A certain type of lens changes the direction of light rays from A to B. What property does
this illustrate?

The linear distance from the center of the pattern to the n = 4 dark fringe is 0.7142m

Dark fringes are formed by destructive interference where the waves are out of the phase. Bright fringes are formed by constructive interference where waves are in phase.

d= 1.5 x 10^-6m

D = 510 x 10^-3

n=4

lamda = 545 x 10^-9m

Distance= 4 xD x λ/d

Distance= 4 x545 x 10^-9/1.5 x 10^-6

Distance= 0.7142mm

The distance between 2 adjacent dark or bright color fringes is mainly denoted as “fringe width”, calculated as the formula: “β = λD/d”. If the “resultant amplitude” is zero then the interference is determined as “destructive”.

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a)The radius is 2.6 cm and b) The mass is measured to 4.76 g/cm³ and c)0.00476 kg/m³  is the density kg/m³ in kg/m³.

The quantity of matter per unit volume is referred to as densities (volumetric mass density or specific mass). Density is most frequently represented by the lowercase Greek letter rho, but the Latin letter D is also acceptable. Density is calculated mathematically by dividing mass by volume.

a. The formula: gives the surface area of a spherical.

A = 4 * pi * r²

where A is the surface area, pi is approximately 3.14, and r is the radius of the sphere.

Given the surface area A = 85 cm², we can write the equation for the radius as:

85 = 4 * pi * r²

Solving for r, we get:

r = sqrt(85 / (4 * pi)) = sqrt(85 / 12.56) = sqrt(6.77) = 2.6 cm (approx)

b. The density of an object is given by the formula:

density = mass / volume

The following formula determines a sphere's volume:

V = (4/3) * pi * r³

where V is the volume and r is the radius of the sphere.

Given the mass of the ball M = 160 g, we can calculate the density as:

density = mass / volume = 160 g / [(4/3) * pi * (2.6 cm)^3] = 160 g / (33.51 cm^3) = 4.76 g/cm³

c. To convert the density from g/cm³ to kg/m³, we need to divide the value by 10³.

density = 4.76 g/cm³ / (10³) = 0.00476 kg/m³

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Point charges +4.3 µC and -2.2 µC are placed on the x-axis at (10 m, 0) and (-10 m, 0) . Point to the left of the negative charge where the electric potential vanishes is at x = 6.77 m

Charge [tex]Q_{1[/tex] (4.3μC) is places at x=10 m and charge [tex]Q_{2}[/tex] (-2.2μC) is placed at x=-10 m . Let at point A the electric potential vanishes and it is at a distance a to left from charge [tex]Q_{2}[/tex] Formula for potential due to point charge at a distance r from it is  [tex]\frac{KQ}{r}[/tex].

As potential at point A is 0 . So net potential due to all the charges will be 0

Distance of point A from point B is 20+a

Potential at A  is

[tex]-\frac{KQ_{2} }{a}[/tex] + [tex]\frac{KQ_{1} }{20+a}[/tex]  =0  

[tex]\frac{Q_{2}}{a}= \frac{Q_{1}}{20+a}[/tex]  

[tex]20Q_{2}+aQ_{2}=aQ_{1} \\\\a(Q_{1}-Q_{2})=20Q_{2}\\\\a=\frac{20Q_{2}}{Q_{1}-Q_{2}}[/tex]

Putting values of  [tex]Q_{1}[/tex] and [tex]Q_{2}[/tex] we get

[tex]\frac{20*(2.2)}{4.3+2.2}\\ \\=\frac{44}{6.5} \\\\= 6.77[/tex]m  

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The coefficient of static friction on a horizontal surface is found to be 0.83.

The ratio between the perpendicular force pushing the objects together and the resistive frictional force is known as the coefficient of friction. The formula for the friction coefficient is = F N. Depending on the items creating friction, the coefficient of friction changes. The value might be larger than 1 but is often between 0 and 1.

Force (f)= 65N ;  Mass (m) = 8Kg ; Acceleration due to gravity (g) =  9.8 m/s²  

μ = Coefficient of static friction.

