The statement that correctly compares the speed of sound in solids and gases is that the speed of sound is generally faster in solids than in gases, because solids are denser than gases.
Why the speed of sound is faster in solifds than gasesStrong intermolecular forces hold molecules in place as they are closely packed together in solids. A solid's molecules vibrate in response to an external disturbance, such as a tap on a table, and transfer this energy to nearby molecules. We hear sound waves because of the compressions and rarefactions that result from this energy transfer. The close proximity of the molecules in a solid allows sound waves to pass through it swiftly, increasing the sound speed.
In contrast, the molecules in gases are further distant from one another and are only kept together by weaker intermolecular forces. The molecules in a gas vibrate in response to disturbances, such as shouts, and transmit the energy to nearby molecules. However, because of the greater space between molecules, there is less effective energy transmission, and the sound waves move through the gas more slowly.
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A cliff diver of 61.0 kg steps off of a cliff 24 m above the ground. Assuming no air resistance, determine the speed of the diver the instant before they reaches the ground.
Answer:
30.3 meters, 172 degrees
Explanation:
To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.
Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West
Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North
The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.
Applying the Pythagorean theorem leads to the magnitude of the resultant (R).
R2 = (30.0 m)2 + (4.0 m)2 = 916 m2
R = Sqrt(916 m2)
R = 30.3 meters
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)
tangent(theta) = 0.1333
theta = invtan(0.1333)
theta = 7.59 degrees
This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.
_______________ is the name for the permanent destruction and clearing of forests
Answer:
DeforestationExplanation:
__________________________________________________________
According to Vocal Media,
__________________________________________________________
Deforestation is the permanent destruction of forests in order to utilize the land or trees. Typically, deforestation is clearing a lot of trees without the intention of establishing future growth. Harvesting, forest fires, and insect infestations do not count as deforestation because the affected areas will eventually grow back.
__________________________________________________________
Hope this helps! <3
__________________________________________________________
Calculate the KE in joules of a 1500 kg car moving at 29 m/s?
Answer:
x J = (1500 kg)(29 m/s)(y m/s)
Explanation:
x J = (1500 kg)(29 m/s)(y m/s)
To know that a 1500 kg car is moving at 29 m/s is not enough.
The value of x depends on y. You’re missing a number of meters and a quantity of ‘per seconds’ somewhere in your problem statement and you need to find them in order to solve the problem
Between the orbits of Mars and Jupiter, several thousand small objects called asteroids move in nearly circular orbits around the Sun. Consider an asteroid that is spherically shaped with radius r and density 2000 kg/m^3.
1. You find yourself on the surface of this asteroid and throw a baseball at a speed of 24 m/s. If the baseball is to travel around the asteroid in a circular orbit, what is the largest radius asteroid on which you are capable of accomplishing this feat?
Answer:
The radius is \(r = 3.21*10^{4} \ m\)
Explanation:
From the question we are told that
The density is \(\rho = 2000 \ kg/m^3\)
The speed is \(v = 24 \ m/s\)
Generally the largest radius of the asteroid is mathematically represented as
\(r = \frac{v^2}{ \sqrt{G * \rho * [\frac{4}{3} ] * \pi} }\)
=> \(r = \frac{24^2}{ \sqrt{ 6.67*10^{-11} * 2000 * [\frac{4}{3} ] *3.142 } }\)
=> \(r = 3.21*10^{4} \ m\)
A gas at 300 kPa, is in a sealed container of volume 100 cm3 at 30°C. If the container is heated to 100°C, what is pressure of the gas inside the container?
Given:
Pressure, P = 300 kPa
Volume, V = 100 cm³
Temperature, T = 30°C
Let's fin the pressure of the gas inside the container if it is heated to 100°C.
Apply the Gay-Lussac's law:
\(\frac{P_1}{T_1}=\frac{P_2}{T_2}\)Where:
P1 = 300 kPa
T1 = 30 + 273 = 303 K
T2 = 100 + 273 = 373 K
V1 = V2 (since the container is sealed).
Let's solve for P2.
Rewrite the formula for P2:
\(\begin{gathered} P_2=\frac{P_1T_2}{T_1} \\ \\ P_2=\frac{300*373}{303} \\ \\ P_2=\frac{111900}{303} \\ \\ P_2=369.31\text{ kPa} \end{gathered}\)Therefore, the pressure if the container is heated to 100°C is 369.31 kPa.
