The volume of a gas decreases from 15.7 mºto 11.2 m3 while the pressure changes from 1.12 atm to 1.67 atm. If the
initial temperature is 245 K, what is the final temperature of the gas?
O 117 K
230 K
261K
.
O 512K

Answers

Answer 1

Answer:

Approximately [tex]261\; \rm K[/tex], if this gas is an ideal gas, and that the quantity of this gas stayed constant during these changes.

Explanation:

Let [tex]P_1[/tex] and [tex]P_2[/tex] denote the pressure of this gas before and after the changes.

Let [tex]V_1[/tex] and [tex]V_2[/tex] denote the volume of this gas before and after the changes.

Let [tex]T_1[/tex] and [tex]T_2[/tex] denote the temperature (in degrees Kelvins) of this gas before and after the changes.

Let [tex]n_1[/tex] and [tex]n_2[/tex] denote the quantity (number of moles of gas particles) in this gas before and after the changes.

Assume that this gas is an ideal gas. By the ideal gas law, the ratios [tex]\displaystyle \frac{P_1 \cdot V_1}{n_1 \cdot T_1}[/tex] and [tex]\displaystyle \frac{P_2 \cdot V_2}{n_2 \cdot T_2}[/tex] should both be equal to the ideal gas constant, [tex]R[/tex].

In other words:

[tex]R = \displaystyle \frac{P_1 \cdot V_1}{n_1 \cdot T_1}[/tex].

[tex]R =\displaystyle \frac{P_2 \cdot V_2}{n_2 \cdot T_2}[/tex].

Combine the two equations (equate the right-hand side) to obtain:

[tex]\displaystyle \frac{P_1 \cdot V_1}{n_1 \cdot T_1} = \frac{P_2 \cdot V_2}{n_2 \cdot T_2}[/tex].

Rearrange this equation for an expression for [tex]T_2[/tex], the temperature of this gas after the changes:

[tex]\displaystyle T_2 = \frac{P_2}{P_1} \cdot \frac{V_2}{V_1} \cdot \frac{n_1}{n_2} \cdot T_1[/tex].

Assume that the container of this gas was sealed, such that the quantity of this gas stayed the same during these changes. Hence: [tex]n_2 = n_1[/tex], [tex](n_2 / n_1) = 1[/tex].

[tex]\begin{aligned} T_2 &= \frac{P_2}{P_1} \cdot \frac{V_2}{V_1} \cdot \frac{n_1}{n_2}\cdot T_1 \\[0.5em] &= \frac{1.67\; \rm atm}{1.12\; \rm atm} \times \frac{11.2\; \rm m^{3}}{15.7\; \rm m^{3}} \times 1 \times 245\; \rm K \\[0.5em] &\approx 261\; \rm K\end{aligned}[/tex].


Related Questions

Review please help.

Answers

Answer:

1 and 3

Explanation:

because they are going up from 0

A fox runs at a speed of 16 m/s and then stops to eat a rabbit. If this all took 120
seconds, what was his acceleration?

Answers

Answer:

a = 52s²

Explanation:

How to find acceleration

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction.

Solve

We know initial velocity (u = 16), velocity (v = 120) and acceleration (a = ?)

We first need to solve the velocity equation for time (t):

v = u + at

v - u = at

(v - u)/a = t

Plugging in the known values we get,

t = (v - u)/a

t = (16 m/s - 120 m/s) -2/s2

t = -104 m/s / -2 m/s2

t = 52 s

Balance the equation by choosing the correct coefficient numbers in the drop down menus.
[Select]
SO2 +
[Select]
VH₂ →
[Select]
S +
[ Select]
H20
It is suggested you write this on scratch paper and balance it before choosing your answers :)

Answers

Answer:

SO₂ + 2H₂ —> S + 2H₂O

The coefficients are: 1, 2, 1, 2

Explanation:

SO₂ + H₂ —> S + H₂O

The above equation can be balance as follow:

SO₂ + H₂ —> S + H₂O

There are 2 atoms of O on the left side and 1 atom on the right side. It can be balance by writing 2 before H₂O as shown below:

SO₂ + H₂ —> S + 2H₂O

There are 2 atoms of H on the left side and 4 atoms the right side. It can be balance by writing 2 before H₂ as shown below:

SO₂ + 2H₂ —> S + 2H₂O

Now, the equation is balanced.

