[/tex] is the electric field and [tex]e[/tex] is the charge on the electron.
So, the potential energy can be written as,
[tex]P=Fd[/tex]
Hence, the potential energy is related to electric force.
For more information, follow the link given below.
https://brainly.com/question/1413008.
A loop of area 0.250 m^2 is in a uniform 0.020 0-T magnetic field. If the flux through the loop is 3.83 × 10-3T· m2, what angle does the normal to the plane of the loop make with the direction of the magnetic field?
Answer:
40.0⁰
Explanation:
The formula for calculating the magnetic flux is expressed as:
[tex]\phi = BAcos\theta[/tex] where:
[tex]\phi[/tex] is the magnetic flux
B is the magnetic field
A is the cross sectional area
[tex]\theta[/tex] is the angle that the normal to the plane of the loop make with the direction of the magnetic field.
Given
A = 0.250m²
B = 0.020T
[tex]\phi[/tex] = 3.83 × 10⁻³T· m²
3.83 × 10⁻³ = 0.020*0.250cosθ
3.83 × 10⁻³ = 0.005cosθ
cosθ = 0.00383/0.005
cosθ = 0.766
θ = cos⁻¹0.766
θ = 40.0⁰
Hence the angle normal to the plane of the loop make with the direction of the magnetic field is 40.0⁰
An alligator crawls 25\,\text m25m25, start text, m, end text to the left with an average velocity of -1.2\,\dfrac{\text m}{\text s}−1.2
s
m
minus, 1, point, 2, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction.
Answer:
21 s.
I hope this helps!
Answer:21s
Explanation:
A motor in a radio control car uses 7.2 volts and draws 14.4 Amps of electricity. What is the resistance of the motor?
Answer :
0.5 Ω
Explanation:
The following data were obtained from the question:
Voltage (V) = 7.2 V
Current (I) = 14.4 A
Resistance (R) =..?
The resistance of the motor can be obtained by applying the ohm's law equation as shown below:
V = IR
7.2 = 14.4 × R
Divide both side by 14.4
R = 7.2/14.4
R = 0.5 Ω
Therefore, the resistance is 0.5 Ω
Answer:
Answer :
0.5 Ω
Explanation:
The following data were obtained from the question:
Voltage (V) = 7.2 V
Current (I) = 14.4 A
Resistance (R) =..?
The resistance of the motor can be obtained by applying the ohm's law equation as shown below:
V = IR
7.2 = 14.4 × R
Divide both side by 14.4
R = 7.2/14.4
R = 0.5 Ω
Therefore, the resistance is 0.5 Ω
If the briefcase hits the water 6.0 s later, what was the speed at which the helicopter was ascending?
Complete Question
In an action movie, the villain is rescued from the ocean by grabbing onto the ladder hanging from a helicopter. He is so intent on gripping the ladder that he lets go of his briefcase of counterfeit money when he is 130 m above the water. If the briefcase hits the water 6.0 s later, what was the speed at which the helicopter was ascending?
Answer:
The speed of the helicopter is [tex]u = 7.73 \ m/s [/tex]
Explanation:
From the question we are told that
The height at which he let go of the brief case is h = 130 m
The time taken before the the brief case hits the water is t = 6 s
Generally the initial speed of the briefcase (Which also the speed of the helicopter )before the man let go of it is mathematically evaluated using kinematic equation as
[tex]s = h+ u t + 0.5 gt^2[/tex]
Here s is the distance covered by the bag at sea level which is zero
[tex]0 = 130+ u * (6) + 0.5 * (-9.8) * (6)^2[/tex]
=> [tex]0 = 130+ u * (6) + 0.5 * (-9.8) * (6)^2[/tex]
=> [tex]u = \frac{-130 + (0.5 * 9.8 * 6^2) }{6}[/tex]
=> [tex]u = 7.73 \ m/s [/tex]
What is the mass of an object that has a volume of 56 ml and a density of 1.24 g/ml
Answer:
The answer is 69.44 gExplanation:
The mass of a substance when given the density and volume can be found by using the formula
mass = Density × volumeFrom the question
volume = 56 ml
density = 1.24 g/ml
We have
mass = 56 × 1.24
We have the final answer as
69.44 gHope this helps you
Hollywood and video games often depict the bad guys being "blown away" when they’re shot by a bullet (i.e. once hit, their feet leave the ground and they fly backwards). Assuming that even if a handgun cartridge did generate enough momentum for the bullet to do this, why is it still nonsense on-screen?
