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1. The order of magnitude of energy received from sun at earth surface is 10-1 joule/cm2-sec. Calculate the order of magnitude of total force due to solar
radiation on the earth (assumed perfectly absorbing) given earth’s diameter =107 meter. [ Hint P=E/C and F= P x4πr2] .Ans: 1.05x105N
2. Calculate the maximum amount of heat which may be lost per sec by radiation from a sphere of 10 cm in diameter at a temperature of 2270C when
placed in an enclosure at a temperature of 270C when placed in an enclosure at a temperature of 270C [σ=5.7 x 10-12 Watts cm-2(℃−1 )]
[Hint E= σ[T4 - 𝑻𝟒𝟎] and Q= Ex 4πr2] Ans. 23.3 Cal/sec.
3. Luminosity of Rigel star in orion constellation is 17000 times that of our sun. If the surface temperature of the sun is 6000 K , Calculate the
temperature of the star. [ Hint E= σT4 and
𝑬𝟏
𝑬𝟐
=
𝑻𝟒𝟏
𝑻𝟒𝟐
] Ans: 68520 K.
4. Two ideal black bodies A and B at temperature 2270C and 3270C respectively are placed in an evacuated enclosure whose walls are blackened and kept
𝝈(𝑻𝟒−𝑻𝟒)
𝑬
at 270C . Compare their rates of losses of heat. [Hint E= σ(T4 - 𝑻𝟒𝟎) , 𝑬𝟏 = 𝝈(𝑻𝟏𝟒−𝑻𝟎𝟒)] Ans : 544:1215
𝟐
𝟐
𝟎
5. A body of mass 10 gm is kept in an enclosure of temperature 270C. If the temperature of the body is 1270C, its specific heat is 0.2 kilo calorie per kg per
℃ and area of emitting surface of the body is 10-3 m2. Find out the rate of cooling of the body. [σ=5.72 x 10-8 Jm-2sec-1℃−4 ] [Hint: Q=Aσ(T4 - 𝑻𝟒𝟎 )𝒕 ,
𝐝𝐐
6.
7.
8.
9.
10.
𝒅𝑻
𝑨𝝈(𝑻𝟒 − 𝑻𝟒)
𝟎
= 𝑨𝝈(𝑻𝟒 − 𝑻𝟒𝟎 )𝒘𝒉𝒆𝒓𝒆 𝑸 = 𝒎𝒔𝒅𝑻 𝒂𝒏𝒅 𝒅𝒕 =
. Ans : 0.23Ksec-1]
𝐝𝐭
𝒎𝒔
A black body with initial temperature of 30000C is allowed to cool inside an evacuated enclosure surrounded by melting ice at the rate of 0.35 0C per
sec. If the mass, specific heat and surface area of the body are 32 gm , 0.10 cal/gm and 8 cm2 respectively. Calculate Stefan’s constant.[Hint Q=
𝝈(𝑻𝟒 − 𝑻𝟒𝟎 )𝑨 and Q=msΔθ imply 𝝈(𝑻𝟒 − 𝑻𝟒𝟎 )𝑨 = 𝒎𝒔𝜟𝜽.]
Calculate the energy radiated per minute of the filament of an incandescent lamp at 2000K if the surface area is 5x10-5m2 and its relative emittance
e=0.85 [ σ=5.7 x 10-8 MKS unit] [Hint E=σeT4 A] Ans: 2315 Joules.
Calculate the surface temperature of the sun.Given for solar radiations λm= 4753 A0 and Wien’s constant b= 2.898 x 10-3 meter-kelvin. [Hint
λmT=constant = 0.2898 x 10-2]. Ans: 6097K].
Find the pressure exerted by sunlight on earth’s surface if the value of solar constant is 2 cal/min-cm2. [Hint P=E/C and E = 2 cal/min-cm2.]
Calculate the average energy 𝐸̅ of an oscillator of frequency 0.6 x 1014 sec-1 at T= 1800K treating its as (i) classical oscillator (ii) Planck’s oscillator (iii)
ℎ𝜈
[Hint 𝐸̅ = 𝐾𝑇 (𝑐𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙) and 𝐸̅ = ℎ𝜈/𝑘𝑇 (planck’s) Ans: 2.48 x 10-20 joule), 1.o1 10-20 joules.
𝑒
−1
𝟖𝝅𝝂𝟐
11. Calculate the number of modes in a chamber of volume 50 cm3 in the frequency range 4x1014 and 4.01 x 1014 sec-1. Hint: modes per c.c., N= 𝒄𝟑 𝒅𝝂
where ν= 4x1014 sec-1 and dν=(4.01-4)x 1014 sec-1. Total mode = N x Volume (V). Ans: 7.5 1012. For wavelength range given we can use formula N=
𝟖𝝅
𝒅𝝀.
𝝀𝟒
12. A black body is placed in an evacuated enclosure whose walls are blackened and kept at 300k . Compare net amount of heat gained or lost by the body
𝝈(𝑻𝟒 −𝑻𝟒)
𝑬
(i) when its temperature is 600K and (ii) When its temperature is 100K .[Hint Use E= σ(T4 - 𝑻𝟒𝟎) , 𝑬𝟏 = 𝝈(𝑻𝟏𝟒 −𝑻𝟎𝟒) ] Ans: 243:16
𝟐
𝟐
𝟎
13. For a particular temperature the emissivity and absorption coefficient at wavelength 100A 0 for a body is 8 and 0.5 units respectively . Deduce the
𝒆
emissivity for a black-body at the same temperature and wavelength. [ Hint 𝝀 = 𝑬𝝀 ] 𝑨𝒏𝒔 ∶ 𝟏𝟔
𝒂𝝀
14. Find the energy radiated from 1 cm2 of a surface in 1 sec by a black-body if the minimum energy density corresponds to a wavelength of 4840 Å. Given
Wien’s constant b= 2.9 x 10-3 m-k and Stefan’s constant σ=5.67 x 10-8 W m-2K-4. Ans 7.3 x 107 Jm-2sec-1 or 7.3x103J cm-2 sec-1 ] [Hint :λmT= b and E=σT4]
15. Obtain an expressin for the wavelength corresponding to maximum energy of emission according to formula of planck.
16. From planck’s law deduce the value of ν corresponding to peak Eν , ν curve at 100K. In what spectral region does this frequency lie ?