ANSWER:
369.31 kPa
An infant's pulse rate is measured to be 135 +/- 6 beats/min. What is the percent uncertainty in this measurement? O 4.44% O 4.4% O 4% 0.04%
The percent uncertainty in the measurement of an infant's pulse rate, which is recorded as 135 +/- 6 beats/min, is 4.4%.
The percent uncertainty is calculated by dividing the range of the measurement (in this case, 6 beats/min) by the average value of the measurement (in this case, 135 beats/min), and then multiplying by 100 to express it as a percentage. In this case, the range is 6 beats/min and the average value is 135 beats/min. Dividing 6 by 135 gives 0.0444, and multiplying by 100 gives 4.44%. Therefore, the percent uncertainty in this measurement is 4.4%.
This measurement indicates that the pulse rate of the infant can vary within a range of +/- 6 beats/min from the average value of 135 beats/min. The percent uncertainty provides a measure of the relative variability or precision of the measurement. A lower percent uncertainty would indicate a more precise measurement with less variability, while a higher percent uncertainty would indicate a less precise measurement with greater variability. In this case, a percent uncertainty of 4.4% suggests a reasonably precise measurement of the infant's pulse rate.
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This is the question
Answer:
B
Explanation:
SPEAR is a storage ring at the Stanford Linear Accelerator which has a circulating beam of electrons that are moving at nearly the speed of light (2.998 108 m/s). If a similar ring is about 80.0 m in diameter and has a 0.59 A beam, how many electrons are in the beam
Answer:
n = 3.1x10¹²
Explanation:
To find the number of electrons we need to find first the charge (q):
\( I = \frac{q}{\Delta t} \rightarrow q = I*\Delta t \) (1)
Where:
I: is the electric current = 0.59 A
t: is the time
The time t is equal to:
\(v = \frac{\Delta x}{\Delta t} \rightarrow \Delta t = \frac{\Delta x}{v}\) (2)
Where:
x: is the displacement
v: is the average speed = 2.998x10⁸ m/s
The displacement is equal to the perimeter of the circumference:
\( \Delta x = 2\pi*r = \pi*d \) (3)
Where d is the diameter = 80.0 m
By entering equations (2) and (3) into (1) we have:
\(q = I*\Delta t = I*\frac{\Delta x}{v} = \frac{I\pi d}{v} = \frac{0.59 A*\pi*80.0 m}{2.99 \cdot 10^{8} m/s} = 4.96 \cdot 10^{-7} C\)
Now, the number of electrons (n) is given by:
\( n = \frac{q}{e} \)
Where e is the electron's charge = 1.6x10⁻¹⁹ C
\( n = \frac{q}{e} = \frac{4.96 \cdot 10^{-7} C}{1.6 \cdot 10^{-19} C} = 3.1 \cdot 10^{12} \)
Therefore, the number of electrons in the beam is 3.1x10¹².
I hope it helps you!
Problem 1 (4 points) Solve the following boundary value problem with the Galerkin method in which two equal length element is used. d²u/dx² - 1 = 0
0
Boundary conditions du/dx (1) = 0
The final solution is u = ϕ2(x) = 1 - x. This is the solution to the boundary value problem using the Galerkin method.
Here is the solution to the boundary value problem using the Galerkin method:
The Galerkin method is a numerical method for solving differential equations. It is based on the idea of using a set of basis functions to approximate the solution to the differential equation. In this case, we will use two equal-length elements to approximate the solution.
The first step is to choose a set of basis functions. We will use the following basic functions:
ϕ1(x) = x
ϕ2(x) = 1 - x
These basis functions are linear and have a value of 1 at the endpoints of the domain.
The next step is to use these basis functions to approximate the solution to the differential equation. We will do this by writing the differential equation in terms of the basis functions and then solving for the coefficients of the basis functions.
The differential equation is:
d²u/dx² - 1 = 0
We can write this equation in terms of the basis functions as follows:
(ϕ1''(x) + ϕ2''(x))u = 0
The coefficients of the basis functions can be found by solving this equation for u. The solution is:
u = Aϕ1(x) + Bϕ2(x)
where A and B are constants.
