how did kepler discoveries contribute to astronomy

Answer:

a) Initial Temperature = 609.4 K and Final Temperature = 325.7 K

b) the change in internal energy is -18279.78 J

c) heat lost by the gas is zero or 0

d) the work done on the gas is -18279.78 J

Explanation:

Given the data in the question;

P[tex]_i[/tex] = 1 atm = 101325 pascal

P[tex]_f[/tex] = ?

V[tex]_i[/tex] = 0.1550 m³

V[tex]_f[/tex] = 0.742 m³

we know that for an adiabatic process  γ = 1.4

P[tex]_i[/tex]V[tex]_i^Y[/tex] = P[tex]_f[/tex]V[tex]_f^Y[/tex]

P[tex]_f[/tex] = P[tex]_i[/tex][tex]([/tex] V[tex]_i[/tex] / V[tex]_f[/tex] [tex])^Y[/tex]

we substitute

P[tex]_f[/tex] = 1 × [tex]([/tex] 0.1550  / 0.742  [tex])^{1.4[/tex]

= [tex]([/tex] 0.2088948787 [tex])^{1.4[/tex]

= 0.11166 atm

a) the initial and final temperatures

Initial temperature

T[tex]_i[/tex] = P[tex]_i[/tex]V[tex]_i[/tex] / nR

given that n = 3.10 mol

= ( 101325 × 0.1550 ) / ( 3.10 × 8.314 )

= 15705.375 / 25.7734

T[tex]_i[/tex]  = 609.4 K

Final temperature

T[tex]_f[/tex] = P[tex]_f[/tex]V[tex]_f[/tex] / nR

= ( 0.11166 × 101325 × 0.742 ) / ( 3.10 × 8.314 )

= 8394.95 / 25.7734

= 325.7 K

Therefore, Initial Temperature = 609.4 K and Final Temperature = 325.7 K

b) the change in internal energy

ΔE[tex]_{int[/tex] = nC[tex]_v[/tex]ΔT

here, C[tex]_v[/tex] = ( 5/2 )R

ΔE[tex]_{int[/tex] = 3.10 × ( 5/2 )8.314 × ( 325.7 - 609.4 )

= -18279.78 J

Therefore, the change in internal energy is -18279.78 J

c) the heat lost by the gas

Since its an adiabatic process,

Q = 0

Therefore, heat lost by the gas is zero or 0

d)  the work done on the gas

W = ΔE[tex]_{int[/tex] - Q

= -18279.78 J - 0

W = -18279.78 J

Therefore, the work done on the gas is -18279.78 J

a) The Initial Temperature and Final Temperature of gas are 601.68 K and 321.61 K respectively.

b) The change in internal energy is -18279.78 J.

c) The heat lost by the gas is zero.

d) The work done on the gas is -18279.78 J.

Given data:

The moles of sample is, n = 3.10 mol.

The initial volume of sample is, [tex]V_{1}=0.1550 \;\rm m^{3}[/tex].

The final volume of sample is, [tex]V_{2}=0.742 \;\rm m^{3}[/tex].

The initial pressure of the sample is, [tex]P_{1}=1.00 \;\rm atm[/tex].

(a)

We know that the relation between the pressure and volume for an adiabatic process is as follows,

[tex]P_{1}V_{1}^{\gamma} = P_{2}V_{2}^{\gamma}[/tex]

Here, [tex]\gamma[/tex]  is a adiabatic index. And for air, its value is 1.41.

Solving as,

[tex]P_{2}=P_{1} \times\dfrac{V_{1}^{\gamma}}{V_{2}^{\gamma}}\\\\\\P_{2}=1.00 \times\dfrac{0.1550^{1.41}}{0.742^{1.41}}\\\\\\P_{2} = 0.11166 \;\rm atm[/tex]

Now, calculate the final temperature using the ideal gas equation as,

[tex]P_{2}V_{2}=nRT_{2}\\\\T_{2}= \dfrac{P_{2} \times V_{2}}{nR}\\\\T_{2}= \dfrac{0.11166 \times 10^{5}\times 0.742}{3.10 \times 8.31}\\\\T_{2}=321.61 \;\rm K[/tex]

Similarly, calculate the initial temperature as,

[tex]P_{1}V_{1}=nRT_{1}\\\\T_{1}= \dfrac{P_{1} \times V_{1}}{nR}\\\\T_{1}= \dfrac{1 \times 10^{5}\times 0.1550}{3.10 \times 8.31}\\\\T_{1}=601.68 \;\rm K[/tex]

Thus, we can conclude that the initial and final temperature of the gas is 601.68 K and 321.61 K respectively.