Answer:
Taking a look at Newton's third law of motion which states "for every force exerted, their is an opposite force equal in magnitude and opposite in direction on the first force".
Similarly if a bullet had enough forces behind it to hurl someone through the air when they were hit, a similar force would act on the person holding the gun that fired the bullet.
What we load into the gun is called a 'cartridge' Each piece is composed of four basic substance the casing, the bullet, the primer, and the powder.
The primer explodes lighting the powder which causes a buildup of pressure behind the bullet. This powder can be used in rifle cartages because the bullet chamber is designed to withstand greater pressures.
It is difficult in practice to measure the forces within a gun bagel, but the one easily measured parameter is the velocity with which the bullet exits muzzle velocity, therefore assuming that even if a handgun cartridge which generate enough momentum for the bullet to do this, it is still nonsense on screen in Hollywood and video.
The gravitational force acting on a lead ball is much larger than that acting on a wooden ball of the same size. Which statement is true about when they are dropped
Complete question is;
The gravitational force acting on a lead ball is much larger than that acting on a wooden ball of the same size. Which statement is true about when they are dropped?
A) The acceleration due to gravity is the same for both balls.
B) The lead ball’s acceleration due to gravity is larger than the wooden ball’s.
C) The lead ball’s acceleration due to gravity is less than the wooden ball’s.
Answer:
Option A) The acceleration due to gravity is the same for both balls.
Explanation:
Density of Lead is 11.34 g/cm³ while density of hard wood is around 1.3 g/cm³
Thus, it means lead is the heavier object when both have same masses.
We are told that the wood and lead both have same size but from the density given above, it's clear that the mass of the lead ball is more than that of the wooden ball and thus, the force from would be more for the lead ball than the wooden ball.
Now, If we were to measure the position of both balls when falling, we will observe that they do not fall fall with a constant speed. This is because they fall with a constant acceleration and as such the speed increases.
Therefore both balls will hit the ground at the same time because they both start from a position of rest and both will have the same acceleration.
Derek is watching steam form swirling patterns above the boiling water in his beaker.
Which type of thermal energy transfer is he observing?
A.Conduction
B.Translation
C.Convection
D.Radiation
Answer:
Convection
Explanation:
Answer:
C. Convection
Explanation:
I just did it
How will the motion of an object that is moving to the right change, if it is pushed in the opposite direction with a greater force?
Оооо
The object will move at a constant speed in the same direction for a while and then slow down and stop.
The object will slow down for a while and then move at a slower constant speed in the same direction.
The object will slow down and then begin to move faster and faster in the opposite direction.