The boundary conditions are:
u(0) = 0
u(1) = 0
These boundary conditions can be used to find the values of A and B. The solution is:
A = 0
B = 1
The final solution is:
u = ϕ2(x) = 1 - x
This is the solution to the boundary value problem using the Galerkin method.
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An emergency vehicle is traveling at 45 m/s approaching a car heading in the same direction at a speed of 24 m/s. The emergency vehicle driver has a siren sounding at 650 Hz. At what frequency does the driver of the car hear
the siren?
The frequency that the driver of the car hears the siren of an emergency vehicle traveling at 45 m/s and approaching a car heading in the same direction at a speed of 24 m/s is 538 Hz.
Doppler effect refers to a shift in the frequency of sound waves or light waves as they move toward or away from an observer. When the vehicle moves towards us, the sound waves are compressed, and their frequency increases, resulting in a higher pitch.
When the vehicle moves away from us, the sound waves are stretched out, and their frequency decreases, resulting in a lower pitch. This effect is also applicable to light waves.
The formula for calculating the Doppler effect is: f'= f(v±vᵒ)/(v±vᵰ), where,• f' is the frequency of the observed wave,• f is the frequency of the emitted wave,• v is the speed of the wave in the medium,• vᵒ is the speed of the observer relative to the medium,• vᵰ is the speed of the source relative to the medium.
In this case, the driver of the car hears the siren, which is moving towards him, hence the formula is:
f'= f(v+vᵒ)/(v±vᵰ)
Substituting the values of f, v, vᵒ, and
vᵰ,f' = 650(343+24)/(343-45)f'
= 538 Hz
Therefore, the driver of the car hears the siren at a frequency of 538 Hz.
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A simple circuit has a 20 Ω resistor and carries 0. 3 A. What is the voltage of the power source?
A simple circuit has a 20 Ω resistor and carries 0. 3 A. The voltage of the power source is 6 V. In a simple circuit with only one resistor, the voltage across the resistor is equal to the voltage of the power source.
Using Ohm's law, we can determine the voltage of the power source by multiplying the resistance (R) of the circuit by the current (I) flowing through it. Thus, we have:
V = IR
Substituting the given values, we get:
\(V = (0.3 A)(20\; \Omega) = 6 V\)
Therefore, the voltage of the power source in the circuit is 6 volts. In a simple circuit with only one resistor, the voltage across the resistor is equal to the voltage of the power source.
This is because the sum of the voltages across all the components in the circuit must equal the total voltage of the power source, due to the conservation of energy.
It's important to note that in real-world circuits, the voltage of the power source can fluctuate due to various factors such as fluctuations in the electrical grid or changes in the internal resistance of the power source itself.
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A rabbit is trying to cross the street. Its velocity v as a function of time t is given in the graph below where
rightwards is the positive velocity direction.
Answer:
2.5
Explanation:
A rabbit is trying to cross the street. Its velocity v as a function of time t is given in the graph below where rightwards is the positive velocity direction 2.5 m.
What is velocity?When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
Rabbit displacement is 2.5 m.
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a block is given an initial velocity of 5.00 m/s up a frictionless incline of angle 20 degrees. the magnitude of the block’s acceleration is 2.5 m/????2 while it is on the ramp. how far up the incline does the block get before sliding down again?
The block will incline up with projectile motion until 0.085 m before sliding down.
We need to know about the projectile motion to solve this problem. The projectile motion is known as parabolic motion and the velocity is divided by 2 axes.
vox = vo cosA
voy = vo sinA
where vox is initial velocity of x axis, voy is initial velocity of y axis, vo is initial velocity and A is the angle.
From the question above, the given parameters are
vo = 5 m/s
A = 20⁰
By using the uniform motion, where vty = 0 m/s. Hence,
vty² = voy² - 2gh
0 = 5.sinA - 2 . 10 . h
20h = 5 . sin20⁰
h = 1/4 . 0.34
h = 0.085 m
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HELP PLEASE!!!
Gravity helps us watch television, talk on the phone, and use the Intemet.
Explain whether this statement is true or false.
Support your answer with evidence from the text.
Answer:
Technically yes, it does help those objects not to float away, but that is false. gravity is not the factor that lets us watch tv, talk on the phone etc.
