Question:
Two spheres of the same material have radii $ 1 \,m $ and $ 4\, m $ and temperatures $ 4000\, K $ and $ 2000\, K $ respectively., The ratio of energy radiated per second by the first sphere to the second is
Two spheres of the same material have radii $ 1 \,m $ and $ 4\, m $ and temperatures $ 4000\, K $ and $ 2000\, K $ respectively., The ratio of energy radiated per second by the first sphere to the second is
Updated On: May 5, 2023
- $ 1 : 1 $
- $ 16 : 1 $
- $ 4 : 1 $
- $ 1 : 9 $
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The Correct Option is A
Solution and Explanation
Energy radiated per second by a body which has surface area $A$ at temperature $T$ is given by Stefan's law,
$E = \sigma AT^4$
Therefore
$\frac{E_{1}}{E_{2}} = \left(\frac{r_{1}}{r_{2}}\right)^{2}\left(\frac{T_{1}}{T_{2}}\right)^{4}$
$ = \left(\frac{1}{4}\right)^{2}\left(\frac{4000}{2000}\right)^{4}$
$ \frac{E_{1}}{E_{2}} = \frac{16}{16} = \frac{1}{1}$
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Concepts Used:
Radiation
Radiation is the energy or particles from a source that travels from one media to other. It travels through a medium after its emission from a source and is absorbed by matter.
Forms of Radiation:
- Particle Radiation includes the alpha (α), beta (β), and neutron radiations.
- Gravitational Radiation includes the radiation that takes the form of gravitational waves or as ripples in the curvature of space-time.
- Acoustic Radiation includes ultrasound, seismic and sound waves.
- Electromagnetic Radiation is inclusive of radio waves, gamma radiation (γ), x-rays, and visible light.
Types of Radiation:
- Ionizing Radiation - It carries more than 10 eV, that is enough to ionize atoms and molecules and break chemical bonds.
- Non-ionizing Radiation – It consists of alpha particles, beta particles, and gamma particles, whereas ionizing radiation consists of microwave radiation, infrared radiation and radio waves.
Read More: Types of Radiation