Physics · Thermal Properties Of Matter · NEET
Radiated power depends on the surface area, not on the radius directly. For a sphere the area is A = 4 pi r squared. Since power P = sigma e A T to the fourth, and A carries r squared, the power is proportional to r squared. So doubling the radius makes the area 4 times bigger and the power 4 times bigger (temperature unchanged).
No. Handle each factor with its correct power. Radius halved: (1/2) squared = 1/4. Temperature doubled: (2) to the fourth = 16. Multiply them: 1/4 times 16 = 4. So the power becomes 4 times larger, not the same. The strong T to the fourth term wins over the r squared term.
It is r squared T to the fourth for a sphere. The r squared comes from the area (4 pi r squared) and the T to the fourth comes from the Stefan-Boltzmann law. Write P proportional to r squared T to the fourth and never mix them up.
For NEET problems emissivity e is treated as a constant property of the surface, so it cancels out in a ratio. When you take P' over P, sigma, e, and 4 pi all cancel and you are left only with (r' over r) squared times (T' over T) to the fourth.
Then the r factor is 1, so the ratio is just (T' over T) to the fourth. For example, if temperature is doubled, power becomes 2 to the fourth = 16 times larger. This is the pure Stefan-Boltzmann result E proportional to T to the fourth.
A spherical black body of radius 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated (in watt) would be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
P = sigma e (4 pi r squared) T to the fourth, where sigma is the Stefan-Boltzmann constant, e is emissivity, r is radius and T is absolute temperature in kelvin. In short, P is proportional to r squared T to the fourth.
This comes from the Stefan-Boltzmann law, which states the energy radiated per unit area per second is proportional to T to the fourth. It is an experimental law later proved by Boltzmann.
Always kelvin. The T to the fourth law uses absolute temperature. Convert celsius to kelvin by adding 273 before you take the fourth power, otherwise the ratio is wrong.
Power becomes 4 times larger, because area is proportional to r squared and 2 squared = 4. Temperature stays the same, so only the r squared factor acts.
No. For a black body e = 1, but the dependence P proportional to r squared T to the fourth is the same. For a grey body e is a constant less than 1 that cancels in ratio problems.
