1- The amount of heat added at constant pressure: The amount of heat added at constant pressure can be calculated by using the formula qp = cv(T2 - T1).
What is constant pressure ?Constant pressure is a type of pressure that remains the same even when external forces are applied to it. It is also known as unchanging pressure or steady pressure. Constant pressure is usually measured with a barometer, which is a device used to measure atmospheric pressure. Constant pressure is most commonly seen in the form of air pressure, which is the pressure of the air around us. It is important to note that although the pressure remains constant, the temperature and density of the air can change. Constant pressure is essential for a variety of applications, such as in aircraft, where the air pressure in the cabin must remain constant for the comfort of the passengers.
In this case, qp = 0.719 kJ/kg.K (2200 - 273) = 1418.7 kJ/kg. 2- The amount of heat added at constant volume: The amount of heat added at constant volume can be calculated by using the formula qv = cp(T2 - T1). In this case, qv = 1.007 kJ/kg.K (2200 - 273) = 1810.7 kJ/kg. 3- The net work done by the cycle: The net work done by the cycle can be calculated by using the formula Wnet = qp - qv. In this case, Wnet = 1418.7 - 1810.7 = -392 kJ/kg. 4- The thermal efficiency of the cycle: The thermal efficiency of the cycle can be calculated by using the formula nth = (Wnet/qp) x 100. In this case, nth = (-392/1418.7) x 100 = -27.6%. 5- The mean effective pressure: The mean effective pressure can be calculated by using the formula m = (2/1-r) x (P2/P1). In this case, m = (2/1-18) x (2200/100) = 733.3 kPa.
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1. if u is a velocity, x a length, and t is time, what are the dimensions (in the mlt system) of a) ∂∂∂∂/∂∂∂∂ b) ∂∂2uu/∂∂∂∂∂∂∂∂ c) ∫(∂∂∂∂/∂∂∂∂)dddd
The dimensional formulae of
a) du/dt is -LT⁻²
b) d²u/dx dt is -T⁻²
c) ∫(du/dt) dx is -L²/2T² +C
Dimensional formulae for velocity, length and time are:
Velocity = Distance/Time = LT⁻¹
Length = L
Time = T
a) du/dt:
du = d( LT⁻¹)
dt = d(T)
du/dt = d( LT⁻¹)/d(T) = -LT⁻²
b) d²u/dx dt:
d²u = d²(LT⁻¹)
dt = d(T)
dx = d(L)
d²u/dx dt = d²(LT⁻¹)/d(L) d(T) = -T⁻²
c) ∫(du/dt) dx:
du = d( LT⁻¹)
dt = d(T)
dx = d(L)
du = d( LT⁻¹)
∫(du/dt) dx = ∫ (-LT⁻²)d(L) = -L²/2T² +C
Thus, the dimensions in MLT system are formulated.
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What property is primarily responsible for determining the type of electromagnetic energy and peak wavelength emitted by a star such as the sun?.
The temperature of the emitting object affects the wavelength of the peak emission and is primarily responsible for determining the type of electromagnetic energy
What does the term "radiation" mean?
Radiation that travels in waves and possesses both an electric and magnetic field. Both natural and artificial sources contribute to it. The energy levels of electromagnetic radiation can range from low to high. It consists of x-rays, gamma rays, infrared light, visible light, ultraviolet light, radio waves, and microwaves.
Wien's displacement law is applied to determine wavelength. According to this equation, a body that resembles the sun emits a wide range of wavelengths and is therefore almost completely black. The peak wavelength that a black body emits is inversely proportional to the body's temperature. It is possible to determine energy from wavelength.
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how much energy is stored when a railroad car spring is compressed 10 cm?(the spring requires about 10,000 n to be compressed 3.0 cm.
When the railroad car spring is compressed 10 cm, it stores 16,666.7 J of elastic potential energy.
The energy stored in a spring can be calculated using the formula for elastic potential energy, which is given by U = 1/2 k x^2, where U is the elastic potential energy, k is the spring constant, and x is the displacement from the spring's rest position.
Given that the spring requires 10,000 N to be compressed 3.0 cm,
we can calculate the spring constant, k, using the equation F = kx,
where F is the force and x is the displacement.
Solving for k,
we find that k = F/x = 10,000 N / 3.0 cm = 3,333.3 N/cm.
Now that we have k, we can calculate the energy stored in the spring when it is compressed 10 cm.
Using the formula for elastic potential energy, U = 1/2 k x^2,
we find that U = 1/2 * 3,333.3 N/cm * (10 cm)^2 = 16,666.7 J.