Static friction force, f = μmg

μ = f/mg ;

  => 65/(8 x 9.8) = 0.83

The nature and roughness of the surfaces in contact affect the coefficient of static frictional force. It does not depend on the size or surface area of the surfaces. The value might be larger than 1 but is often between 0 and 1.

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To maintain an electric potential difference and maintain a voltage, a sustained electric current needs a proper pumping mechanism.

There must be some form of pushing force in order to keep an even (or sustained) passage of electric charge across a conductor. The term "emf" for this is electromotive force. Voltage affects current, in other words. Current can be made to flow through a conductor by using a potential difference or voltage. In order for charge to go across a circuit, there needs to be a closed conducting loop and an energy source that can provide an electric potential difference. A supply of freely flowing electric charges (electrons), some sort of push to move the charges across the circuit, and a path to carry the charges are necessary for the production of an electric current.

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Answer:

Explanation:

To construct a graph of force due to gravity vs. distance, we need to collect data for force due to gravity (Fg) and distance (d) and plot the data points on a graph. From the information given, we have the mass of the object (1.23 kg) and the angle of the incline (35º), but we do not have any data for force due to gravity or distance. Without this data, it is not possible to construct a graph for force due to gravity vs. distance.

Since we don't have the data for force due to gravity or distance, it's not possible to calculate the work done by gravity using the data table.

Without the data for force due to gravity, distance, or time it's not possible to construct a free-body diagram or calculate work done by gravity. Also, we don't have the angle of the incline, so we cannot calculate the work done by gravity by multiplying it by the cosine of the angle.

It's important to note that work done by gravity (W) = force due to gravity (Fg) x distance (d) x cos(theta), where theta is the angle between the force of gravity and the distance.

It's also important to remember that work is a scalar quantity and not a vector, and it's the angle between the force and the displacement that is important to calculate the work done by gravity, not the angle of the incline.

Answer:

4.09 m/s

Explanation:

1/2 * k * x^2 = 1/2 * 241 N/m * (0.024 m)^2

= 1.56 Nm

KE = 1/2 * m * v^2

v^2 = 2 * KE/m

v = √(2*1.56 Nm / 0.24 kg)

v = 4.09 m/s

The gravitational force exerted on uranus by neptune can be deduced with newtons law of gravitation. The value is, 2.240×10^17 Newton.

According to newtons law of gravitation, "any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them." Now we know that gravitational force F= G (m1m2 ÷ r²). Here m1 and m2 are  the masses of uranus and neptune. r is the diostance between them. G is gravitational constant. So we know its value. it is 6.673 x 10^-11 N m²/kg². We also know the values of m1 and m2. Mass of neptune is 102.42×10^24 kg. And the mass of uranus is 86.81×10^24 kg. Now after knowing the distance between them, we get r= 1.627×10^12 meters. We have to put all the values in the formula. After doing thyat we get 2.240×10^17 N of force.

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Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2.

The components of a vector, which is symbolized by an arrow, are a magnitude (the size of a measurement) and a direction (the direction the arrow is pointing), for example, 2 meters south. A solitary vector is a vector that exists by itself. A resultant vector is produced by adding two or more single vectors.

A combined force that is smaller than either individual force is created when two forces engage in opposition to one another. Subtract the magnitude of the smaller force from the magnitude of the bigger force to determine the resultant force. The smaller force and the resultant force both have the same direction.

|A| stands for the magnitude of a vector A, which represents its length. It is the sum of the squares of the vector's component parts' square roots.

A two-dimensional vector's magnitude can be calculated from its coordinates by:

How to Find Magnitude of a Vector?

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According to the question of circuit, the value of resistor R will be 10 Ω.

What is circuit?
Circuit is an electrical network consisting of connected components that allow electrical signals or power to pass through it. The components are usually connected by conductors such as wires, cables, or printed circuit boards. Circuits can be simple and consist of only a few components, or extremely complex containing thousands of components. Circuits can be used to control machines, computers, household appliances, and more. They are used in almost every area of electronics and electrical engineering, from the communication signals in a cellphone to the power distribution in a skyscraper.