The coefficients are: 1, 2, 1, 2

A box having a weight of 8 lb is moving around in a circle of radius rA = 2 ft with a speed of (vA)1 = 5 ft/s while connected to the end of a rope. If the rope is pulled inward with a constant speed of vr = 4 ft/s, determine the speed of the box at the instant rB = 1 ft. How much work is done after pulling in the rope from A to B? Neglect friction and the size of the box

Answers

Answer:

W = 1.875 J

Explanation:

For this exercise let's use the relationship between work and kinetic energy

          W = ΔK

The kinetic energy of rotational motion is

         K₀ = ½ I w²

we can assume that the box is small, so it can be treated as a point object, with moment of inertia

          I = m rₐ²

angular and linear velocity are related

          v = w r

          w = v / r

we substitute in the equation, for point A

         K₀ = ½ (m rₐ²) (v / rₐ)²

         K₀ = ½ m v²

For the final point B, as the system is isolated the angular momentum is conserved

initial        L₀ = Io wo

final          L_f = I_f w_f

                L₀ = L_f

                 I₀ w₀ = I_f w_f

               

                (m rₐ²) w₀ = (m  [tex]r_{b} ^2[/tex]) w_f

                 w_f = (rₐ/r_b)² w₀

with this value we find the final kinetic energy

         K_f = ½ I_f w_f²

         K_f = ½ (m [tex]r_{b}^2[/tex]) ( (rₐ / r_b)²  w₀) ²

         K_f = ½ m [tex]\frac{r_a^4}{r_b^2} \ w_o^2[/tex]

 

we substitute in the realcion of work

          W = K_f - K₀

          W = ½ m  [tex]( \( \frac {r_a^2 }{r_b} )^2[/tex] w₀² - ½ m v²

          W = ½ m  [tex]\frac{r_a^4}{r_b^2} ( \frac{v}{r_a} ) ^2[/tex] - ½ m v²

           W = ½ m [tex]\frac{r_a^2}{r_b^2} \ v^2[/tex] - ½ m v2

          W = ½ m v² (([tex]( \ (\frac{r_a}{r_b})^2 -1)[/tex]

let's calculate

           W = ½ ( [tex]\frac{8}{32}[/tex] ) 5 ((2/1)² -1)

           W = 0.625 (3)

           W = 1.875 J

         

if the density of a napthalene ball is 0.02kg.what is the mass of the napthalene ball if it has a volume of 100m³

Answers

Density=mass/volume
Mass=100x0.02=2

The eight plants of the Solar System orbit the Sun in a chaotic random way.

True
False

Answers

Answer:

The Solar System has plants? I assume you meant planets. If so, that is false

Explanation:

In the past, asteroids striking the earth have produced disastrous results. If we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed.

Required:
How would this deflect the asteroid?

Answers

Answer:

Explained below.

Explanation:

We are told that the surface material is ejected into space at a high speed. This means that it will have a likely high momentum as well.

Now, we can say that the total momentum is conserved because the entire asteroid system behaves like an isolated system.

Also, as the surface material is moving with the high momentum like we established earlier, it will cause the asteroid to move with a speed in an opposite direction which also means deflection in an opposite direction.

Answer:

Explained below.

Explanation:

The material ejected from the surface of the asteroid would have a significant momentum. Since the asteroid and all its material is an isolated system, the ejection would cause an oppositely directed change in momentum of the asteroid, according to the law of conservation of momentum.

The ejected material is analogous to gases expelled from a rocket, and the asteroid is analogous to a rocket.

A carnival ride starts at rest and is accelerated from an initial angle of zero to a final angle of 6.3 rad by a rad counterclockwise angular acceleration of 2.0 s2 What is the angular velocity at 6.3 rad?​

Answers

The final angular velocity of the carnival ride at a displacement of 6.3 rad is 25.2 rad/s.

Final angular velocity of the carnival ride

The final angular velocity of the carnival ride is determined by applying third kinematic equation as shown below;

ωf = ωi + 2αθ

where;

ωf  is the final angular velocity of the carnival ride = ?ωi is the initial angular velocity of the carnival ride = 0α is the angular acceleration = 2.0 rad/s²θ is the angular displacement of the carnival ride = 6.3 rad

ωf = 0 + 2(2.0) x 6.3

ωf = 25.2 rad/s

Thus, the final angular velocity of the carnival ride at a displacement of 6.3 rad is 25.2 rad/s.