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Which one of the following statements is true concerning the strength of the electric field between two oppositely charged parallel plates?a. It is the same everywhere between the plated if any edge effect is ignored.b. It is a maximum near the negatively charged plate.c. It is a maximum near the positively charged plate.d. It is a maximum midway between the plates.
The statement that is true concerning the strength of the electric field between two oppositely charged parallel plates is : It is the same everywhere between the plates if any edge effect is ignored. Option A. is the correct answer.
What is strength of electric field?This refers to a quantity used to express the intensity of an electric field at a particular location. The standard unit is the volt per meter (V/m or V·m-1). A field strength of 1 V/m represents a potential difference of 1 V between points separated by 1 meter. It is also called electric field intensity.
strength of the electric field is calculated using the formula :
E = F/q
Where,
E = strength of the electric field
F = Force in Newton
q = Charge in Columbus
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when two clean vertical glass plates, separated by a distance of 2 mm, are partially immersed in a pool of water, the liquid is drawn upward between the plates to a height of 6.5 mm. is the water temperature above or below the typical room temperature?
As, 12.57° C < 20°C avg, the water temperature below the typical room temperature.
What is room temperature?The temperature of a room as measured by a thermometer is referred to as room temperature. The ideal temperature is one at which people are content to wear everyday clothing. For the majority of people, it's either the normal temperature of their home or the setting they made on the thermostat. The term "room temperature" is frequently used in science. Here are the various room temperature readings.
Let F be the face carved
due to surface tension
F=TL
Capillary use can found out
as the rise of fluid due
to surface forces
Let h be the use from
the surface
Using newton's laws, we can found the Weight
Surface tension force = weight of fluid
2σ=ρ×(d&h)×g
h= 2σ/ρhgd
h= 2σ/ρgd
As L = h
T = F/2σ/ρgd
T = 6.5/2σ/ρgd
T = 12.57° C
Room temperature = 20°C avg.
As, 12.57° C < 20°C avg, the water temperature below the typical room temperature.
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Complete question:
what is the initial velocity of the particle, v0 ?
The initial velocity of the particle is the value of v at t = 0, which is given by the equation v = v0. Therefore, v0 is the initial velocity of the particle. Hence, the initial velocity is 0.5m/s.
Velocity is the rate of change of an object’s position relative to a frame of reference, and is a function of time. It is usually described in terms of the speed and direction of an object's movement. Velocity can be either a vector quantity (having both magnitude and direction) or a scalar quantity (just magnitude). Initial velocity is the velocity of an object at the start of its motion. To calculate the initial velocity of an object, you will need to know the final position, final velocity, acceleration, and time.
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complete question: A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call v the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. What is the initial velocity of the particle, v0 ?
Patrick walks 70 m south in 150 seconds. He then walks 20 meters east in 30 seconds. What is his average velocity for the trip?
Group of answer choices
0.35 m/s southeast
0.27m/s southeast
0.41 m/s southeast
0.66 m/s southeast
Patrick's average velocity for the trip is 0.41 m/s along southeast.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Resultant displacement of Patrick = √(70² +20²) meter southeast
= 72.801 meter southeast.
Total time interval = 150 second + 30 second = 180 second
Hence, his average velocity for the trip is = resultant displacement/ Total time interval
= 72.801 meter ÷ 180 second
= 0.41 m/s along southeast
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Why does sodium chloride conduct electricity when it is molten or in its aqueous form?
Sodium chloride conducts electricity when it is molten or in its aqueous form because it dissociates into ions, (Na+) and (Cl-), which are free to move and carry electrical charge. The movement of these ions creates an electric current and allows for the flow of electricity.
What is electric current?Electric current is the flow of electric charge through a material, usually a conductor such as a metal wire. It is often measured in amperes (A) and is a measure of the rate at which electric charge flows through a circuit. The flow of electric charge is due to the movement of electrons in a conductor and is what enables the transfer of electrical energy from one point to another.
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Bet example of kinetic energy being tranformed into potential energy
A) a ball rolling up a hill
B) bending a paperclip
C)tarting an automobile
Answer:
Probably C
Explanation:
What is needed for states of matter to change phase?
For a substance to change phase, it must either gain or lose thermal energy.
This can be achieved in several ways, including:
Heating or cooling: When a substance is heated, its temperature increases, causing the molecules to move faster and eventually overcome the intermolecular forces holding them in place. This leads to a change in phase, such as from solid to liquid or from liquid to gas. Conversely, cooling a substance can cause its molecules to slow down and solidify.