R is calculated by Ohm's law, which states that the voltage (V) across a resistor is equal to the current (I) multiplied by the resistance (R). Therefore, R = V/I = 6V/0.86A = 10 Ω.

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In astronomy, a dynamically hot population refers to a group of stars or other celestial objects that have high velocities and a wide range of orbits.

They are characterized by high kinetic energy and low potential energy, and are typically found in the halo of a galaxy or in the outskirts of galaxy clusters.

On the other hand, a dynamically cold population refers to a group of stars or celestial objects that have low velocities and a narrow range of orbits. They are characterized by low kinetic energy and high potential energy, and are typically found in the disk of a galaxy or in the central regions of galaxy clusters.

In summary, a dynamically hot population is one that is characterized by high velocities, wide range of orbits, high kinetic energy and low potential energy, while a dynamically cold population is one that is characterized by low velocities, narrow range of orbits, low kinetic energy and high potential energy.

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7.1 m/s. allows us to determine the angular velocity of the rod after it has been struck by the bullet. Calculated value: = 29.1 s-1.

The angular velocity (w), a vector quantity in uniform circular motion, is determined by dividing the angular displacement (), also a vector quantity, by the change in time (t).

If the ball is rolling without slipping, the rotational acceleration and the provided acceleration will be perpendicular at point B, and the no slip condition will be satisfied at point O by applying mr=I. nevertheless I=mr 2

α= \sr \sω

​Angle acceleration is equal to r.

If a ball rolls without slipping, the acceleration caused by rotation and the supplied acceleration will be perpendicular at point B, making the total acceleration at point A equal to a 2 + (r) 2.​

s = \s2 \s​ \s ω

Point A's velocity is 2

t=2 /2.5*2

= 7.1 m/s.

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Inductance is a measure of a component or circuit's ability to store electrical energy in the form of a magnetic field when an electric current is flowing through it.

What is  Inductance?

Inductance is a property of a circuit or electronic component that opposes changes in current, producing a voltage in the circuit proportional to the rate at which the current is changing. This voltage is known as an inductive reactance, and is related to the frequency of the current. Inductance is a fundamental property of materials, and is the basis of many electrical components, including transformers, chokes, and inductors. Inductance is also responsible for the generation of electromagnetic fields, which are used in many applications, such as motors and generators.

The equation for the period of an LC oscillator is:

T = 2π √(L x C)

Thus,

2.4 = 2π √(L x 18 x 10^-3)

L = 6.8 x 10^-3 H = 6.8 mH

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The angle in degrees. It is the middle angle of the arc or the angle that separates the two arc radii. 180 r, where r is the radius and L is the length of an arc.

We may get the length of an arc using the following formula given an angle and a circle's diameter:

ArcLength = (angle / 360) * (2 * pi * radius)

where diameter equals 2 * radius, angle is in degrees, and

pi = 22/7.

The arc length formula for a circle is times the radius of a circle. When r is in radians, the formula for arc length can be written as arc

length = r.

Arc Length

= (/180) r,

where r is the radius and L is the length of an arc.

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The electric potential is zero when there is no difference in electric potential energy between two points. Therefore, the value of xx between 0 and 1.00 mm where the electric potential is zero is 0.500 mm.

The electric potential at a given point is the amount of electric potential energy per unit charge at that point in space. This can be found by measuring the electric potential difference between two points, one of which is the point at which we are interested in finding the electric potential. In this case, the electric potential at any point between 0 and 1.00 mm is zero since there is no difference in electric potential energy between the two points. Therefore, the value of xx where the electric potential is zero is 0.500 mm.

The electric potential is zero when there is no difference in electric potential energy between two points. Therefore, the value of xx between 0 and 1.00 mm where the electric potential is zero is 0.500 mm.

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If you walk 5 meters north, 2 meters west, 4 meters south, and 7 meters east....then the displacement is      [tex]\sqrt{26}[/tex].