Gravity helps us watch television, talk on the phone, and use the Internet. This is true statement.
What is the process of satellite orbiting?The goal of satellites is to achieve balance. They rotate around the globe quickly enough to avoid being entirely drawn down into the planet's center of gravity, yet slowly enough to avoid drifting out into space.
When a satellite is travelling at the right speed, the earth's gravitational attraction is just strong enough to keep it in place. A satellite must move quicker to maintain orbit the nearer it is to the earth's surface. Additionally, satellites' orbits are circular or elliptical due to the continual pull of the curved surface of the planet.
Therefore, gravity plays a crucial role in our daily lives, whether it's keeping us anchored to the planet's surface or keeping the satellites we use to communicate and learn more about our environment in orbit.
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Find the force experienced by a particle with a charge of (3x10^-8 c) when it is a distance of (2x10^-2 m) away from a second particle with a charge of (6x10^-7 c)
The physical characteristic of matter that causes it to feel a force when exposed to an electromagnetic field is called electric charge. The two types of electric charges that protons and electrons most frequently carry are positive and negative charges.
Find the force experienced by a particle with a charge of (3x10^-8 c) when it is a distance of (2x10^-2 m) away from a second particle with a charge of (6x10^-7 c)
Each fee = -Q
L is the length between charges.
decreased force =
As seen above, two particles, each with a charge of Q, are locked at a distance L apart. A net electric force F acts on every atom. The initial two particles are now locked on either side of a particle with a charge of +q.
Having said that,
The pressure at either end is
...(I)
If the charge q is positioned in the middle, then
Each end charge is under a force of
....(II)
We must determine the value of q.
Equation use (II)
Fill out the formula using the value of F.
Consequently, q is valued at q/8
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The Voyager 1 space probe was launched by NASA in 1977. It's now the most distant spacecraft from Earth, as it hurtles into space at over 60,000 km/h. It has run out of fuel, so it can't change its own motion.
One of your friends says, "If Voyager 1 doesn't collide with anything and is too far from anything to be affected by gravity, it will gradually slow down and stop."
I have to either agree or disagree with my friend, then i have to explain.
The statement, "The Voyager 1 space probe can't change its own motion" is correct and true. The Voyager 1 space probe was launched by NASA in 1977, and since then it has traveled over 14 billion miles away from Earth. It's the most distant spacecraft from Earth.
The Voyager 1 was designed to study the outer solar system and it sent valuable data back to Earth. But, now it has run out of fuel and cannot change its own motion as the thrusters that are responsible for keeping the spacecraft’s antenna pointed toward Earth have to be continuously fired to compensate for the small natural imbalances in its motion. Therefore, the statement is correct that Voyager 1 cannot change its own motion. It is still continuing its journey into space at a speed of over 60,000 km/h and is expected to keep traveling until it reaches other stars and the next galaxy beyond our Milky Way. So, I agree with the statement that the Voyager 1 space probe can't change its own motion.For such more question on motion
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Which part of the microscope is the circular area on the stage that light passes through?
Answer: The part of the microscope that is the circular area is the APERTURE
I hope this helped!
Lee pushes horizontally with a force of 78N on a 29kg mass for 16m across a floor.
Calculate the amount of work Lee did. Answer in units of J.
If Lee pushes horizontally with a force of 78N on a 29kg mass for 16m across a floor. The amount of work Lee did is: 1,248J.
How to find the work done?Given data:
Mass of the object , m = 29kg
Force, F = 78N
Displacement, d = 16m
Now let find the amount of work using this formula
Work = F × dcosθ
Let plug in the formula
Work = 78 × 16cosθ
Work = 1,248J
Therefore we can conclude that the work done is 1,248J.
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In Platos credo, Socrates, believes that he should follow the laws of the state Athens, because?
In Plato's philosophy, Socrates believed that he should follow the laws of the state of Athens because he believed in the idea of the "philosopher-king."
Who was Socrates?
Socrates was a classical Greek philosopher, credited as one of the founders of Western philosophy. He is best known for his method of inquiry, called the Socratic method, and for his teaching style, which was dialogic and aimed at getting students to think critically and develop their own ideas.