Pressure: Changing the pressure on a substance can also cause it to change phase. Increasing the pressure on a gas will cause it to condense into a liquid, while decreasing the pressure can cause a liquid to boil and become a gas. Similarly, changing the pressure on a solid can cause it to change into a liquid or gas.
Evaporation: When a liquid is heated, some of its molecules will escape into the surrounding air and become a gas, a process called evaporation.
The specific conditions required for a substance to change phase will depend on the substance's unique properties, including its boiling point, melting point, and vapor pressure.
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What is 85 degrees Celsius in Fahrenheit?
The formula for converting temperature 85 degrees Celsius to Fahrenheit is a linear function: [°F] = ([85] x 9 5) + 32. As a result, we get: 85 C to F = 185 °F
What exactly is temperature?
Temperature, like any other physical quantity, is defined as the measurement of the warmth or coldness of a substance or object in relation to some standard value. Temperature, while used to express hot and cold conditions, is usually measured with a thermometer marked in several temperature scales, the most common of which are Celsius and Fahrenheit. There are a variety of other temperature units.
What is the SI Temperature Unit?
The SI unit of temperature is Kelvin, which is represented by the symbol K in the International System of Units. The Kelvin scale is widely accepted or used in science and engineering. Temperature is usually measured in degrees Celsius or Fahrenheit in most parts of the world.
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Which description includes a scalar quantity?
Group of answer choices
Louis used a force of 5 Newtons.
Michael weighed 170 pounds before the match.
Jason rode his bicycle at 10 m/s to the east.
Ryan walked for 3 minutes.
Jason rode his bicycle at 10 m/s to the east is a scalar quantity.
What is Scalar quantity?
It is possible to express in words how an object moves. There are many terminologies that can be used to describe moving objects, even for those without a background in physics.
A adequate vocabulary for expressing the motion of objects is provided by words and expressions like "moving quickly," "stopped," "slowing down," "speeding up," and "turning."
We will add terms like distance, displacement, speed, velocity, and acceleration to this vocabulary list.
Therefore, Jason rode his bicycle at 10 m/s to the east is a scalar quantity.
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Which of the following statements about specific heat capacity is true?
Group of answer choices
A. Specific heat capacity is the amount of heat per unit mass required to raise the temperature of a substance by one Kelvin (or degree Celcius)
B. Specific heat capacity is the same per unit mass for any substance.
C. Specific heat capacity defines the relationship between heat and density for a given substance.
D. The SI unit used to measure specific heat capacity is expressed as calories per gram degrees Celsius (cal/g °C)
Specific heat or specific heat capacity of a body is the amount of heat required for a unit mass of body to raise the temperature by 1 degree Celsius
What is Specific heat capacity ?The ease with which a material's temperature varies when it loses energy can be described using specific heat capacity. A lot of energy is required to adjust the temperature of materials with high specific heat capacity.
The composition of a body affects its specific heat, specific heat can be calculated using the provided heat energy. Hence The rise in temperature has no bearing on specific heat.
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A break-down truck tows a car of mass 1000kg along a level road and accelerates at 0-5m/s. What is the tension in the tow line.
If the tow line breaks when the car reaches a speed of 36 km/hr, how far will the car travel before coming to rest if a braking force of 5000N is applied
(a) The tension in the tow line is 500 N.
(b) The distance travelled by the car before coming to rest is 10 m.
What is the tension in the tow line?
The tension in the tow line is calculated by applying the following formula as shown below.
T = ma
where;
m is the mass of trucka is the accelerationT = 1000 kg x 0.5 m/s²
T = 500 N
The distance travelled by the car before coming to rest is calculated as follows;
a = F / m
a = ( 5000 N ) / ( 1000 kg )
a = 5 m/s²
v² = u² - 2as
where;
v is the final velocity when the car stops = 0u is the initial velocity = 36 km/h = 10 m/sa is the acceleration2as = u²
s = ( u² ) / ( 2a )
s = ( 10² ) / ( 2 x 5 )
s = 10 m
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Is a chemical formula and chemical equation the same?
Answer: No
Explanation:
A chemical for formula is combined of atomic that is has a chemical compounds
To directly lift a crate 0. 6 meters, joaquin would need to apply 312 newtons of force. Instead, he uses a lever with a mechanical advantage of 3 to lift the crate. How much force does he save by using the lever?.
Joaquin reduces his force by using the lever by applying 208 N of force.
