Problem 5 (20 points) A spherical black body of radius r at absolute temperature T is surrounded by a thin concentric spherical shell of radius R. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume `u=U/V propT^4` and Mar 5, 2022 · A spherical black body emits radiation with power P when its temperature is T. To solve the problem, we need to analyze the relationships between the given parameters: the radius of the spherical black body (r), the power it radiates (H), and its rate of cooling (C). The assumed data from the question are Sun is assumed to be a spherical body of the radius, R Distance between the sun and the earth, r Radius of the earth, r 0 Assuming the sun as the spherical black body, Stefan’s law is applicable to it. Both sides of the thin shell have the absorptivity of a=0. 3600 D. [6][7] Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. The factor by which this radiation shield reduces the rate of cooling of the body (considering the space between spheres evacuated, with no thermal conduction losses) is given by the following This calculator computes the surface area of a number of common shapes, including sphere, cone, cube, cylinder, capsule, cap, conical frustum, and more. If the radius were halved and the temperature doubled, the power radiated in watt would be :- Solution For A spherical black body of radius r radiates Pow er P and its rate of cooling is (i) P∝r (ii) P∝r2 (iii) R∝r2 (iv) R∝r1 (I) (i), (ii) (2 A spherical black body of radius r at absolute temperature Tlis surrounded by a thin spherical and concentric shell of radius R. From the above question, we are given that the radius of the spherical block is r and it is radiating the power is P. If the radius were halved and the temperature be doubled, the power radiated in watt would be: A. A spherical black body of radius rr (4) 34R P and its rate of cooling is R, where radiates power (i) P∝r (ii) P∝r2 (iii) R∝r2 (iv) Q. r2 (B) R Par (C) RP a 1/2 (D) RP a A spherical black body has a radius R and steady surface temperature T, heat sources in it ensure the heat evolution at a constant rate and distributed uniformly over its volume. Added by Patricia N. If the radius were halved, and the temperature doubled, th A thin spherical conducting shell of radius r1 carries a charge Q. As an example, consider a charged spherical shell S of negligible thickness, with a uniformly distributed charge Q and radius R. In the given question, we are given a spherical black of radius r and which radiated power of magnitude P . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U/V ∝ T4 and pressure p = (1/3) (U/V). Explanation: To solve this problem, we need to understand the relationship between the power radiated by a black body and its radius, as well as the rate of cooling. Assuming sun to have spherical outer surface of radius 'r', radiating like a black body at temperature t^0C, the power received by a unit surface at a unit distance R normal to the Ray's from the centre of the sun is ? Building upon prior theoretical work in understanding drag on a spherical particle from low to high speed, and continuum to rarefied flows, the purpose of this work is to develop physics-based expression for the drag coefficient, applicable under general conditions, i. Dec 6, 2023 · The question is asking about a spherical black body of radius r that radiates power P and its rate of cooling, which is represented by R. 850 A spherical black body has a radius R and steady surface temperature T, heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. The absolute temperature of X is double that of Y. What would be the new steady surface temperature of the object if the radius is decreased by half? A solid spherical black body has a radius R and steady surface temperature T. The new steady surface temperature of the object if the radius is decreased by half is T 2 x. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U V ∝ T 4 and pressure P = 1 3 (U V). We are asked to find the rate of cooling of the black body. If the temperature doubled and the radius was cut in half, the power radiated in watts would be: (1) A spherical black body of radius r radiates power P, and its rate of cooling is R. We would like to show you a description here but the site won’t allow us. A spherical black body of radius r radiated power P at temperature T when placed in surroundings at temprature T 0 ( < < T ) If R is the rate of colling . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume `u=U/V propT^4` and However, the radius is also often denoted r or s, the azimuth by θ or t, and the third coordinate by h or (if the cylindrical axis is considered horizontal) x, or any context-specific letter. Concept: Power radiated by a black body is E = σ A T4 Where A = Area; T = Temperature of the body in Kelvin Calculation: Given: σ = A spherical black body with a radius of 12cm radiates 450W power at 50K If the radius were halved and the temperature doubled the power radiated in watts would be A 225 B 450 C 900 D 1800 Assuming the sun to be a spherical body of radius R at a temperature T K, Evaluate the total radiant power incident on the Earth. The temperature of a spherical black body in a steady state is found by applying the Stefan-Boltzmann law, which relates the energy emission rate to the fourth power of temperature. Show that the factor by which this radiation shield reduces the rate of the cooling body is given by the following expression: aR^2/ (R^2+br^2), and find the numerical coefficients and a and b. If the radius is decreased by half, what would be the new temperature of the surface at steady state ? The correct answer is Energy radiated per sec by the Sun in all possible directions (Assume the Sun as perfect black body)E=4πR2σT4Intensity (I) of the Sun on the Earth surfaceI=σ4πR2T44πr2=σRr2T4Total radiant energy per sec as received on earth=πr02I=πσRr2r02T4[∴The area of the Earth which receives the energy is only 14 th of total surface area of the Earth (r >> R) whose disc has A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the shell now undergoes an adiabatic expansion the relation between T and R is: A. T ∝ e R B. It emits power 'P' and its rate of colling is R then (A) RP a. Concentric with it is another thin metallic spherical shell of radius r2(r2>r1). If the radius were halved and the temperature doubled, the power radiated in wat Consider a spherical shell of radius R at temperature T. . 0k views Jul 21, 2023 · A thin spherical conducting shell of radius r1 carries a charge Q. a point charge a uniformly distributed spherical shell of charge any other charge distribution with spherical symmetry The spherical Gaussian surface is chosen so that it is concentric with the charge distribution. A proton, a deuteron and an alpha particle having equal kinetic energy are moving in circular path of radius rp, rd and ra resp. Show that the factor by which this radiation shield reduces the rate of cooling of the body (consider space between spheres evacuated, with no thermal conduction losses) is given by the following Dec 11, 2019 · A spherical black body of radius r radiates power P, and its rate of cooling is R. University Physics with Modern Physics Hugh D. rce on the earth. If the radius is decreased by half, what would be the new temperature of the surface at steady state ? Two spherical black bodies of same material and radii r1 and r2 radiate power initially at the same temperature. The radiations emitted by the sun are analyzeed and the spectral energy distribution curve is plotted. A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. The radiation emitted by a black body in thermal equilibrium with its environment is called black-body radiation. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U V ∝ T 4 and pressure P = 1 3(U V) . Show that the factor by which this radiation shield reduces the rate of cooling of the body (consider space between spheres evacuated, with no thermal conduction losses) is given by the following A spherical black body has a radius R and steady surface temperature T, heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. the - 54640365 To analyze the relationship between the rate of cooling $$R$$R, power emitted $$P$$P, and the radius $$r$$r of a solid spherical black body, we can follow these steps: Nov 9, 2021 · A spherical black body of radius r radiates power P, and its rate of cooling is R (i)P prop r (i - YouTube May 13, 2025 · A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. What Apr 4, 2018 · A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U/v ∝ T4 and pressure p = 1/3 (U/V). Oct 31, 2018 · Consider a spherical shell of radius ii at temperature T. (G = universal constant of gravitational, M = mass of the earth and g= acceleration due to gravity) Watch solution Dec 11, 2019 · A spherical black body of radius r radiates power P, and its rate of cooling is R. View Solution Explanation: To solve this problem, we need to understand the relationship between the power radiated by a black body and its radius, as well as the rate of cooling. (iii) Compare these results with those for an interplanetary \chondrule" in the form of a spherical, perfectly con-ducting black-body with a radius of R = 0:1 cm, moving in a circular orbit around the sun with a radius equal to the eart Solution: (i) The radiation received per second by the earth from the sun is approximately R2 A spherical black body has a luminosity L, radius R and temperature T. Sep 7, 2022 · A spherical black body with radius \ ( 12 \mathrm {~cm} \) radiates \ ( 450 \mathrm {~W} \) power at \ ( 500 \mathrm {~K} \). Another spherical black body of radius r/2 and at temperature T1 emits a power of P1. Let the surrounding temperature be To. , over a wide range of Mach (M ) number and Knudsen (Kn ) numbers (and A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. T ∝ e 3 R C. T Solution For A spherical black body of radius r radiates power P and its rate of cooling is R, where : (i) P∝r (ii) P∝r2 (iii) R∝r2 (iv) R∝r1 (1) (i) A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. Calculate electric field at distance r when (i) r<r1 , (ii) r1<r<r2 and (iii) r>r2. Radiated Power from Blackbody When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. The radiation emitted by another black body of same material but of double the radius and half of the temperature as the initial one, will have power A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. SUD 0. 