Home
Class 11
PHYSICS
The earth receives solor radiation at a ...

The earth receives solor radiation at a rate of `8.2Jcm^(-2)min^(-1)` . Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is `0.53^(@)` and the stefan constant `sigma=5.67xx10^(-s)Wm^(-2)K^(-4)` .

Text Solution

Verified by Experts


Let surface temperature of sun be `T_s`. Then total energy radiated by sun per second is given as
`E=sigmaT_s^4.(4piR_s^2)`
Energy reveibed by earth per second per square metre is give as
`(dQ)/(dt)=(E)/(4piR_(es)^2)=sigmaT_s^4((R_s)/(R_(es)^(2)))` ..(i)
It is given that angular diameter of sun as observed from earth is 32 min of arc. Thus. we have
`(R_s)/(R_(es))=(theta)/(2)=(1)/(2)xx(32)/(60)=4.655xx10^-3`
and it is given that `(dQ)/(dt)=(2xx4.2xx10^4)/(60) J//s-m^(2)` ....(ii)
Now from Eqs. (i) and (ii) we have
`5.67xx10^-8xxT_s^4xx[4.655xx10^-3]^2=(2xx4.2xx10^4)/(60)`
or `T_s^4=(2xx4.2xx10^4)/(60xx5.67xx10^-8xx(4.655xx10^-3)^2)`
or `T_s^4=1.14xx10^(15)`
or `T_s=5810.67K`
Promotional Banner

Topper's Solved these Questions

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 1.1|23 Videos

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 1.2|22 Videos

  • BASIC MATHEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.6|20 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS ENGLISH|Exercise INTEGER_TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Calculate the temperature at which a perfect black body radiates at the rate of 1 W cm^(-2) , value of Stefan's constant, sigma = 5.67 xx 10^(-5) W m^(-2) K^(-8)

Assume that the total surface area of a human body is 1.6m^(2) and that it radiates like an ideal radiator. Calculate the amount of energy radiates per second by the body if the body temperature is 37^(@)C . Stefan constant sigma is 6.0xx10^(-8)Wm^(-2)K^(-4) .

Calculate the effective temperature of the sun . Given that the wavelength of maximum energy in the solar spectrum is 475 mm and Wien's constant is 2.898xx10^(-3) mK.

The earth receives solar energy at the rate of 2 cal Cm^(-2) per minute. Assuming theradiation tobeblack body in character, estimate the surface temperature of the sun. Given that sigma =5.67 xx10^(-8) Wm^(-2)K^(-4) and angular diameter of the sun =32 minute of arc.

Calculate the colour temperautre of the sun assuming that the wavelength of maximum energy in the solar spectrum is 0.48 micron and the Wien's constant is 0.228xx10^(-2) mK.

The sun radiates energy at the rate of 6.4xx10^(7)Wm^(-2) . Calculate its temperature assuming it to be a black body.

If each square cm of the sun's surface radiates energy at the rate of 6.42xx10^(3) Js^(-1) cm^(-2) , calculate the temperature of the sun's surface in degree celsius, assuming Stefan's law applies to the radiation. (Stefan's constant = 5.67xx10^(-8)Wm^(-2)K^(-4) )

The sun radiates maximum energy at wavelength 4753Å . The surface temperature of the sun if b=2.888xx10^(-3)mK , is

An electric heater emits 1000W of thermal radiation. The coil has a surface area of 0.02m^(2) . Assuming that the coil radiates like a blackbody, Find its temperature. sigma=6.0xx10^(-8)Wm^(-2)K^(-2) .

A body at a temperature of 727^(@)C and having surface area 5 cm^(2) , radiations 300 J of energy each minute. The emissivity is(Given Boltzmann constant =5.67xx10^(-8) Wm^(-2)K^(-4)