A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.

Solution:

As per the given statement when  you walk 5 meters north, 2 meters west, 4 meters south, and 7 meters east... then you will be resulting in forming a right angled triangle from origin to ending point.

That right angled triangle will have

base=5m

perpendicular=1cm

hypotenuse=?

to find hypotenuse we use Pythagoras theorem:

[tex]h^{2}[/tex]=[tex]b^{2}+ p^{2}[/tex]

On putting values we get

[tex]h^{2}[/tex]=[tex]b^{2}+ p^{2}[/tex]

h=[tex]\sqrt{25+1}[/tex]

h=[tex]\sqrt{26}[/tex]

Hence, the displacement is      [tex]\sqrt{26}[/tex].

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Answer:

horizontal distance it traveled is 45 m

the height of the building is 15 m

Explanation:

X = Vo cos 53.1 . t = 25 x 0.6 x 3

X = 45 m

Y = Vo sin 53.1  t - 1/2 g t²

Y = 25 x 0.8 x 3 - 1/2 x 10 x 9

Y = 60 - 45

Y = 15 m

The nuclei are observed to decay by emitting a β− particle releases a positively charged beta particle called a positron, and a neutrino.

The mechanism of contact between subatomic particles that causes the radioactive disintegration of atoms is known as the weak interaction, also known as the weak force or weak nuclear force, in nuclear physics and particle physics.

The three most frequent types of decay are beta decay, gamma decay, and alpha decay, all of which entail the emission of one or more particles. While the nuclear force and electromagnetism are in charge of the other two, the weak force is the process that causes beta decay.

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The unit vector to express a displacement of 120 km at 29° counterclockwise from x- axis is 104.9544kmi + 58.17715kmjl

A = Aχ × i + Aу × j

= 120km × cos (29) × i + 120km × sin (29) × j

let i, j be the unit ve cot s along x and y axis

Vector A = 104.9544kmi + 58.17715kmjl

The displacement vector d from P1 to P2 can be written as d = (x2 - x1)i + (y2 - y1)j. The displacement d is (x2-x1) units in the x direction and (y2-y1) units in the y direction.

These unit vectors are commonly used to indicate direction, and scalar coefficients indicate magnitude. A vector decomposition can be written as a sum of unit vectors and scalar coefficients.

A unit vector is a vector whose magnitude is exactly one unit. They are very useful for many reasons. In particular, the unit vectors [0,1] and [1,0] can be taken together to form other vectors.

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Moles in gas refer to the number of molecules of a given gas present in a sample of the gas.

What does Moles in gas mean?

Moles in gas refer to the number of molecules of a given gas present in a sample of the gas. This is typically expressed as a ratio of the number of moles of the particular gas compared to the total number of moles of all gases present in the sample. For example, if a sample of air contains 20 moles of oxygen, 10 moles of nitrogen, and 10 moles of carbon dioxide, the mole fraction of oxygen in the sample would be 0.5, meaning that for every mole of gas present in the sample, half of it is oxygen.

The total work W for the cycle:

W = (Cp)(Tc-Ta) + (Cp)(Tb-Tc) +(Cv)(Tb-Ta)

W = (29.1 J/mol K)(492K-300K) + (29.1 J/mol K)(600K-492K) + (20.8 J/mol

K)(600K-300K)

W = 84460 J

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A. 40 cm

We can use Coulomb's law to calculate the distance between the two Cheetos:

F = k * (q1 * q2) / r^2

where F is the force acting on the first Cheeto, q1 and q2 are the charges on each Cheeto, k is the Coulomb constant and r is the distance between the two Cheetos.

Given that the force acting on the first Cheeto is 5.73 E−1 N, the charge on the first Cheeto is 1.2 E−5 C, the charge on the second Cheeto is 2.5 E−6 C and the Coulomb constant is 8.99 E9 N*m2/C2.