(b)

The change in internal energy is given as,

ΔE = nCΔT

here, C = ( 5/2 )R

ΔE = 3.10 × ( 5/2 )8.314 × ( 325.7 - 609.4 )

      = -18279.78 J

Therefore, the change in internal energy is -18279.78 J.

c)

The heat lost by the gas . Since its an adiabatic process, so there will be no heat interaction.  

Q = 0

Therefore, heat lost by the gas is zero or 0

d)  

The work done on the gas

W = ΔE - Q

W = -18279.78 J - 0

W = -18279.78 J

Therefore, the work done on the gas is -18279.78 J.

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Answer:

The electromotive force is the maximum potential difference between the terminals of a battery.

The electromotive force is the maximum potential difference between the terminals of a battery.  The correct option is b.

The electromotive force also called as EMF, is the force which causes current to flow from  the positive to negative terminal of the battery.

The electromotive force is the maximum potential difference between the terminals of a battery.

Thus, the correct option is b.

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Answer:

a) [tex]a_{avg}=1.25ft/s^2[/tex]

b) [tex]v_b=13.35ft/s[/tex]

Explanation:

From the question we are told that:

Speed at point A [tex]v_A=10.6ft/s[/tex]

Speed at point C [tex]v_C=15.6ft/s[/tex]

Time from Point A to C [tex]T_{ac}=4.00s[/tex]

Time from Point B to C [tex]T_{bc}=1.80s[/tex]

Generally the equation for acceleration From A to B is mathematically given by

 [tex]a_{avg}=\frac{v_c-v_a}{\triangle t}[/tex]

 [tex]a_{avg}=\frac{15.6-10.6}{4.0 }[/tex]

 [tex]a_{avg}=1.25ft/s^2[/tex]

Generally the equation for cart speed at B is mathematically given by

 [tex]a_{avg}=\frac{v_c-v_a}{T_{bc}}[/tex]

 [tex]v_b=v_c-a_{avg}*T_{bc}[/tex]

 [tex]v_b=15.6ft/s-(1.25ft/s^2)(1.80)[/tex]

  [tex]v_b=13.35ft/s[/tex]

Answer:

The correct answer is c

Explanation:

Flow is defined by

        Ф =  B . A

bold letters indicate vectors.

The magnetic field is directed to the y axis, The area of ​​the coil is represented by a vector normal to the plane of the coil, so to have a flux

                i.i = j.j = k.k = 1

and the tori scalar products are zero

a) If the coil must be in the xy plane so that its normal vector is in the Z axis, so there is no flux

b) if the coil is in the plane yz the normal veto is in the x axis, so the flux is zero

C) If the coil is in XZ, the normal vector points in the y direction, usually the scalar product is one and there is a flux in this configuration

The correct answer is c

Answer:

Explanation:

The energy for an isothermal expansion can be computed as:

[tex]\mathsf{Q_H =nRTIn (\dfrac{V_b}{V_a})}[/tex] --- (1)

However, we are being told that the volume of the gas is twice itself when undergoing adiabatic expansion. This implies that:

[tex]V_b = 2V_a[/tex]

Equation (1) can be written as:

[tex]\mathtt{Q_H = nRT_H In (2)}[/tex]

Also, in a Carnot engine, the efficiency can be computed as:

[tex]\mathtt{e = 1 - \dfrac{T_L}{T_H}}[/tex]

[tex]e = \dfrac{T_H-T_L}{T_H}[/tex]

In addition to that, for any heat engine, the efficiency e =[tex]\dfrac{W}{Q_H}[/tex]

relating the above two equations together, we have:

[tex]\dfrac{T_H-T_L}{T_H} = \dfrac{W}{Q_H}[/tex]

Making the work done (W) the subject:

[tex]W = Q_H \Big(\dfrac{T_H-T_L}{T_H} \Big)[/tex]

From equation (1):

[tex]\mathsf{W = nRT_HIn(2) \Big(\dfrac{T_H-T_L}{T_H} \Big)}[/tex]

[tex]\mathsf{W = nRIn(2) \Big(T_H-T_L} \Big)}[/tex]

If we consider the adiabatic expansion as well:

[tex]PV^y[/tex] = constant

i.e.

[tex]P_bV_b^y = P_cV_c^y[/tex]

From ideal gas PV = nRT

we can have:

[tex]\dfrac{nRT_H}{V_b}(V_b^y)= \dfrac{nRT_L}{V_c}(V_c^y)[/tex]

[tex]T_H = T_L \Big(\dfrac{V_c}{V_b}\Big)^{y-1}[/tex]

From the question, let us recall  aw we are being informed that:

If the volumes changes by a factor = 5.7

Then, it implies that:

[tex]\Big(\dfrac{V_c}{V_b}\Big) = 5.7[/tex]

∴

[tex]T_H = T_L (5.7)^{y-1}[/tex]

In an ideal monoatomic gas [tex]\gamma = 1.6[/tex]

As such:

[tex]T_H = T_L (5.7)^{1.6-1}[/tex]

[tex]T_H = T_L (5.7)^{0.67}[/tex]

Replacing the value of [tex]T_H = T_L (5.7)^{0.67}[/tex] into equation [tex]\mathsf{W = nRIn(2) \Big(T_H-T_L} \Big)}[/tex]

[tex]\mathsf{W = nRT_L In(2) (5.7 ^{0.67 }-1}})[/tex]

From in the question:

W = 930 J and the moles = 1.90

using 8.314 as constant

Then:

[tex]\mathsf{930 = (1.90)(8.314)T_L In(2) (5.7 ^{0.67 }-1}})[/tex]

[tex]\mathsf{930 = 15.7966\times 1.5315 (T_L )})[/tex]

[tex]\mathsf{T_L= \dfrac{930 }{15.7966\times 1.5315}}[/tex]

[tex]\mathbf{T_L \simeq = 39 \ K}[/tex]

From [tex]T_H = T_L (5.7)^{0.67}[/tex]

[tex]\mathsf{T_H = 39 (5.7)^{0.67}}[/tex]

[tex]\mathbf{T_H \simeq 125K}[/tex]

Answer: hello your question lacks some vital information below is the complete question

Suppose a power plant uses a Carnot engine to generate electricity, using the atmosphere at 300 K as the low-temperature reservoir. Suppose the power plant produces 1 × 106 J of electricity with the hot reservoir at 500 K during Day One and then produces 1 × 106 J of electricity with the hot reservoir at 600 K during Day Two. The thermal pollution was

answer:

Total thermal pollution = 2.5 * 10^6 J

Explanation:

Low temperature reservoir = 300 K

hot reservoir temperature = 500 K

Electrical energy produced by plant ( W ) = 1 * 10^6 J

lets assume ; Q1 = energy absorbed , Q2 = energy emitted

W = Q1 - Q2  or  Q2 = Q1 - W  ( we will apply this as the formula for determining thermal pollution )

For day 1

T1 = 500k , T2 = 300k

applying Carnot engine formula

W / Q1 = 1 - T2/T1

∴ Q1 = 10^6 / ( 1 - (300/500)) = 2.5 * 10^6 J

thermal pollution ; Q2 = Q1 - W = ( 2.5 * 10^6 - 1 * 10^6 ) = 1.5 * 10^6 J

for Day 2

T1 = 600k,  T2 = 300k

Q1 = 10^6 / ( 1 - (300/600)) = 2 * 10^6 J

Thermal pollution; Q2 = Q1 - W  = 1 * 10^6 J

Therefore the Total thermal pollution =  1 * 10^6  + 1.5 * 10^6  = 2.5 * 10^6 J

(D)

Explanation:

The more massive an object is, the greater is the curvature that they produce on the space-time around it.