06 User A solid spherical black body of radius r and uniform mass distribution is in free space. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U V ∝ T 4 and pressure P = 1 3(U V). If the radius were halved and the temperature doubled, the power radiated in watt would be: The correct answer is The power at which the body radiates is directly proportional to area A spherical black body has a radius R and steady surface temperature T, heat sources in it ensure the heat evolution at a constant rate and distributed uniformly over its volume. A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. According to the Stefan-Boltzmann law, the power radiated by a black body is proportional to the surface area, which is proportional to the square of the radius (P ∝ r2). If the radius were halved and the temperature doubled, the power radiated in watt would be A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. Q. Heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. If the radius were halved and the temperature doubled, the power radiated in watt would be: Two spherical black-bodies A and B, having radii r A and r B , where r B = 2 r A emit radiations with peak intensities at wavelengths 400 n m and 800 n m respectively. Calculate electric field at distance r when (i) r <r1 , (ii) r1 <r <r2 and (iii) r> r2. Dec 29, 2018 · Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t°C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is In many ways, a black hole acts like an ideal black body, as it reflects no light. The radius of the sun is R , the earth is situated a distance 'd' from the sun. Nov 9, 2021 · A spherical black body of radius r radiates power P, and its rate of cooling is R (i)P prop r (i - YouTube 69. P = σ A T 4 Substituting the formula for area in the above equation P = 4 σ π R 2 T 4 A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. and that those bodies orbit their common center of mass. black on both sides. In terms of L, what is the luminosity of a spherical black body of radius R/2 and temperature 7? A body of mass m is raised to a height 10 R from the surface of the earth, where R is the radius of the earth. The factor by which this radiation shield reduces the rate of cooling of the body (consider space between spheres evacuated, with no thermal conduction losses) is given by the following expression Solution For A spherical black body of radius r radiates power P and its rate of cooling is R, where : (i) P∝r (ii) P∝r2 (iii) R∝r2 (iv) R∝r1 (1) (i) A thin spherical conducting shell of radius r1 carries a charge Q. (Stefan's constant = sigma , Wien's constant =b , speed of light =c ) If the Jan 20, 2025 · Solution For A 10 cm radius, spherical black body emits 500 watts of power at 600 K . If the radius is doubled and the temperature is halved then the radiative power will be. Jul 31, 2022 · A spherical black body of radius r radiates powerand its rate of cooling is R. Dec 17, 2022 · A spherical black body of radius r at absolute temperature t is surrounded by a thin spherical and concentric shell of radius r, black on both sides. Find the increase in potential energy. and uniform mass distribution is in free space. a and b are numerical coefficient A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. What would be the new steady surface temperature of the object if the radius is decreased by half? A solid spherical black body of radius r. P = σ A T 4 Substituting the formula for area in the above equation P = 4 σ π R 2 T 4 X and Y are two spherical black-body radiators. T Assuming the sun to be a spherical body of radius R at a temperature T K, evaluate the total radiant power incident on earth. Find the ratio of time of cooling of black body of radius r1 to the time of cooling of the other body to the same lower temperature. (r is the distance between the sun and the earth, r0 is the radius of earth and σ is stefans constant) : Answer to X and Y are two spherical black-body radiators that emit the same total power. It emits power 'P' and its rate of colling is R then - A R P a p2 B RPar CRPa 1/p2 DRPC The assumed data from the question are Sun is assumed to be a spherical body of the radius, R Distance between the sun and the earth, r Radius of the earth, r 0 Assuming the sun as the spherical black body, Stefan’s law is applicable to it. If the radius were halved and the temperature doubled, the power radiated in watt would be: A spherical black body of radius r radiates