We can rearrange the equation to solve for the distance r:

r = (k * q1 * q2 / F)^(1/2)

r = (8.99 E9 N*m2/C2 * 1.2 E−5 C * 2.5 E−6 C / 5.73 E−1 N)^(1/2)

r = 0.04 m

So the distance between the two Cheetos is 40 cm.

255.102 m is minimum radius of the circle be in order for the acceleration at this point not to exceed 4.00g

What is acceleration ?

Acceleration is defined as the rate of change of velocity over time for both velocity and direction. A point or object which is moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated as it always changes direction even at constant velocity. For all other exercise types both effects contribute to acceleration.

It is a vector quantity because it has magnitude and direction and velocity is also a vector quantity.

We are given that

Mass =m=56 kg

a. Speed , v=100 m/s

We have to find the minimum radius of the circle for the acceleration at this point not to exceed 4 g.

We know that ,

Radial acceleration, a= V^{2} /R

Therefore , R= 100 * 100/4g

Using the formula

We know that g=9.8 m /s^{2},

we get , R = 255.102 m

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Consider the first-order decomposition of A molecules (red spheres) in three vessels of equal volume - A) 2:4:3 , B) 1:1:1 , C) increase by a factor of 2, D) remain the same.

What is first-order decomposition ?

When the reaction's pace is proportional to the concentration of the reactant, it is referred to as a first-order reaction. On the other hand, as the concentration rises, the reaction rate doubles. One or two reactants are used in the decomposition process, an illustration of a first-order reaction.

What is molecules ?

A molecule is a collection of at least two chemically bound atoms from the same or distinct elements. One molecule of water, for instance, is created when two hydrogen atoms and one oxygen atom combine.

Therefore, the first-order decomposition of A molecules (red spheres) in three vessels of equal volume - A) 2:4:3 , B) 1:1:1 , C) increase by a factor of 2, D) remain the same.

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Answer:

After the inelastic collision, the velocity of the 8 kg mass would be the same as the center of mass velocity. Which is the velocity of the combined system of both masses. To find the velocity of the center of mass, we can use the following formula:

vcm = (m1v1 + m2v2) / (m1+m2)

where m1 = 8kg, v1 = 9.6 m/s east, m2 = 6kg, v2 = 14.8 m/s west

vcm = (89.6 + 6(-14.8)) / (8 + 6) = -0.8 m/s (west)

Therefore, after the inelastic collision, the velocity of the 8 kg mass would be -0.8 m/s (west)

Part A Rank in order, from largest to smallest, their wave speeds va, Ub, and U is Va = Vb = Vc.

What is wave ?

An energy-conducting disturbance in a medium known as a wave is one that does not involve any net particle motion. It could manifest as elasto-deformation, a shift in pressure, electric or magnetic intensity, electric potential, or temperature.

What is speed ?

A shift in an object's location, either in direction or speed. How fast something is travelling is determined by how far it has travelled in relation to how long it took. Speed is considered a scalar quantity because it only has a direction and no magnitude.

Wave velocity depends on the tension in the string and mass per unit length of the string.

As these two variables will remain same for all the 3 strings so they will have equal velocities.

Va = Vb = Vc

Therefore, Part A Rank in order, from largest to smallest, their wave speeds va, Ub, and U is Va = Vb = Vc.

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Saturn's core is too deep for impactors to reach, even for dense gas and metallic hydrogen with volcanic lavas

At its center, Saturn has a dense core of metals such as iron and nickel, surrounded by rocks and other compounds that are solidified by intense pressure and heat. Similar to Jupiter's core, but surrounded by liquid metallic hydrogen with a much smaller layer of liquid hydrogen. Researchers have concluded that the planet's core is 55 times the mass of Earth, while rock and ice are 17 times the mass of Earth. Temperatures up to 21,000 F (11,700 C) can be reached inside. Because Saturn is an average of 886 million miles (1.4 billion kilometers) from the Sun, most of Saturn's heat comes from its core.

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7.58 ohms , 22.39 A and 3800 W are the correct answers .

What is resistance ?