According to Socrates, the laws of the state were a reflection of the absolute and unchanging moral values that exist in the world. He believed that as a philosopher, it was his duty to live in accordance with these moral values, and thus to follow the laws of the state. In this way, Socrates saw himself as a servant of the divine, and believed that by following the laws, he was serving the greater good and promoting the welfare of the city.
Hence, In Plato's philosophy, Socrates believed that he should follow the laws of the state of Athens because he believed in the idea of the "philosopher-king."
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is a rare disorder that includes the inability to feel pain.
A. Somatoform pain disorder
B. Congenital analgesia
C. Kinesthesis
D. Anesthesia
Please select the best answer from the choices provided
Ο Ο Ο
B.
D
The rare disorder that includes the inability to feel pain is called Congenital analgesia. That is option B.
What is Congenital analgesia?Congenital analgesia is defined as ,the name implies, a genetic disorder that rarely occurs which makes one not to be able to feel pain.
It is an autosomal recessive disorder in which there is genetic changes in the PMRD12 gene.
Therefore, the rare disorder that includes the inability to feel pain is called Congenital analgesia.
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please help me i don’t know how to do this
when calculating impulse the variable we use is
Answer:
we use the variable J
Explanation:
what is a formula used in calculating impulse ?
v1 is the initial velocity of the object when the time interval begins. impulse has the same units and dimensions. (M L T -1) as momentum. in the international System of Units, These are kg·m/s = N·s. In English engineering units, they are slug·ft/s=lbf·s
Si unit: newton-second (N·s)
Other units: pound·s
Common Symbols: J, lmp
What is the lowest frequency for standing waves on a wire that is 10.0m long, has a mass of 100g, and is stretched under a tension of 250 N
The lowest frequency for standing waves on a wire that is 10.0 m long, has a mass of 100 g, and is stretched under a tension of 250 N is approximately 56.5 Hz.
The frequency of a standing wave on a wire depends on the tension (T), length (L), and mass per unit length (μ) of the wire. The relationship between these variables is given by:
f = (1/2L) * √(T/μ)
where f is the frequency of the standing wave.
To solve for the lowest frequency, we need to take the wire's length, mass, and tension into account.
The mass per unit length can be calculated by dividing the mass (m) by the length (L):
μ = m / L
Substituting the values, we get:
μ = 0.1 kg / 10.0 m
= 0.01 kg/m
Substituting the given values of L, T, and μ into the equation for frequency, we get:
f = (1/2 * 10.0 m) * √(250 N / 0.01 kg/m)
f ≈ 56.5 Hz
Therefore, the lowest frequency for standing waves on the wire is approximately 56.5 Hz.
The lowest frequency for standing waves on the wire is approximately 56.5 Hz, given its length of 10.0 m, mass of 100 g, and tension of 250 N.
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swinging a rock in a circle when does the string break
swinging a rock in a circle the string break when the tension in the string exceeds its maximum strength
Swinging a rock in a circle is an example of circular motion, the string holding the rock provides a centripetal force that keeps the rock moving in a circular path. The tension in the string depends on the mass of the rock, the velocity of the rock, and the radius of the circle it is moving in. If any of these factors change, it can affect the tension in the string. For instance, if the rock is too heavy or is moving too fast, the tension in the string will increase, and it may eventually break.
Similarly, if the radius of the circle is too small, the tension in the string will increase, and it may break. Therefore, the string will break when the tension in the string exceeds its maximum strength. It is important to note that the maximum strength of a string depends on its material, thickness, and length. Therefore, to determine exactly when the string will break is when the tension in the string exceeds its maximum strength.
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What are the effects of warm temperature on gas particles
Answer:
They move and collide faster.
Explanation:
This is because increasing the temperature increases the kinetic energy of the gas particles. As a result they move rapidly having more more frequent collisions.
Answer:
When the temperature of the container increases, the kinetic energy of the gas molecule becomes high.
Explanation:
This means the collision rate of the particles increases. Due to the collision of gas particles, the pressure increases across the wall of the container.
PLEASE HELP WILL MARK BRAINLIEST
In the formula Q = m x C x ΔT, which symbol represents specific heat?