Learn more about angular velocity here: https://brainly.com/question/6860269

Answer: 5.0 rad/s

Explanation: Because that’s what khan said so try it out.

What kind of energy is in a moving skateboard

Answers

Answer:

I guess it is kinetic energy

Answer:

kinetic energy because my dog told me

A woman shouts at a boy who is underwater what happens to the speed of the sound wave as it moves from the air into the water

Answers

Answer:

B. it increases

Explanation:

As shown in the table provided, the speed of sound in water (1493 m/s) is greater than the speed of sound in air (346 m/s).

Answer:

B is the correct answer.

Explanation:

Which nucleus completes the following equation?

Answers

Answer:

Option D. ²³⁹₉₃Np

Explanation:

From the question given above, the following data were:

²³⁹₉₂U —> ⁰₋₁e + __

Let ⁿₘX represent the unknown. Thus, the equation above becomes

²³⁹₉₂U —> ⁰₋₁e + ⁿₘX

Next, we shall determine n, m and X. This can be obtained as follow:

239 = 0 + n

239 = n

n = 239

92 = –1 + m

Collect like terms

92 + 1 = m

93 = m

m = 93

ⁿₘX => ²³⁹₉₃X => ²³⁹₉₃Np

Thus, the balanced equation becomes:

²³⁹₉₂U —> ⁰₋₁e + ⁿₘX

²³⁹₉₂U —> ⁰₋₁e + ²³⁹₉₃Np

Option D gives the correct answer to the question.

Answer:

D

Explanation:

239 93 Np

A 4.0 kg block is moving at 5.0 m/s along a horizontal frictionless surface toward and ideal spring that is attached to a wall , After the block collides with the spring, the spring is compressed a maximum distance of 0.68m . what is the speed of the block when the spring is compressed to only one-half of the maximum distance?

Answers

A 4.0 kg block is moving at 5.0 m/s along a horizontal frictionless surface toward an ideal spring that is attached to a wall, the maximum speed of the block when the spring is compressed to one-half of the maximum distance is 4.33 m/s

From the conservation of energy; the kinetic energy of the mass is equal to the work done on the spring.

i.e.

[tex]\mathbf{\dfrac{1}{2} mv^2 = \dfrac{1}{2}kx^2_{max}}[/tex]

Given that:

the mass of the block = 4.0 kg the speed at which it is moving = 5.0 m/scompression of the spring = 0.68 m

From the equation above, multiplying both sides with 2, we have:

[tex]\mathbf{mv^2 =kx^2_{max}}[/tex]

Making (k) the subject of the formula;

[tex]\mathbf{k = \dfrac{mv^2}{x^2_{max}}}[/tex]

[tex]\mathbf{k = \dfrac{4 \times 5^2}{0.68^2}}[/tex]

k = 216.26 N/m

However, when compressed to one-half of the maximum distance; the speed is computed as follows:

x = 0.68/2 = 0.34 m

[tex]\mathbf{\dfrac{1}{2}mv_o^2 - \dfrac{1}{2}mv^2 = \dfrac{1}{2}kx^2}[/tex]

[tex]\mathbf{m(v_o^2 -v^2) =kx^2}[/tex]

[tex]\mathbf{(v_o^2 -v^2) =\dfrac{kx^2}{m}}[/tex]

[tex]\mathbf{(5^2 -v^2) =\dfrac{216.26 \times 0.34^2}{4.0}}[/tex]

25 - v² = 6.25

25 -6.25 = v²

v² = 18.75

[tex]\mathbf{ v= \sqrt{18.75 }}[/tex]

v = 4.33 m/s

Therefore, we can conclude that the speed of the block when the spring is compressed to only one-half of the maximum distance is 4.33 m/s

Learn more about speed here:

https://brainly.com/question/22610586?referrer=searchResults

Water can form large dewdrops in nature how would droplets made of isopropyl alcohol instead of water be different

Answers

Answer:

isopropyl alcohol would form smaller droplets, because it has lower surface tension than water has

Explanation:

Ap3x

The droplets made of isopropyl alcohol instead of water be smaller due to surface tension.

What is droplets?

The single drop of a liquid in the form of sphere is called droplet.

Water can form large dewdrops in nature. Isopropyl alcohol would form smaller droplets, because it has lower surface tension than water.

