Home
Class 12
PHYSICS
A sphere of 8cm radius behaves like a bl...

A sphere of `8cm` radius behaves like a black body. It is in thermal equilibrium with the surrounding and absorbs `10 W` of power radiated to it from surrounding. The temperature of the sphere (`sigma=5.67xx10^(-8)W//m^(2)K^(4)`) is approximately.

A

`160 K`

B

`217 K`

C

`283 K`

D

`347 K`

Text Solution

AI Generated Solution

To solve the problem, we need to find the temperature of a sphere that behaves like a black body, given that it absorbs 10 W of power from its surroundings. We will use the Stefan-Boltzmann law to relate the absorbed power to the temperature of the sphere. ### Step-by-step Solution: 1. **Understand the Given Information:** - The radius of the sphere \( r = 8 \text{ cm} = 0.08 \text{ m} \) (conversion from cm to m). - The power absorbed by the sphere \( P = 10 \text{ W} \). - The Stefan-Boltzmann constant \( \sigma = 5.67 \times 10^{-8} \text{ W/m}^2\text{K}^4 \). ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Calculate the amount of radiant energy from a black body at a temperature of (i) 27^(@) C (ii) 2727^(@) C. sigma = 5.67xx10^(-8)Wm^(-2)K^(-4) .

If the filament of a 100 W bulb has an area 0.25cm^2 and behaves as a perfect black body. Find the wavelength corresponding to the maximum in its energy distribution. Given that Stefan's constant is sigma=5.67xx10^(-8) J//m^(2)s K^(4) .

If the filament of a 100 W bulb has an area 0.25cm^2 and behaves as a perfect block body. Find the wavelength corresponding to the maximum in its energy distribution. Given that Stefan's constant is sigma=5.67xx10^(-8) J//m^(2)s K^(4) .

Ac cording to Stefan' law of radiation, a black body radiates energy sigma T^4 from its unit surface area every second where T is the surface temperature of the black body and sigma = 5.67 xx 10^(-8) W//m^2 K^4 is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius 0.5 m When detoneted, it reachs temperature of 10^6 K and can be treated as a black body. (a) Estimate the power it radiates. (b) if surrounding has water at 30^@C how much water can 10% of the energy produced evaporate in 1s ? [s_w = 4186.0 J//Kg K and L_(upsilon) = 22.6 xx 10^5 J//kg] (c ) If all this energy U is in the form of radiation, corresponding momentum is p = U//c. How much momentum per unit time does it impart on unit area at a distance of 1 km ?

One end of a rod of length 20cm is inserted in a furnace at 800K The sides of the rod are covered with an insulating material and the other end emits radiation like a black body. The temperature of this end is 750K in the steady state The temperature of the surrounding air is 300K Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod Stefan's constant sigma = 6.0 xx 10^(-8) W m^(-2) K^(-4) .

A spherical body of radius 10cm radiates 300 W at 227°C . If the radius is doubled and temperature is remain same, the power radiated will be

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) .

One end of a rod length 20cm is inserted in a furnace at 800K. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750K in the steady state. The temperature of the surrounding air is 300K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant sigma=6.0xx10^(-1)Wm^(-2)K^(-4) .

One end of a rod length 20cm is inserted in a furnace at 800K . The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750K in the steady state. The temperature of the surrounding air is 300K . Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant sigma=6.0xx10^(-1)Wm^(-2)K^(-4) .

A solid body X of very large heat capacity is kept in an atmosphere whose temperature is 300 K. The body X is connected to a rod of length 1 m and cross sectional area S, as shown in the figure. Thermal conductivity of rod AB is 0.0567W//mK . Assuming that there is no heat exchange with the surrounding except fom the end B of the rod i.e., neither by any surface of X nor by the curved surface of rod. The end B has emissivity e=0.8 . If the steady state temperature of the end B is 400 K then find the temperature of X in steady state. (Stefan constant sigma-5.67xx10^(-8)W//m^(2)K^(4) )