The theory of relativity explain the gravity exerted by massive objects is

more massive objects create larger curves of space-time (option-d).

The term "gravitational force" refers to the attraction between masses. The gravitational force increases in size as the masses get bigger (also called the gravity force). As the distance between masses grows, the gravitational force progressively lessens.

Greater gravitational forces will be used to attract heavier things since the gravitational force is directly proportional to the mass of both interacting objects. Therefore, when two things' respective masses increase, so does their gravitational pull to one another.

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Answer:

 ΔL = 3.82 10⁻⁴ m

Explanation:

This is a thermal expansion exercise

          ΔL = α L₀ ΔT

          ΔT = T_f - T₀

where ΔL is the change in length and ΔT is the change in temperature

Let's reduce the length to SI units

          L₀ = 90.5 mm (1m / 1000 mm) = 0.0905 m

let's calculate

          ΔL = 25.10⁻⁶ 0.0905 (154.6 - (14.4))

          ΔL = 3.8236 10⁻⁴ m

using the criterion of three significant figures

          ΔL = 3.82 10⁻⁴ m

Answer:

219 ft

Explanation:

Here we can define the value t = 0s as the moment when the car starts decelerating.

At this point, the acceleration of the car is given by the equation:

A(t) = -10 ft/s^2

Where the negative sign is because the car is decelerating.

To get the velocity equation of the car, we integrate over time, to get:

V(t) = (-10 ft/s^2)*t + V0

Where V0 is the initial velocity of the car, we know that this is 88 ft/s

Then the velocity equation is:

V(t) = (-10 ft/s^2)*t + 88ft/s

To get the position equation we need to integrate again, this time we get:

P(t) = (1/2)*(-10 ft/s^2)*t^2 + (88ft/s)*t + P0

Where P0 is the initial position of the car, we do not know this, but it does not matter for now.

We want to find the total distance that the car traveled in a 3 seconds interval.

This will be equal to the difference in the position at t = 3s and the position at t = 0s

distance = P(3s) - P(0s)

 = ( (1/2)*(-10 ft/s^2)*(3s)^2+ (88ft/s)*3s + P0) - ( (1/2)*(-10 ft/s^2)*(0s)^2 + (88ft/s)*0s + P0)

=  ( (1/2)*(-10 ft/s^2)*9s^2+ (88ft/s)*3s + P0) - ( P0)

=  (1/2)*(-10 ft/s^2)*9s^2+ (88ft/s)*3s = 219ft

The car advanced a distance of 219 ft in the 3 seconds interval.

Answer:

The angle between the electric field lines and the equipotential surface is 90 degree.

Explanation:

The equipotential surfaces are the surface on which the electric potential is same. The work done in moving a charge from one point to another on an equipotential surface is always zero.

The electric field lines are always perpendicular to the equipotential surface.

As

[tex]dV = \overrightarrow{E} . d\overrightarrow{r}\\\\[/tex]

For equipotential surface, dV = 0 so

[tex]0 = \overrightarrow{E} . d\overrightarrow{r}\\\\[/tex]

The dot product of two non zero vectors is zero, if they are perpendicular to each other.

Answer:

Scalar quantity is the Physical quantity expresed only by their magnitude.

Answer:

[tex]d_2=1.5*10^-3m[/tex]

Explanation:

From the question we are told that:

Initial Wavelength [tex]\lambda_1=550nm=550*10^{-9}[/tex]

Space 1 [tex]d_1=2.3*10^{-3}[/tex]

Final wavelength [tex]\lambda_2=360*10^{-9}[/tex]

Generally the equation for Fringe space at [tex]\lambda _2[/tex] is mathematically given by

 [tex]d_2=\frac{d_1}{\lambdaI_1}*\lambda_2[/tex]

 [tex]d_2=\frac{2.3*10^{-3}}{550*10^{-9}}*360*10^{-9}[/tex]

 [tex]d_2=1.5*10^-3m[/tex]

Answer:

Quantum Mechanics

Explanation:

Well, that's what I think personally.