0 The object will speed up and then begin to move at a slower speed in the opposite direction.
g A cylinder of mass m is free to slide in a vertical tube. The kinetic friction force between the cylinder and the walls of the tube has magnitude f. You attach the upper end of a lightweight vertical spring of force constant k to the cap at the top of the tube, and attach the lower end of the spring to the top of the cylinder. Initially the cylinder is at rest and the spring is relaxed. You then release the cylinder. What vertical distance will the cylinder descend before it comes momentarily to rest
Answer:
The vertical distance is [tex]d = \frac{2}{k} *[mg + f][/tex]
Explanation:
From the question we are told that
The mass of the cylinder is m
The kinetic frictional force is f
Generally from the work energy theorem
[tex]E = P + W_f[/tex]
Here E the the energy of the spring which is increasing and this is mathematically represented as
[tex]E = \frac{1}{2} * k * d^2[/tex]
Here k is the spring constant
P is the potential energy of the cylinder which is mathematically represented as
[tex]P = mgd[/tex]
And
[tex]W_f[/tex] is the workdone by friction which is mathematically represented as
[tex]W_f = f * d[/tex]
So
[tex] \frac{1}{2} * k * d^2 = mgd + f * d [/tex]
=> [tex] \frac{1}{2} * k * d^2 = d[mg + f ][/tex]
=> [tex] \frac{1}{2} * k * d = [mg + f ][/tex]
=> [tex]d = \frac{2}{k} *[mg + f][/tex]
a 12000.0-kg car is traveling at 19 m/s. the driver suddenly slams on the brakes and skids to a stop. The coefficient of kinetic friction between the tires and the road is 0.80. for what length of time is the car skidding?
calculate sound intensity
Answer:
I dont know sorry,I hope you find what are you looking for.
A 6.13-g bullet is moving horizontally with a velocity of 361 m/s, where the sign indicates that it is moving to the right (see part a of the drawing). The bullet is approaching two blocks resting on a horizontal frictionless surface. Air resistance is negligible. The bullet passes completely through the first block (an inelastic collision) and embeds itself in the second one, as indicated in part b. Note that both blocks are moving after the collision with the bullet. The mass of the first block is 1233 g, and its velocity is 0.741 m/s after the bullet passes through it. The mass of the second block is 1646 g. (a) What is the velocity of the second block after the bullet imbeds itself
Answer:
v₃ = 0.786 m/s
Explanation:
Here, we will use the law of conservation of momentum, which states the following:
Total Momentum of System Before Collision =
Total Momentum of System After Collision
m₁u₁ + m₂u₂ + m₃u₃ = m₁v₁ + m₂v₂ + m₃v₃
where,
m₁ = mass of bullet = 6.13 g = 0.00613 kg
m₂ = mass of 1st block = 1233 g = 1.233 kg
m₃ = mass of 2nd block = 1646 g = 1.646 kg
u₁ = speed of first bullet before collision = 361 m/s
u₂ = speed of first block before collision = 0 m/s
u₃ = speed of 2nd block before collision = 0 m/s
v₁ = speed of bullet after collision
v₂ = speed of 1st block after collision = 0.741 m/s
v₃ = speed of 2nd block after collision = ?
Therefore,
(0.00613 kg)(361 m/s) + (1.233 kg)(0 m/s) + (1.646 kg)(0 m/s) = (0.00613 kg)(v₁) + (1.233 kg)(0.741 m/s) + (1.646 kg)(v₃)
2.2129 kg m/s + 0 kg m/s + 0 kg m/s - 0.9136 kg m/s = (0.00613 kg)(v₁) + (1.233 kg)(0.741 m/s) + (1.646 kg)(v₃)
1.2992 kg m/s = (0.00613 kg)(v₁) + (1.646 kg)(v₃)
since, the bullet is embedded in 2nd block after collision. Thus, there velocities will become same. (v₁ = v₃)
Therefore,
1.2992 kg m/s = (0.00613 kg)(v₃) + (1.646 kg)(v₃)
v₃ = (1.2992 kg m/s)/(1.6521 kg)
v₃ = 0.786 m/s
Cells make proteins on small structures called vesicles.
True
False
The statement about making of protein on small structure by cell is True.
Vesicles can be regarded as small, fluid-filled sacs which its appearance can be seen on our skin. Transport vesicles is the vesicle that helps in transportation of materials from one part of the cell to other. this material could be proteins as well as other molecules.When protein is been made by a cell , then the transporter vesicles will then be responsible for the movement of this proteins to the Golgi apparatus, where actions like sorting and refining will be performed.With the help of vesicle pressure in the cell can be regulatedThe fluid that is contained inside these sacs is usually clear, and sometimes it could be white or yellow with blood.The diameter of a Vesicles are about 5 to 10 millimeters.Therefore, vesicles helps in movement of molecules.