a power P at temperature T. From the above question, we are given that the radius of the spherical block is r and it is radiating the power is P. The factor by which this radiation shield reduces the rate of cooling of the body ( consider space between spheres evacuated, with no thermal conduction losses) is given by the following Click here:point_up_2:to get an answer to your question :writing_hand:a spherical solid black body of radius r radiates power h and its rate of A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. The factor by which this radiation shield reduces the rate of cooling of the body ( consider space between spheres evacuated, with no thermal conduction losses) is given by the following expression: aR2/(R2+br2). When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant. (a) P ∝ r (b) P ∝ r2 (c) R ∝ r2 (d) R ∝ 1/r NTA Abhyas 2022: A spherical black body with a radius of 12cm radiates 450W power at 500K . X has a radius R and emits half the total power of Y. Treat the sun as perfectly black body which radiates power at constant rate fill till its store of hydrogen gets exhausted. e. Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t∘C, the power received by a unit surface, (normal to the incident rays) at distance R from the centre of the Sun is:- Answer to X and Y are two spherical black-body radiators that emit the same total power. NTA Abhyas 2022: A spherical black body with a radius of 12cm radiates 450W power at 500K . A spherical black body of radius r at absolute temperature T is surrounded by a thin spher-ical and concentric shell of radius R, black on both sides. in a uniform magnetic field, then 1) rd>rp ; ra=rd 2) rp>ra ; ra=rd 3) rd>rp ; ra=rp 4) ra>rd>rp. It emits power P and its rate of cooling is R, then: Consider a spherical shell of radius R at temperature T. If the radius is halved and \ ( \mathrm {P} \) temperature is doubled A spherical black body with a radius of 20 cm radiates 440 W power at 500 K. Jul 18, 2019 · Consider a spherical shell of radius R at temperature T. (r is the distance between the sun and the earth, R 0 is the radius of Earth and σ is Stefan’s Constant) A spherical black body of radius r radiated power P, and its rate of cooling is R View Solution Q 5 The total radiative power emitted by spherical blackbody with radius R and temperature T is P. Concentric with it is another thin metallic spherical shell of radius r2(2> 1). 20 (i. Jul 21, 2023 · Step by step video & image solution for A spherical black body of radius r radiates power P, and its rate of cooling is R (i)P prop r (ii)P prop r^ (2) (iii)R prop r^ (2) (iv)R prop (1)/ (r) by Physics experts to help you in doubts & scoring excellent marks in Class 12 exams. Show that the factor by which this radiation shield reduces the rate of cooling of the body (consider space between spheres evacuated, with no thermal conduction losses) is given by the following A solid spherical black body of radius r and uniform mass distribution is in the free space. 900 C. Then (i) P ∝ r (ii) P ∝ r^2more Jul 5, 2020 · Consider a spherical shell of radius R at temperature T. According to Stefan's law, the power radiated by a black body is proportional to the fourth power of its temperature. If the radius were halved, and the temperature doubled, th A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. Mar 26, 2025 · However, to compute the total power, we need to make an assumption that the energy radiates through a spherical surface enclosing the star, so that the surface area is A = 4 π R 2, where R is its radius. ← Prev Question Next Question → 0 votes 15. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = V U ∝ T 4 and pressure p = 31(V U) If the shell now undergoes an adiabatic expansion, the relation between T and R is Dec 11, 2019 · Correct Answer is: (b) (T2 / T1)2 For spherical black body of radius r and absolute temperature T, the power radiated = (4πr2) (σT4). The coordinate surfaces of the cylindrical coordinates (ρ, φ, z). The factor by which this radiation shield reduces the rate of cooling of the body ( consider space between spheres evacuated, with no thermal conduction losses) is given by the following Sep 12, 2025 · A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. Physics 303 November 25 and December 2, 2014 1. T ∝ 1 R D. [15] Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. If the radius is halved and the temperature doubled, the power radiated in watt would be Solution For 13. as shown. Young 14th Edition Instant Answer Solved by Expert Aakash Goyal Step 1 May 13, 2025 · A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and concentric shell of radius R, black on both sides. Concentric with it is another thin metallic spherical shell of radius r2. Jul 5, 2020 · Consider a spherical shell of radius R at temperature T. , it absorbs 20% of radiation), and the heat capacity of the thin shell is negligible. 1800 B.

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