By using a lever with a mechanical advantage of 3,
Joaquin needs to apply only 1/3 of
The force he would need to lift the crate directly.
This means he needs to apply only 312 N / 3 = 104 N.
Therefore, Joaquin saves
312 N - 104 N = 208 N of force by using the lever.
The force amplified by utilising a tool, mechanical device, or machine system is known as mechanical advantage. To achieve the necessary output force amplification, the gadget trades off input forces against movement. The law of the lever serves as a paradigm for this.
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compasses line up with magnetic fields. a compass will line up to_____
A compass will line up to b) Parallel to magnetic field lines, with the north pole pointing in the direction of the field.
The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is traveling through a magnetic field.
The magnetic field of a permanent magnet pulls on ferromagnetic substances like iron and attracts or repels other magnets. Paramagnetism, diamagnetism, and antiferromagnetism are three additional magnetic effects that a nonuniform magnetic field can have on "nonmagnetic" materials, albeit these forces are often so minute that they can only be detected by laboratory equipment.
Therefore, A compass will line up to b) Parallel to magnetic field lines, with the north pole pointing in the direction of the field.
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a cyclist rides a bicycle 4.0 km west, then 3.0 km north. what is the cyclists displacement?
The cyclists displacement when he rides a bicycle 4.0 km west, then 3.0 km north is 5km towards north-west.
Given the distance he travels towards west (d1) = 4km
The distance he travels towards north (d2) = 3km
An object's position changes if it moves with respect to a reference frame. Displacement describes this shift in location. The word "displacement" denotes the movement or displacement of an object. The displacement is the shortest distance covered in a certain direction. If we assume the distances he travelled as two sides of triangle then we the displacement which is the hypotenuse side.
So, displacement = √4^2+3^2 = 5km
The direction the cyclist travels is north-west and covers 5km.
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A 62. 1 kg runner has a speed of 4. 70 m/s at one instant during a long-distance event. What is the kinetic energy (in j) of the runner?.
The kinetic energy of the runner is: 685.89 Joules
What is kinetic energy?
It is the energy possessed by a body due to its relative motion. It is usually expressed in Joules (J).
The kinetic energy formula and the procedure we will use is:
K.E. = 1/2 * m * v²
Where:
v = speedm = massJoules = Kg m²*s²Information of the problem:
v = 4.70 m/sm = 62.1 kgK.E=?Applying kinetic energy formula we get:
K.E. = 1/2 * 62.1 kg * (4.70 m/s)²
K.E. = 1/2 * 62.1 kg * 22.09 m²/s²
K.E. = 685.89 kg*m²/s²
K.E. = 685.89 Joules
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calculate the amount of energy needed to raise the temperature at 3.0kg of steel of 30°C-120°C. The specific latent heat of steel is 490JKg^-1K^-1.
The energy needed to raise the temperature of 1 kg of lead from 40 °C to 60°C will be 2600 Joules.
Calculate the amount of energy ?We can calculate the energy of a substance by using the given formula:
Q = mc∆T
where;
Q = quantity of heat absorbed or released
m = mass of the substance
c = specific heat capacity
∆T = change in temperature(°C)
Now, according to the given question, 1 kg of lead has to be raised from 40°C to 60°C and we also have the specific heat capacity(c) of lead that is 130J/kg°C.
We can calculate the energy by putting the given values in the above equation:
Q = mc∆T
= 1 × 130 × (60-40)
= 20 × 130
Q = 2600J
Therefore, the amount of energy required to raise the temperature of 1 kg of lead from 40°C to 60°C is 2600J.
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The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam
The gauge pressure in the water at the foot of the dam is 1.09 * 10^6 Pa.
Pressure is a measure of the force exerted per unit area on the boundaries of a substance. The standard unit for pressure in the SI system is the Newton per square meter or pascal (Pa)The pressure of a fluid of density ρ, at a depth h is:
p = ρ.g.h
Where g is the acceleration due to gravity.
h is height = 111 m,
the fluid is water so its density is ρ = 1000 kg/m³ and
we can use for the gravity g = 9.8 m/s².
The pressure at the foot of the dam is: p = 1000 * 111 * 9.8 = 1.09* 10^6 Pa
When pressure is measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The term gauge pressure is applied when the pressure is greater than the atmospheric pressure, patm.To know more about pressure visit:
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what is the linear charge density of a thin wire bent into a circle (or ring) of radius 6.59 cm if the total charge on the wire is 3.20 µc? give your answer in µc/m.
The required value of linear charge density of a thin wire bent into a circle is 0.00077 μc/m.