Surface tension is the property of the liquid to acquire minimum surface area.

Thus, droplets made of isopropyl alcohol instead of water be smaller.

Learn more about droplet.

https://brainly.com/question/2926487

#SPJ2

PLEASE HELP!! :)
Which of the following options would increase the electric force the most?

a. tripling the charge on one particle

b. changing the sign of one of the particles.

c. doubling the charge on one particle

d. doubling the charge on both particles

Answers

Im not sure but i guess you should try A

Which of the following best describes our
atmosphere?
A. envelope of gases that surround Earth
B. a specific range of altitude where plant life flourishes
C. The air, water, and land that form our planet
D. the water vapor in the air surrounding our planet

Answers

I am positive the answer is C!
The answer is c the air water and land that form out planet

6) Which of the following describes a good team member?
A) She is willing to compromise.
B) He is aggressive.
C) She is stubborn.
D) He is conceited.

Answers

A she is willing to compromise because she is okay with having to sacrifice what she wants to make it work

Answer: A

Explanation:

Because someone who is aggressive, stubborn, or proud of theirselves are more likely to think they're above everyone else and be a bully. However someone who is willing to compromise is better since you can generally make everyone happy that way

HOPE THIS HELPS ^^

The water pressure to an apartment is increased by the water company. The water enters the apartment through an entrance valve at the front of the apartment. Where will the increase in the static water pressure be greatest when no water is flowing in the system

Answers

Answer:

Option C

Explanation:

Options for the question are as follows -

A. At a faucet close to entrance valve

B. At a faucet away from the entrance valve

C. It will be the same at all faucets

D. There will be no increase in the pressure at the faucets

Solution -

The static force will be the same at all faucets and also the area of the faucets be same.

Thus, the pressure created at all faucets will be the same.

Thus, option C is correct

What is the reason that the moon looks dimmer before eclipse? Why does it take some time to be brighter again after eclipse?​

Answers

Answer:

Why does it take sometimes to be brighter again after eclipse? The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.

Explanation:

Answer: The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.

Explanation:

Fill in the blanks using the following words: Solid, Liquids, Gasses, More, Less, Gas, Fluids, Higher, Lower, Sun, Radiation, Conductors

● Radiation transfers heat best through _________ because there is _______ space between the particles.

● Conduction transfers heat best through _______ because there is space between the particles.

● Convection transfers heat best through _______ which includes _______ and ______.

● Heat always moves from _________ temperature to _________ temperature.

● Heat from ______ travels to earth by ___________.

● Solids that transfer heat well ate known as _____________.

Answers

Answer:

Blank 1: Gasses

Blank 2: More

Blank 3: Solids

Blank 4: Fluids

Blank 5: Liquid

Blank 6: Gas

Blank 7: Higher

Blank 8: Lower

Blank 9: Sun

Blank 10: Radiation

Blank 11: Conductors

P.S. order of answers does not matter between Blank 5 and 6.

Explain, step by step, how to calculate the amount of current (I) that will go through the resistor in this circuit

Answers

Answer:

0.03 A

Explanation:

From the question given above, the following data were obtained:

Voltage (V) = 12 V

Resistor (R) = 470 Ω

Current (I) =?

From ohm's law, the voltage, current and resistor are related by the following formula:

Voltage = current × resistor

V = IR

With the above formula, we can obtain the current in the circuit as follow:

Voltage (V) = 12 V

Resistor (R) = 470 Ω

Current (I) =?

V = IR

12 = I × 470

Divide both side by 470

I = 12 / 470

I = 0.03 A

Thus, the current in the circuit is 0.03 A

Answer:

0.03 A

Explanation:

Explain, step by step, how to calculate the amount of current (I) that will go through the resistor in this circuit

0.03 A

Example of the center of the gravity

Answers

Answer:

The example of the center of the gravity is the middle of a seesaw

Explanation:

I hope this will help you and plz mark me brainlist

The elastic energy stored in your tendons can contribute up to 35 % of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch 41 mm , while nonathletes' stretch only 33 mm .

Answers

Hello. Your question is incomplete. However, I managed to find it completely on the internet and I realized that you forgot to mention that the question asks you for the maximum energy difference between velovistas and non-athletes, considering that the spring constant for the tendon of the two groups is equal to 33n/mm.