Resistance is measured in ohms and represented by the Greek letter omega (Ω). Ohm is named after German physicist Georg Simon Ohm (1784-1854), who studied the relationship between voltage, current and resistance. He has been credited with formulating Ohm's law.

All substances resist the flow of electricity to some degree. They fall into one of two broad categories:

conductor: A material that offers very little resistance through which electrons can easily move. example:

silver, copper, gold, aluminium.

Insulator:

A substance that has a high resistance and restricts the flow of electrons. example:

Rubber, paper, glass, wood, plastic.

a) R= V^2/P = 120*120/1900 = 7.58 ohms

b) P= IV

I=1900/120 = 15.83A

I peak = sqrt2*15.83= 22.39 A

c) average power= 2*average power = 2*1900= 3800 W

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Nuclei of the same element can have different values of A and Nuclei of the same element can have different values of N and Nuclei of the different elements can have the same values of A.

On the basis of the 1909 Geiger-Marsden gold foil experiment, Ernest Rutherford identified the atomic nucleus in 1911, which is the compact, dense region made up of protons and neutrons at the heart of an atom.

There are 118 species of atoms listed in the periodic table of elements, and each of these can be found (either naturally or artificially) in several iterations with various neutron counts, leading to a total of around 3,000 distinct atomic nuclei.

Both nuclei are held together by the electron, which "orbits" them. We have a molecular ion because the total charge is undoubtedly non-zero. According to Wikipedia, this system is referred to as the dihydrogen cation and goes by the symbol H+2.

the solution is

The proton ratio (Z) for a particular element is fixed. The mass number can vary depending on the number of neutrons (N) in the same element and other elements (A).

Atoms having the same Z and different N (and hence different A) are called isotopes. They are usually forms of the same element.

Sometimes atoms of different element can have the same mass number (A) but different atomic number (Z) and neutron number (N) that makes up the same mass number (A). They are called isobars

Also,atoms of different element can have the same neutron number (N) but different atomic (Z) and mass number (A). they are called isotones

therefore

A) Option 3 and 4

B) Option 3 and 4

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According to the given statement So, the volume occupied by 55.85 g of iron is 7.12 cm³.

The quantity of matter per unit volume is referred to as dense (volumetric mass density or specific mass). Density is most frequently represented by the lowercase Greek letter rho, but the Latin letter D is also acceptable.

The density of matter varies with temperature and pressure. This variation is typically small for solids and liquids and much larger for gases. Increasing the pressure on an object decreases the volume of the object, thus increasing its density. Increasing the temperature of a substance.

The following formula determines an object's density:

density = mass / volume

Given that the density of iron is 7.86 g/cm³ and the mass of the iron is 55.85 g, we can calculate the volume occupied by the iron as:

volume = mass / density = 55.85 g / 7.86 g/cm³ = 7.12 cm³

So, the volume occupied by 55.85 g of iron is 7.12 cm³.

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molar heat capacity=2R is the correct answer .

What is molar heat capacity ?

Molar heat capacity is expressed in units of J/K/mol or J/mol·K. where J is Joules, K is Kelvin, and m is moles. This value assumes no phase change occurs. We usually start with molar mass values ​​in kg/mol. A less common unit of heat is the kilogram calorie (cal) or its cgs variant the gram calorie (cal). You can also express heat capacity in pound-mass at temperatures in Rankine or degrees Fahrenheit. Molar heat capacity reflects heat capacity per mole, while the related term specific heat capacity is heat capacity per unit mass. Specific heat capacity is also called simply specific heat. Engineering calculations sometimes use volumetric heat capacity rather than mass-based specific heat.

Since this is a  2-D lattice, an atom can only oscillate in 2 independent directions. So the degree of freedom=2. So system cn be considered as 2*N harmonic oscillators. Where N-number of Carbon atoms

Also, each harmonic oscillator has a energy of kBT;  where kB-boltzmann constant and T-temperature

So, Total internal energy(E)= 2N*kBT

But, N*kB=n*R ; where n-moles

E=2nRT;

molar heat capacity(constant volume)= (dE/dT)/n ;

molar heat capacity=2R

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