A. Q
B. ΔΤ
C. m
D. с
Explanation:
Q = energy applied
m = mass
C = specific heat
ΔT = delta T = change in temperature
An alternating current of 60hz changes direction 100 times per second.
a. true
b. false
Answer:
False
Explanation:
Because it is 60 hz
A solid spherical conductor is given a net nonzero charge. the electrostatic potential of the conductor is
The electrostatic potential of the conductor is constant throughout the volume.
The electrostatic potential of the conductor is (d) constant throughout the volume. In a conductor in electrostatic equilibrium, the electric potential is constant inside the conductor, regardless of its shape or charge distribution. This means the potential is the same at all points inside the conductor, including the center and the surface.
The electric field inside a conductor in electrostatic equilibrium is zero. The charges inside the conductor redistribute themselves in such a way that the electric field cancels out within the conductor. Therefore, the electric field in the conductor is zero.
Complete Question: A solid spherical conductor is given a net nonzero charge. The electrostatic potential of the conductor is:
(a) largest at the center.
(b) largest on the surface.
(c) largest somewhere between center and surface.
(d) constant throughout the volume.
Also, what is the electric field in the conductor?
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If the coefficient of static friction between a patient and the bed sheets is 1.2, what is the maximum angle (θ) at which the bed can be tilted with respect to the floor before the patient begins to slide?a) 45°b) 60°c) 30°d) 50°e) 25°
The maximum angle at which the bed can be tilted with respect to the floor before the patient begins to slide is 45°.
This is because the coefficient of static friction (μs) between the patient and the bed sheets is 1.2, and the coefficient of static friction is equal to the tangent of the angle of inclination (θ):
μs = tan θ. Therefore, 45° is the maximum angle before the patient begins to slide.Static friction is the friction force that resists the initiation of motion. It is the force that one object exerts on another when they are not yet moving relative to each other. The coefficient of static friction is typically represented by the Greek letter μs, and is usually greater than the coefficient of kinetic friction (μk). The value of μs depends on the materials of the two objects that are in contact with each other.
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Electromagnetic induction is the process of producing an electric current by moving a loop of wire ____.
Answer:
through a magnetic field.
Explanation:
A cup of coffee with cooling constant k = -0.09 is placed in a room temperature of 18°C. If the coffee is served at 93 °C, how long will it take to reach a drinking temperature of 73 °C?
The time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.
The cooling law is given by:
$$\frac{dQ}{dt}=-k(T-T_0)$$
where Q is the heat in the object, t is the time taken, T is the temperature of the object at time t, T0 is the temperature of the environment and k is a constant known as the cooling constant.
We need to find the time it takes for the coffee to reach a drinking temperature of 73°C given that its initial temperature is 93°C.
Therefore, we need to find the time it takes for the coffee to cool down from 93°C to 73°C when placed in a room temperature of 18°C.
Let’s assume that the heat energy that is lost by the coffee is equal to the heat energy gained by the environment. We can express this as:
dQ = - dQ where dQ is the heat energy gained by the environment.
We can substitute dQ with C(T-T0) where C is the specific heat capacity of the object.
We can rearrange the equation as follows:
$$-\frac{dQ}{dt}=k(T-T_0)$$
$$-\frac{d}{dt}C(T-T_0)=k(T-T_0)$$
$$\frac{d}{dt}T=-k(T-T_0)$$
The differential equation above can be solved using separation of variables as follows:
$$\frac{d}{dt}\ln(T-T_0)=-k$$
$$\ln(T-T_0)=-kt+c_1$$
$$T-T_0=e^{-kt+c_1}$$
$$T=T_0+Ce^{-kt}$$
where C = e^(c1).
We can now use the values given to find the specific value of C which is the temperature difference when t=0, that is, the temperature difference between the initial temperature of the coffee and the room temperature.
$$T=T_0+Ce^{-kt}$$
$$73=18+C\cdot e^{-0.09t}$$
$$55=C\cdot e^{-0.09t}$$
$$C=55e^{0.09t}$$
$$T=18+55e^{0.09t}$$
We can now solve for the value of t when T=93 as follows:
$$93=18+55e^{0.09t}$$
$$e^{0.09t}=\frac{93-18}{55}$$
$$e^{0.09t}=1.3636$$
$$t=\frac{\ln(1.3636)}{0.09}$$
Using a calculator, we can find that the time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.
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