The wire is curved into a circular form.
The radius of the circle is given as R = 6.59 cm = 6.59 × 10⁻² m
The total charge on the wire Q = 3.2 µc = 3.2 × 10⁻⁶ c
The relation between total charge, radius and linear charge density is known as,
Q = 2 π R α
where, Q is the total charge
R is the radius of the wire bent into a circle
α is linear charge density
Making α as subject, we have,
α = Q /(2 π R) = (3.2 × 10⁻⁶)/(2 π ×6.59 × 10⁻²) = (3.2 × 10⁻⁶)/(41.41 × 10⁻²) = 0.077 × 10⁻⁴ c/m = 0.00077 μc/m
Thus, the value of linear charge density of a thin wire is calculated to be 0.00077 μc/m
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you are driving with a speed of 85 mile/hour in interstate 10 from phoenix toward los angeles, when you see a large piece of debris 128m ahead on the highway. you push the brake pedal as hard as you can to try to avoid the collision. if the brake provides an acceleration of -8.50 m/s2, how far will the car go before stopping? can you avoid hitting the debris? a ball is thrown vertically downward with an initial speed of 15.8 m/s from a building whose height is 122 m. how long does it take for the ball to strike the ground? k.t. tsen
The debris is 128 m ahead, the car will hit the debris
4.36 s it take for the ball to strike the ground.
To find the distance the car will travel before stopping, we can use the formula for distance under constant acceleration:
d = v0 * t + (1/2) * a * t^2
where v0 is the initial velocity (85 miles/hour = 38.05 m/s), a is the acceleration (-8.5 m/s^2), and t is the time it takes to stop.
We can rearrange this equation to solve for t:
t = (-v0 ± √(v0^2 + 2ad)) / a
where the negative sign is used since the acceleration is negative (meaning the car is slowing down).
Plugging in the values, we get:
t = (-38.05 ± √(38.05^2 + 2(-8.5)(128))) / -8.5
t = (4.17 s)
Next, we can use this time to calculate the distance the car will travel:
d = v0 * t + (1/2) * a * t^2
d = 38.05 * 4.17 + (1/2) * -8.5 * 4.17^2
d = 159.47 m
Since the debris is 128 m ahead, the car will hit the debris.
To find the time it takes for the ball to strike the ground, we can use the formula for vertical motion under constant acceleration:
h = v0 * t + (1/2) * a * t^2
where h is the height of the building (122 m), v0 is the initial velocity (15.8 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time it takes to fall.
We can rearrange this equation to solve for t:
t = √(2h / a) = √(2 * 122 / -9.8) = 4.36 s.
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if a composite object is electrically neutral, that means it _______.
If a composite object is electrically neutral, that means it has an equal number of positive and negative charges.
Electricity is a form of energy that results from the movement of charged particles, such as electrons. It is the flow of electric charge through materials that conduct electricity, such as metals. Electricity has several key properties, including voltage, which is a measure of the energy per unit charge, and current, which is the flow of charge through a material. Electricity can be generated through a variety of methods, including chemical reactions, thermal processes, and electromagnetic induction. It is used to power a wide range of devices and systems, from light bulbs and computers to power plants and electric vehicles. Electricity has revolutionized the world, making it possible to transmit energy over long distances, power machines, and communicate instantly with people anywhere on the planet.
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two billiard balls collide. identify the type of collision
The type of collision is elastic collision.
An elastic collision is a type of collision in which the total kinetic energy of the colliding objects remains constant. In an elastic collision, the objects bounce back after impact without any permanent deformation, and their kinetic energy is unchanged.
Here are some key features of elastic collisions:
Conservation of kinetic energy: In an elastic collision, the total kinetic energy of the colliding objects remains constant. The sum of the initial kinetic energies of the objects is equal to the sum of the final kinetic energies after the collision.Perfectly elastic objects: For a collision to be considered elastic, the colliding objects must be perfectly elastic, meaning they do not undergo any permanent deformation during the collision.Bounce-back motion: In an elastic collision, the objects bounce back after impact. The direction of motion of the objects after the collision is different from the direction of motion before the collision.No friction: There is no friction between the colliding objects in an elastic collision, meaning that all the energy is conserved as kinetic energy.Therefore, The type of collision is elastic collision.
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calculate approximately the total translational kinetic energy of all the molecules in an e. coli bacterium of mass 2.0×10−15kg at 37 ∘c . assume 70% of the cell, by weight, is water, and the other molecules have an average molecular mass on the order of 105u .