Learn more at: https://brainly.com/question/14540310?referrer=searchResults
A system has the same velocity profile but a depth of 10 feet. The average velocity of the stream with a depth of 10 feet is __________ the stream with a depth of 6 feet.
a. Greater than
b. Less tharn
c. The same as
d. The answer cannot be determined with the given information.
Answer:
The average velocity of the stream with a depth of 10 feet is greater.
(a) is correct option.
Explanation:
Given that,
Depth [tex]h_{1}= 10\ feet[/tex]
Depth [tex]h_{2}=6\ feet[/tex]
We need to calculate the average velocity of the stream
According to question,
[tex]h_{1} > h_{2}[/tex]
The velocity for first case,
[tex]v_{1}=u_{1}\dfrac{x_{1}}{h_{1}}[/tex]
[tex]\dfrac{v_{1}}{x_{1}}=\dfrac{u_{1}}{h_{1}}[/tex]
The velocity for second case,
[tex]v_{2}=u_{2}\dfrac{x_{2}}{h_{2}}[/tex]
[tex]\dfrac{v_{2}}{x_{2}}=\dfrac{u_{2}}{h_{2}}[/tex]
For the same velocity profile,
[tex]\dfrac{dv}{dx}=\dfrac{v_{1}}{x_{1}}=\dfrac{v_{2}}{x_{2}}[/tex]
Then,
[tex]\dfrac{u_{1}}{h_{1}}=\dfrac{u_{2}}{h_{2}}[/tex]
Put the value into the formula
[tex]\dfrac{u_{1}}{10}=\dfrac{u_{2}}{6}[/tex]
[tex]u_{1}=\dfrac{5}{3}u_{2}[/tex]
[tex]u_{1}=1.67u_{2}[/tex]
The velocity is [tex]u_{1} > u_{2}[/tex]
We need to calculate the average velocity for first case
Using formula of average velocity
[tex]v_{avg}_{1}=\dfrac{0+u_{1}}{2}[/tex]
Put the value into the formula
[tex]v_{avg}_{1}=\dfrac{0+u_{1}}{2}[/tex]
[tex]v_{avg}_{1}=\dfrac{u_{1}}{2}[/tex]
We need to calculate the average velocity for second case
Using formula of average velocity
[tex]v_{avg}_{2}=\dfrac{0+u_{2}}{2}[/tex]
Put the value into the formula
[tex]v_{avg}_{2}=\dfrac{0+u_{2}}{2}[/tex]
[tex]v_{avg}_{2}=\dfrac{u_{2}}{2}[/tex]
If [tex]u_{1} > u_{2}[/tex] then [tex]\dfrac{u_{1}}{2} >\dfrac{u_{2}}{2}[/tex]
So, we can say that the average velocity of the stream with a depth of 10 feet will be greater than the stream with a depth of 6 feet.
Hence, The average velocity of the stream with a depth of 10 feet is greater.
(a) is correct option.
The seasons of the year result from Earths movement, or____, around the sun.
Answer:
rotation
Explanation:
The seasons of the year result from Earths movement, or rotation around the sun. The answer for the blanks is rotation .
What is the earth's orbit?The Earth orbits the Sun in a counterclockwise pattern above the Northern Hemisphere at an average distance of 149.60 million km.
The Earth revolves around its axis once every 24 hours and orbits the sun once every 365 days. The Earth's rotation on its axis, not its orbit around the sun, causes day and night.
The term 'one day' refers to the time it takes the Earth to rotate once on its axis, which includes both day and night.
A season is a division of the year that is based on variations in weather, ecology, and the number of daylight hours in a certain place.
Seasons on Earth are caused by Earth's orbit around the Sun and its axial tilt relative to the ecliptic plane.
The seasons of the year result from Earths movement, or rotation around the sun.
Hence, the answer for the blanks is rotation .
To learn more about the earth's orbit, refer to the link;
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Please help me with this
Answer:
7 Newton's East
Explanation:
when the force is going in the same direction in this case east, you add the forces.