To make this calculation you will need to use Hooke's law, using the formula: ¹/2*K*x², where "K" will be the value of the spring constant for the tendon and "X" will be the value of the sprinter and non-athlete terms.

So for the sprinter we will have the calculation:

¹/2*33*41² -------> 0,5*33*1681 = 27736. 5 Nmm

(To facilitate the calculation, first solve the division of ¹/2 and then multiply 41 by 41, lastly, just multiply all the results.)

For the non-athlete we will have the calculation:

¹/2*33*33² -------> 0,5*33*1089 = 17968. 5 Nmm

(To facilitate the calculation, first solve the division of ¹/2 and then multiply 41 by 41, lastly, just multiply all the results.)

Now, to reach the final result, you only need to subtract the two values presented by the sprinter and the non-athlete.

27736.5 - 17968.5 = 9768 Nmm

A 2.0 kg breadbox on a fric-
tionless incline of angle u 40 is
connected, by a cord that runs over a
pulley, to a light spring of spring con-
stant k 120 N/m, as shown in
Fig. 8-43. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10 cm down the in- cline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction (up or down the incline) of the box’s acceleration at the instant the box momentarily stops?

Answers

Dhjwbxuzb wm I known kdn wi. Wlzkk n

Assume a device is designed to obtain a large potential difference by first charging a bank of capacitors connected in parallel and then activating a switch arrangement that in effect disconnects the capacitors from the charging source and from each other and reconnects them all in a series arrangement. The group of charged capacitors is then discharged in series. What is the maximum potential difference that can be obtained in this manner by using ten 500

Answers

Answer:

8 kV

Explanation:

Here is the complete question

Assume a device is designed to obtain a large potential difference by first charging a bank of capacitors connected in parallel and then activating a switch arrangement that in effect disconnects the capacitors from the charging source and from each other and reconnects them all in a series arrangement. The group of charged capacitors is then discharged in series. What is the maximum potential difference that can be obtained in this manner by using ten 500 μF capacitors and an 800−V charging source?

Solution

Since the capacitors are initially connected in parallel, the same voltage of 800 V is applied to each capacitor. The charge on each capacitor Q = CV where C = capacitance = 500 μF and V = voltage = 800 V

So, Q = CV

= 500 × 10⁻⁶ F × 800 V

= 400000 × 10⁻⁶ C

= 0.4 C

Now, when the capacitors are connected in series and the voltage disconnected, the voltage across is capacitor is gotten from Q = CV

V = Q/C

= 0.4 C/500 × 10⁻⁶ F

= 0.0008 × 10⁶ V

= 800 V

The total voltage obtained across the ten capacitors is thus V' = 10V (the voltages are summed up since the capacitors are in series)

= 10 × 800 V

= 8000 V

= 8 kV

A uniform magnetic field is in the positive z direction. A positively charged particle is moving in the positive x direction through the field. The net force on the particle can be made zero by applying an electric field in what direction

Answers

Answer:

We apply an electric field in the negative y direction

Explanation:

Since A uniform magnetic field is in the positive z direction and A positively charged particle is moving in the positive x direction through the field, the magnetic force acting on the positively charged particle is in the positive y direction according to Fleming's right-hand rule.

For the net force on the particle to be zero, we apply an electric field in the negative y direction to create an electric force on the positively charged particle, so as to cancel out the magnetic force.

N4M.6 A board has one end wedged under a rock having a mass of 380 kg and is supported by another rock that touches the bottom side of the board at a point 85 cm from the end under the rock. The board is 4.5 m long, has a mass of about 22 kg, and projects essentially horizontally out over a river. Is it safe for an adult with a mass of 62 kg to stand at the unsupported end of the board

Answers

Answer:

it is safe to stand at the end of the table

Explanation:

For this exercise we use the rotational equilibrium condition

         Στ = 0

         W x₁ - w x₂ - w_table x₃ = 0

         M x₁ - m x₂ - m_table x₃ = 0

where the mass of the large rock is M = 380 kg and its distance to the pivot point x₁ = 850 cm = 0.85m

the mass of the man is 62 kg and the distance

            x₂ = 4.5 - 0.85

            x₂ = 3.65 m

the mass of the table (m_table = 22 kg) is at its geometric center

            x_{cm} = L/2 = 2.25 m

            x₃ = 2.25 -0.85

            x₃ = 1.4 m

let's look for the maximum mass of man

            m_{maximum} = [tex]\frac{ M x_1 -m_{table} x_3}{ x_2}[/tex]

let's calculate

             m_{maximum} = [tex]\frac{ 380 \ 0.85 - 22 \ 1.4}{3.65}[/tex](380 0.85 - 22 1.4) / 3.65

             m_{maximum} = 80 kg

we can see that the maximum mass that the board supports without turning is greater than the mass of man

             m_{maximum}> m

consequently it is safe to stand at the end of the table

a 4.5 Hz wave has a wavelength of 0.8m. what is the speed
0.18 m/s
5.6m/s
5.3m/s
3.6m/s ​

Answers

Answer:

   

Explanation

Hi, here it is!
I hope this help.

Step-by-step explanation

λ= 0,8m
f(frequency)= 4,5Hz

v = f × λ
v = 4,5 × 0,8
v = 3,6m/s

If you live in Melbourne, Australia, the local magnetic field has a strength of about 4x10-5 T. The magnetic field vector is directed northward, making an angle of 30 deg above the horizontal. An electron in Melbourne is moving parallel to the ground, in the west direction, at a speed of 9x105 m/s. What are the magnitude and direction of the magnetic force on the electron

Answers

Answer:

[tex]5.76\times 10^{-18}\ \text{N}[/tex] perpendicular to the velocity and magnetic field

Explanation:

B = Magnetic field = [tex]4\times 10^{-5}\ \text{T}[/tex]

[tex]\theta[/tex] = Angle the magnetic field makes with the horizontal = [tex]30^{\circ}[/tex]

v = Velocity of electron = [tex]9\times 10^5\ \text{m/s}[/tex]

q = Charge of electron = [tex]1.6\times 10^{-19}\ \text{C}[/tex]

Magnetic force is given by

[tex]F=qvB\sin\theta\\\Rightarrow F=1.6\times 10^{-19}\times 9\times 10^5\times 4\times 10^{-5}\sin30^{\circ}\\\Rightarrow F=2.88\times 10^{-18}\ \text{N}[/tex]

The magnitude of the magnetic force is [tex]2.88\times 10^{-18}\ \text{N}[/tex] and the direction is perpendicular to the velocity and magnetic field.

Which of the following best defines
weather?
A. the expanding or contracting of the atmosphere
B. the measurement of the amount of water vapor in the
atmosphere
C. the condition of the atmosphere at a certain time and
place
Help Resources
D. the average air temperature of a specific region

Answers

Answer:

I'd say D

Explanation:

because not all weather happens within the atmosphere, and most weather depends on region (lile if your near the equator or not)

A solenoid that is 93.9 cm long has a cross-sectional area of 17.3 cm2. There are 1270 turns of wire carrying a current of 7.80 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects).

Answers

Answer:

[tex]65.6\ \text{J/m}^3[/tex]

[tex]0.11\ \text{J}[/tex]

Explanation:

B = Magnetic field = [tex]\mu_0 \dfrac{N}{l}I[/tex]

[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi10^{-7}\ \text{H/m}[/tex]

N = Number of turns = 1270

[tex]l[/tex] = Length of solenoid = 93.9 cm = 0.939 m

[tex]I[/tex] = Current = 7.8 A

A = Area of solenoid = [tex]17.3\ \text{cm}^2[/tex]

Energy density of a solenoid is given by

[tex]u_m=\dfrac{B^2}{2\mu_0}\\\Rightarrow u_m=\dfrac{(\mu_0 \dfrac{N}{l}I)^2}{2\mu_0}\\\Rightarrow u_m=\dfrac{\mu_0N^2I^2}{2l^2}\\\Rightarrow u_m=\dfrac{4\pi\times 10^{-7}\times 1230^2\times 7.8^2}{2\times 0.939^2}\\\Rightarrow u_m=65.6\ \text{J/m}^3[/tex]

The energy density of the magnetic field inside the solenoid is [tex]65.6\ \text{J/m}^3[/tex]

Energy is given by

[tex]U_m=u_mAl\\\Rightarrow U_m=65.6\times 17.3\times 10^{-4}\times 0.939\\\Rightarrow U_m=0.11\ \text{J}[/tex]

The total energy in joules stored in the magnetic field is [tex]0.11\ \text{J}[/tex].

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