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taurus [48]
3 years ago
14

At our distance from the Sun, the intensity of solar radiation is 1370 W/m^2. The temperature of the Earth is affected by the gr

eenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic radiation and its temperature is uniform over its surface.
Compute its steady-state temperature. Is it chilly?
Physics
1 answer:
Irina18 [472]3 years ago
4 0

Answer:

The steady-state temperature is  T =  4.85 ^oC

Yes it is chilly

Explanation:

From the question we are told

       The intensity of solar radiation is  I =  1320 \  \frac{W}{m^2}

Generally the Stefan Boltzmann Law is mathematically represented as

          P  =  A \epsilon \sigma T^4

Where

         P is the total power radiated

          A is the surface area of the object

          \epsilon is the emissivity

          T is the temperature of the object

           \sigma is the Boltzmann constant with a value \sigma  =  5.670 *10^{-8} \frac{W}{m^2 K^4}

Generally at steady state  the input power to the object  is equal to the output power from the object

           i.e    P_A = P_B

Now  P_A

which is the input power to the object is not dependent on the object temperature and on the Boltzmann constant

thus P_A  is mathematically represented as

               P_A =  \epsilon IA_a

Where A_a  is  absorptive surface area mathematically represented as

            A_a  = \pi r^2

Thus

        P_A =  \epsilon I \pi r^2

And   P_B which is the output  power to the object is mathematically represented a

                P_B =  A_s \epsilon \sigma T^4

Where A_s is the radiative surface area which is mathematically  as

           A_s =  4\pi r^2

So

            P_B  = 4\pi r^2 \epsilon \sigma T^4

=>         \epsilon I \pi r^2 = 4\pi r^2 \epsilon \sigma T^4

=>          T =  \sqrt[4]{\frac{I}{4 \sigma } }

substituting values

             T =  \sqrt[4]{\frac{1370}{4 * 5.670 *10^{-8} } }

             T = 278 \ K

Converting to degrees

         T = 278 - 273

        T =  4.85 ^oC

This implies that at steady state it is chilly

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Hey there!

When a hurricane is near land the wind and rain cause the most damage.

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4 0
2 years ago
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A bubble, located 0.200 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is 1.01 ???? 10
SIZIF [17.4K]

Answer:

the ratio of the bubble’s volume at the top to its volume at the bottom is 1.019

Explanation:

given information

h = 0.2 m

P_{0} = 1.01  x 10^{5} Pa

P_{1} V_{1} = P_{2} V_{2}

\frac{V_{2} }{V_{1}} = \frac{P_{1} }{P_{2}}

P_{1}  = P_{0}  + ρgh, ρ = 1000 kg/m^{3}

P_{1}  = 1.01 x 10^{5} Pa + (1000 x 9.8 x 0.2) = 1,0296 x 10^{5} Pa

P_{2}  = P_{0}  = 10^{5} Pa

thus,

\frac{V_{2} }{V_{1}} = 1,0296 x [tex]10^{5}/10^{5} = 1.019

8 0
3 years ago
An electron moves in a circular path perpendicular to a uniform magnetic field with a magnitude of 2.14 mT. If the speed of the
JulsSmile [24]

Answer:

(a) 3.9cm

(b) 1.66 x 10⁻⁸s

Explanation:

Since the electron is moving in a circular path, the centripetal acceleration needed to keep it from slipping off is provided by the magnetic force. This force (F), according to Newton's second law of motion is given by,

F = m x a          --------------(i)

Where;

m = mass of the particle

a = acceleration of the mass

The centripetal acceleration is given by;

a = v² / r          [v = linear velocity of particle, r = radius of circular path]

<em>Therefore, equation (i) becomes;</em>

F = m v²/ r             --------------------(ii)

The magnitude of the magnetic force on a moving charge in a magnetic field as stated by Lorentz's law is given by;

F = qvBsinθ          -------------(iii)

Where;

q = charge of the particle

v = velocity of the particle

B = magnetic field

θ = angle between the velocity and the magnetic field

<em>Combine equations (ii) and (iii) as follows;</em>

m (v² / r) = qvBsinθ         [divide both side by v]

m v / r = qBsinθ              [make r subject of the formula]

r = (m v) / (qBsinθ)              ---------(iv)

(a) From the question;

v = 1.48 x 10⁷m/s

B = 2.14mT = 2.14 x 10⁻³T

θ = 90°          [since the direction of velocity is perpendicular to magnetic field]

m = mass of electron = 9.11 x 10⁻³¹kg

q = charge of electron = 1.6 x 10⁻¹⁹C

Substitute these values into equation (iv) as follows;

r = (9.11 x 10⁻³¹ x 1.48 x 10⁷) / (1.6 x 10⁻¹⁹ x 2.14 x 10⁻³ sin 90°)

r = 3.9 x 10⁻²m

r = 3.9cm

Therefore, the radius of the circular path is 3.9cm

(b) The time interval required to complete one revolution is the period (T) of the motion of the electron and it is given by

T = d / v          --------------(*)

Where;

d = distance traveled in the circular path in one complete turn = 2πr

v = velocity of the motion = 1.48 x 10⁷m/s

d = 2 π (3.9 x 10⁻²)            [Take π = 22/7 = 3.142]

d = 2(3.142)(3.9 x 10⁻²) = 0.245m

Substitute the values of d and v into equation (*) as follows;

T = 0.245 / 1.48 x 10⁷

T = 0.166 x 10⁻⁷s

T = 1.66 x 10⁻⁸s

Therefore, the time interval is 1.66 x 10⁻⁸s

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3 years ago
What happenes to our body temperature on a cold winter day or a hot summer day
viva [34]

In cold winter day, the body temperature falls down from normal temperature of 98.6°F (37°C) to 95°F (35°C). In winter body losses heat faster than it generates heat. If the temperature fall further below 95°F (35°C), it is emergency condition known as Hypothermia. One has to consult doctor in this case.

In summer hot days, body evaporates water in the form of sweat, in order to remain itself cool. Rise of temperature up to 100°F is normal. It is recommended to hydrate body to maintain temperature in summer days.

3 0
2 years ago
Desde el balcón de un edificio se deja caer una manzana y llega a la planta baja en 5 s. ¿Desde qué piso se dejó caer, si cada p
miv72 [106K]

Answer: 42

Explanation:

I will answer this in English.

We know that the apple needs 5 seconds to reach the ground.

Each floor of the building has a height of 2.88m.

Now, when we drop something, the only force acting on the object is the gravitational one, so the acceleration of the apple is:

a = -g

for the velocity, we integrate the acceleration over time, and as the apple is dropped, we do not have any initial velocity, so we do not have a constant in the integration:

v = -g*t

for the position we integrate again, now we have an initial height H, so the position is:

p = (-g/2)*t^2 + H

now the apple hits the ground when p = 0, so we can solve this equation to find H.

i will use g = 9.8m/s^2

0 = (-4.9m/s^2)*(5s)^2 + H  

H = 122.5 m

now knowing H, we can divide it by the height of a floor in the building and get the number of the floor.

N = 122.5m/2.88m = 42.5

this means that the apple was dropped in the floor 42 (the 0.5 means that the apple was not right where the floor 42 starts, it was dropped around the middle of the floor 42)

5 0
2 years ago
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