Please help with this science thank you
Answer:acbd
Explanation:
A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the plates are pulled apart to twice their original separation. This process will double the: __________A. capacitance
B. surface charge density on each plate
C. stored energy
D. electricfield between the two places
E. charge on each plate"
Answer: C.
Explanation:
For a parallel-plate capacitor where the distance between the plates is d.
The capacitance is:
C = e*A/d
You can see that the distance is in the denominator, then if we double the distance, the capacitance halves.
Now, the stored energy can be written as:
E = (1/2)*Q^2/C
Now you can see that in this case, the capacitance is in the denominator, then we can rewrite this as:
E = (1/2)*Q^2*d/(e*A)
e is a constant, A is the area of the plates, that is also constant, and Q is the charge, that can not change because the capacitor is disconnected.
Then we can define:
K = (1/2)*Q^2/(e*A)
And now we can write the energy as:
E = K*d
Then the energy is proportional to the distance between the plates, this means that if we double the distance, we also double the energy.
If the plates are pulled apart to twice their original separation, then this will double the stored energy. Hence, option (C) is correct.
The given problem is based on the concept of parallel plat capacitor. For a parallel-plate capacitor where the distance between the plates is d.
The capacitance is:
C = e*A/d
here.
e is the permittivity of free space.
Since, the distance is inversely proportional then if we double the distance, the capacitance halves. Now, the stored energy can be given as,
E = (1/2)*Q^2/C
here,
Q is the charge stored in the capacitor.
Now you can see that in this case, the capacitance is in the denominator, then we can rewrite this as:
E = (1/2)*Q^2*d/(e*A)
e is a constant, A is the area of the plates, that is also constant, and Q is the charge, that can not change because the capacitor is disconnected.
Then we can define:
K = (1/2)*Q^2/(e*A)
And now we can write the energy as:
E = K*d
So, the energy is proportional to the distance between the plates.
Thus, we can conclude that if the plates are pulled apart to twice their original separation, then this will double the stored energy. Hence, option (C) is correct.
Learn more about the energy stored in a capacitor here:
https://brainly.com/question/3611251
To begin your activity, open this Tracker experiment: Car Round Trip. Click play to watch the video. The other video controls allow you to rewind the video or step forward or backward one frame at a time.
Answer:
The car appears to have a constant, positive acceleration for most of the video clip.
When adding the components of a vector, the resultant magnitude is always the sum of the two component magnitudes.
True or false?
Answer:False
Explanation:
Answer:
False
Explanation:
Blood is 92% water. Blood is
drawn using a capillary tube.
Write 1 sentence explaining how it
illustrates this characteristic of
water. Use the terms adhesion
and capillary action.
Answer:
Plasma, which constitutes 55% of blood fluid, is mostly water (92% by volume), and contains proteins, glucose, mineral ions, hormones, carbon dioxide (plasma being the main medium for excretory product transportation), and blood cells themselves.
Explanation:
Capillary motion is crucial for circulating water. Your body's cells would not hydrate without this flow, and crucial communication between your brain and body would slack off, hence blood contains water 92% water helps in capillary action.
What is Capillary action?Capillary action, also known as capillary effect or motion, is the process by which liquid moves through constricted areas without the aid of external forces like gravity but rather with the help of intermolecular forces that exist between the liquid and solid surface (s).
Adhesion: The attraction of two different molecules, such as the hydrogen and oxygen molecules found in water and plastic drinking straws.
Proteins, glucose, mineral ions, hormones, carbon dioxide (plasma is the principal medium for excretory product transfer), and blood cells themselves are contained in plasma, which makes up 55% of blood fluid. Plasma is mostly water (92% by volume) and contains water as well as several other substances.
Therefore, the water contains in the blood helps in capillary action.
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A force is applied to a block sliding along a surface (Figure 2). The magnitude of the force is 15 N, and the horizontal component of the force is 4.5 N. At what angle (in degrees) above the horizontal is the force directed?