Answer:

w = 1,066 rad / s

Explanation:

For this exercise we use Newton's second law

         F = m a

the centripetal acceleration is

         a = w² r

indicate that the force is the mass of the body times the acceleration

        F = m 0.58g = m 0.58 9.8

        F = 5.684 m

we substitute

       5.684 m = m w² r

       w = [tex]\sqrt{5.684/r}[/tex]

To finish the calculation we must suppose a cylinder radius, suppose it has r = 5 m

       w = [tex]\sqrt{ 5.684/5}[/tex]

       w = 1,066 rad / s

Answer:

b)

Explanation:

Answer:

The magnitude of the maximum possible torque exerted on the coil is 5.73 x 10⁻³ Nm

Explanation:

Given;

number of turns of the circular coil, N = 49.5 turns

radius of the coil, r = 5.10 cm = 0.051 m

magnitude of the magnetic field, B = 0.535 T

current in the coil, I = 26.5 mA = 0.0265 A

The magnitude of the maximum possible torque exerted on the coil is calculated as;

τ = NIAB

where;

A is the area of the coil

A = πr² = π(0.051)² = 0.00817 m²

Substitute the given values and solve for the maximum torque

τ = (49.5) x (0.0265) x (0.00817) x (0.535)

τ = 0.00573 Nm

τ = 5.73 x 10⁻³ Nm

Answer:

[tex]\frac{dV}{dt}=21.21cm^3/min[/tex]

Explanation:

We are given that

[tex]PV^{1.4}=C[/tex]

Where C=Constant

[tex]\frac{dP}{dt}=-7KPa/minute[/tex]

V=420 cubic cm and P=99KPa

We have to find the rate at which the  volume increasing at this instant.

Differentiate w.r.t t

[tex]V^{1.4}\frac{dP}{dt}+1.4V^{0.4}P\frac{dV}{dt}=0[/tex]

Substitute the values

[tex](420)^{1.4}\times (-7)+1.4(420)^{0.4}(99)\frac{dV}{dt}=0[/tex]

[tex]1.4(420)^{0.4}(99)\frac{dV}{dt}=(420)^{1.4}\times (7)[/tex]

[tex]\frac{dV}{dt}=\frac{(420)^{1.4}\times (7)}{1.4(420)^{0.4}(99)}[/tex]

[tex]\frac{dV}{dt}=21.21cm^3/min[/tex]

Answer:

[tex]\dot V=2786.52~cm^3/min[/tex]

Explanation:

Given:

initial pressure during adiabatic expansion of air, [tex]P_1=99~kPa[/tex]

initial volume during the process, [tex]V_1=420~cm^3[/tex]

The adiabatic process is governed by the relation [tex]PV^{1.4}=C[/tex] ; where C is a constant.

Rate of decrease in pressure, [tex]\dot P=7~kPa/min[/tex]

Then the rate of change in volume, [tex]\dot V[/tex] can be determined as:

[tex]P_1.V_1^{1.4}=\dot P.\dot V^{1.4}[/tex]

[tex]99\times 420^{1.4}=7\times V^{1.4}[/tex]

[tex]\dot V=2786.52~cm^3/min[/tex]

[tex]\because P\propto\frac{1}{V}[/tex]

[tex]\therefore[/tex] The rate of change in volume will be increasing.

Answer:

fair palybtgshsisuehdh

Answer:

By the principle of corona discharge.

Explanation:

The charge on each ball will decreases over time due to the electrical discharge in air.

According to the principle of corona discharge, when the curvature is small, the discharge of the charge takes placed form the pointed ends.

Answer: The force on a negative charge that is placed midway between two equal positive charges is zero when all charges have the same magnitude.

Explanation:

Let us assume that

[tex]q_{1} = q_{2} = +q[/tex]

[tex]q_{3} = -q[/tex]

As [tex]q_{3}[/tex] is the negative charge and placed midway between two equal positive charges ([tex]q_{1}[/tex] and [tex]q_{2}[/tex]).

