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JEE Advanced Physics Thermal Properties of Matter 2021 JEE Advanced 2021 (Paper 1)

JEE Advanced Physics Question (2021) — Solution

Question

A small object is placed at the centre of a large evacuated hollow spherical container. Assume the container is maintained at  0   K . At time  t = 0 , the temperature of the object is  200   K . The temperature of the object becomes  100   K  at  t = t 1  and  50   K  at  t = t 2 . Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio  t 2 t 1  _________ .

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

Step-by-step solution

Using Stefan-Boltzmann law, P = d Q d t = σ e A T B 4 − T S 4 ,             ∵ T S = 0   K So, d Q d t = e σ A T 4 ,         consider ,   T = T B also,     d Q d t = - m s d T d t = e σ A T 4 - ∫ 200 T d T T 4 = ∫ 0 t k d t ,   where   k = σ A m s ⇒ 1 T 3 − 1 200 3 = 3 k t Now,  For case  1 1 100 3 − 1 200 3 = 3 k t 1               . . . 1 For case  2 1 50 3 − 1 200 3 = 3 k t 2               . . . 2 Divide equation 2 by  1 , 1 50 3 − 1 200 3 1 100 3 − 1 200 3 = t 2 t 1 So,  t 2 t 1 = 9

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