Answer:
Fy = 14.3 [N]
Explanation:
To be able to solve this problem we must know that the force is a vector and has magnitude and direction, therefore it can be decomposed into the force in the X & y components:
When we have the components on the horizontal and vertical axes we must use the Pythagorean theorem.
[tex]F = \sqrt{F_{x}^{2} +F_{y}^{2} }[/tex]
where:
F = 15 [N]
Fx = horizontal component = 4.5 [N]
Fy = vertical component [N]
[tex]15=\sqrt{4.5^{2}+F_{y}^{2}}\\ 15^{2}= (\sqrt{4.5^{2}+F_{y}^{2}})^{2} \\225 = 4.5^{2}+F_{y} ^{2}\\ F_{y}^{2} =225 -4.5^{2}\\ F_{y}^{2}=204.75\\F_{y}=\sqrt{204.75}\\ F_{y}=14.3 [N][/tex]
One way to increase friction is to use (A.wax,B.sand,C.water ,D.oil
Answer:
using sand
Explanation:
We can increase friction by making rough surface.
a tiger leaps with an initial velocity of 55 km/hr at an angle of 13° with respect to the horizontal. what are the components of the tigers velocity?
Answer:
vₓ = 53.6 km/h
vy = 12.4 km/h
Explanation:
if we define two axis perpendicular each other with origin in the point represented by the tiger leaping (assuming we can treat it as a point mass) coincidently with the horizontal (x-axis) and vertical (y-axis) directions, we can obtain the components of the velocity in both independent directions.We can do it simply getting the projections of the velocity vector on both axes, using simple trigonometry, as follows:[tex]v_{x} = v_{o} * cos \theta = 55 km/h * cos 13 = 53.6 km/h[/tex]
[tex]v_{y} = v_{o} * sin\theta = 55 km/h * sin 13 = 12.4 km/h[/tex]
) A 1000-gallon tank currently contains 100.0 gallons of liquid toluene and a gas saturated with toluene vapor at 85°F and 1 atm. (a) What quantity of toluene (lbm) will enter the atmosphere when the tank is filled and the gas displaced? (b) Suppose that 90% of the displaced toluene is to be recovered by compressing the displaced gas to a total pressure of 5 atm and then cooling it isobarically to a temperature T(°F). Calculate T.
Answer:
A) m[tex]_{T}[/tex] = 0.3025 * 0.0476 * 92.13 = 1.327 Ibm
B) T= 63.32°F
Explanation:
Given data:
1000 gallon tank currently contains 100.0 gallons of liquid toluene
and A gas saturated with toluene vapor at 85°F and 1 atm
A) Calculate quantity of toluene ( Ibm ) that will enter the atmosphere when the tank is filled
m[tex]_{T}[/tex] = [tex]n_{gas} * Y_{T} * M_{T}[/tex]
[tex]n_{gas}[/tex] (total mole of gas) = 0.3025 Ib-mole ( calculated using : [tex]\frac{PV}{RT}[/tex] )
[tex]Y_{T}[/tex] (mole fraction of toluene) = 0.0476 ( calculated using [tex]\frac{P_{T} }{P}[/tex] )
M[tex]_{T}[/tex] = 92.13 Ibm/Ib-mole
therefore: m[tex]_{T}[/tex] = 0.3025 * 0.0476 * 92.13 = 1.327 Ibm
B) using Antoine equation to solve for T
Antoine equation : [tex]log_{10} (P_{T} ) = A - \frac{B}{T+C}[/tex]
PT( partial pressure ) = 18.95 ( calculated using : [tex]y_{tb} * P[/tex] )
A = 6.95805
B = 1346.773
T = ?
C = 219.693
to calculate T make T the subject the subject of the equation
T + 219.693 = 1346.773 / 5.68044
∴ T = 17.40°C
convert T to Fahrenheit
T = 1.8 * 17.40 +32
= 63.32°F