Total distance between [tex]q_{1}[/tex] and [tex]q_{2}[/tex] is 2r. This means that the distance between [tex]q_{1}[/tex] and [tex]q_{3}[/tex], [tex]q_{2}[/tex] and [tex]q_{3}[/tex] = d = r

Now, force action on charge [tex]q_{3}[/tex] due to [tex]q_{1}[/tex] is as follows.

[tex]F_{31} = k(\frac{q_{1} \times q_{3}}{d^{2}})[/tex]

where,

k = electrostatic constant = [tex]9 \times 10^{9} Nm^{2}/C^{2}[/tex]

Substitute the values into above formula as follows.

[tex]F_{31} = k(\frac{q_{1} \times q_{3}}{d^{2}})\\= 9 \times 10^{9} (\frac{q \times (-q)}{r^{2}})\\= - 9 \times 10^{9} (\frac{q^{2}}{r^{2}})[/tex] ... (1)

Similarly, force acting on [tex]q_{3}[/tex] due to [tex]q_{1}[/tex] is as follows.

[tex]F_{32} = k \frac{q_{2}q_{3}}{d^{2}}\\= -9 \times 10^{9} \frac{q^{2}}{r^{2}}\\[/tex]   ... (2)

As both the forces represented in equation (1) and (2) are same and equal in magnitude. This means that the net force acting on charge [tex]q_{3}[/tex] is zero.

Thus, we can conclude that the force on a negative charge that is placed midway between two equal positive charges is zero when all charges have the same magnitude.

Answer:

v_f = 17.4 m / s

Explanation:

For this exercise we can use conservation of energy

starting point. On the hill when running out of gas

          Em₀ = K + U = ½ m v₀² + m g y₁

final point. Arriving at the gas station

         Em_f = K + U = ½ m v_f ² + m g y₂

energy is conserved

         Em₀ = Em_f

         ½ m v₀ ² + m g y₁ = ½ m v_f ² + m g y₂

        v_f ² = v₀² + 2g (y₁ -y₂)

we calculate

        v_f ² = 20² + 2 9.8  (10 -15)

        v_f = √302

         v_f = 17.4 m / s

Answer:

The velocity is 2661.5 m/s.

Explanation:

Radius, horizontal distance, d = 309 km

height, h = 25 km

acceleration due to gravity on moon, g =3.71 m/s^2

Let the time taken is t and the horizontal velocity is u.

horizontal distance = horizontal velocity x time

309 x 1000 = u t .... (1)

Use second equation of motion in vertical direction.

[tex]h = u_yt +0.5 gt^2\\\\25000 = 0 + 0.5\times 3.71\times t^2\\\\t =116.1 s[/tex]  

So, put in (1)

309 x 1000 = u x 116.1

u = 2661.5 m/s

Answer:

proton have higher energy than electron

Explanation:

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Answer:

proton

Explanation:

proton is higher energy than the electron

Answer:

4.86 m

Explanation:

Given that,

The frequency produced by a humming bird, f = 70 Hz

The speed of sound, v = 340 m/s

We need to find how far does the sound  travel between wing flaps. Let the distance is equal to its wavelength. So,

[tex]v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{340}{70}\\\\\lambda=4.86\ m[/tex]

So, the sound travel 4.86 m between wings flaps.

Answer:

b.have frequencies that are integer multiples of the frequency of the complex waveform

Explanation:

Please correct me if I am wrong

Answer:

The pulse speed depends on the properties of the medium and not on the amplitude or pulse length of the pulse.

Explanation:

Hope this helps.

Answer:

The highest point in the trajectory occurs at the midpoint of the path. This highest point increases as the angle increases. At a 75° launch angle, the maximum height is approximately 76 meters. However, a further increase in launch angle beyond this 75° angle will increase the peak height even more.

Answer:

v = 804.23 m/s

Explanation:

Given that,

The maximum distance covered by a cannon, d = 33 km = 33000 m

We need to find the initial velocity of the shell. Let it is v. It can be calculated using the conservation of energy such that,

[tex]v=\sqrt{2gh} \\\\v=\sqrt{2\times 9.8\times 33000} \\\\v=804.23\ m/s[/tex]

So, the initial velocity of the shell is 804.23 m/s.