Question

If the temperature of a black body is increased by 50% then the amount of radiation emitted by it will

• A. decrease by 50%
• B. increase by 50%
• C. increase by 400%
• D. decrease by 400%

Answer 1

Answer: (C)

increase by 400%

Given,

$\frac{\Delta T}{T}=50$%

$\frac{\Delta T}{T}=\frac{50}{100}=\frac{1}{2}$

By Stefan's constant,

$E=\sigma eA{T}^4$

$E\propto T^4$

Take log both side,

$ln\left(E\right)=ln\left(T^4\right)$

$\frac{\Delta E}{E}=4\frac{\Delta T}{T}$

$\frac{\Delta E}{E}\times 100$%$=4\times \frac{1}{2}\times 100$%

$\frac{\Delta E}{E}\times 100$%$=400$%

The amount of radiation emitted is increased by $400$%.

The correct option is C.