Total translational kinetic energy = 4.7 x 10-19 J
Total mass = 2.0 x 10-15 kg
Amount of water = 0.7 x 2.0 x 10-15 kg = 1.4 x 10-15 kg
Amount of other molecules = 0.3 x 2.0 x 10-15 kg = 6.0 x 10-17 kg
Average molecular mass of other molecules = 105 u
Number of other molecules = 6.0 x 10-17 kg / (105 u/6.022 x 1023) = 1.3 x 10-20 mol
Average translational kinetic energy of an e. coli bacterium = (3/2) kT
= (3/2) x 8.31 J/molK x 310 K
= 362.68 J/mol
Total translational kinetic energy = 1.3 x 10-20 mol x 362.68 J/mol
= 4.7 x 10-19 J
What is kinetic energy?
Kinetic energy is the energy of a moving object, which is equal to the work done to accelerate the object from rest to its current velocity. It is directly proportional to the mass of the object and to the square of its velocity.
Therefore, Total translational kinetic energy = 4.7 x 10-19 J
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calculate the spring constant and its uncertainty
k = - F/x = - (2 0.05 N) / (25 0.05 cm) = - (2 0.05 N) / (0.25 0.0005 m) = - 8.0 N/m 2.7 is the value of the spring constant. The spring's stiffness is indicated by the spring constant, k.
If the data are not independent, there are statistical techniques for calculating the standard deviation uncertainty.
But in general, this is far more challenging. There are academic articles and books on it.
But at this point in my life, my skills in this area have deteriorated, and I am beyond help.
And unless you are enrolled in a course on the subject of error propagation and sensitivity, I guess it is also beyond what you wish to do.
See:
2) Sensitivity and Doubt
The spring constant is therefore best calculated as follows: k = - F/x = - (2 0.05 N) / (25 0.05 cm) = - (2 0.05 N) / (0.25 0.0005 m) = - 8.0 N/m 2.7%
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an object starts from 30 m/s velocity and reaches 126 km/h in a 1 km distance. assuming a constant acceleration, what was the elapsed time?
The time elapsed is 30.77 seconds in changing the velocity from 30 m/s to 126 km/h.
Initial velocity, u = 30 m/s
Final velocity, v = 126 km/h = 126 × (5/18) = 35 m/s
Distance travelled, S = 1 km = 1000 m
Let the acceleration, a
By the third equation of motion, v² = u² + 2as
35² = 30² + 2 × a ×1000
a = (35² - 30²)/2000
a = 0.1625 m/s²
Now let the time elapsed is t. Then by the first equation of motion.
v = u + at
t = (v - u)/a
t = (35 - 30)/0.1625
t = 30.77 seconds
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considering typical molecules at room temperature, for which degrees of freedom (types of motion) will the equipartition theorem accurately predict contributions to the internal energy?
As an instance, the average kinetic per level of freedom in a molecule's translational motion should be equal to that in its rotational motion. which states that energy is equally distributed among all of its different forms when a system is in thermal equilibrium.
What is the equipartition theorem's conclusion?According to the equipartition theorem, each degree of freedom that is reachable3 contains approximately the same amount of energy, which is equal to k B T / 2. The answer to Eq. is obtained by summing the average kinetic energy in the three directions.
We take into account both the energy and the energy stored when considering vibrations in a harmonic oscillation potential (V, above), meaning that the potential energy serves as an extra degree of freedom. Another thing to note about vibration is that they are highly quantized in molecules and that most of them are in their floor vibrational levels at room temperature, with higher levels being inaccessible thermally. Because of this, equipartition contributions of vibrational freedom levels often only need to be taken into account at very low.
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differentiate the function. f(u) = e4/u
Answer:
-( 4 *e^4 /u )/u^2
Explanation:
d/du(e^4/u)= -( 4 *e^4 /u )/u^2
After differentiating the function we get,
[tex]\large f'(u)=\frac{-4}{u^2}*e^\frac{4}{u}[/tex].
What is differentiation?
Apart from integration, differentiation is one of the two key ideas of calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.
The rate of change of x with respect to y is given by dy/dx if x and y are two variables. The universal representation of a function's derivative is given by the equation f'(x) = dy/dx, where y = f(x) is any function.
[tex]f(u)=e^\frac{4}{u}[/tex]
[tex]\large f'(u)=e^\frac{4}{u}*\frac{d(4/u)}{du}[/tex]
[tex]\large f'(u)=\frac{-4}{u^2}*e^\frac{4}{u}[/tex]
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