26. A black body is at temperature of 500 K. It emits energy at rate which is proportional to

1. 1. (500)⁴

   
   
   

   2. (500)³

   
   
   

   3. (500)²

   
   
   

   4. 500

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Stefan's Law E = σeAT⁴;
   E ∝ T⁴ ; so, E ∝ (500)⁴

   Correct Option: A

   According to Stefan's Law E = σeAT⁴;
   E ∝ T⁴ ; so, E ∝ (500)⁴

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27. A beaker full of hot water is kept in a room. If it cools from 80°C to 75°C in t₁ minutes, from 75° C to 70°C in t₂ minutes and from 70°C to 65°C in t₃ minutes, then

1. 1. t₁ = t₂ = t₃

   
   
   

   2. t₁ < t₂ = t₃

   
   
   

   3. t₁ < t₂ < t₃

   
   
   

   4. t₁ > t₂ > t₃

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let θ₀ be the temperature of the surrounding. Then
   

   	80 - 75	= k		80 + 75	- θ0
   	t1			2

   
   

   Or,	5	k(77.5 - θ0)
   	t1

   
   

   Or, t1 =	5	..........(i)
   	k(77.5 - θ0)

   
   

   Similarly, t2 =	5	..........(ii)
   	k(72.5 - θ0)

   
   

   and, t3 =	5	..........(iii)
   	k(67.5 - θ0)

   
   From (1), (2) & (3), it is obvious that
   t₁ < t₂ < t₃

   Correct Option: C

   Let θ₀ be the temperature of the surrounding. Then
   

   	80 - 75	= k		80 + 75	- θ0
   	t1			2

   
   

   Or,	5	k(77.5 - θ0)
   	t1

   
   

   Or, t1 =	5	..........(i)
   	k(77.5 - θ0)

   
   

   Similarly, t2 =	5	..........(ii)
   	k(72.5 - θ0)

   
   

   and, t3 =	5	..........(iii)
   	k(67.5 - θ0)

   
   From (1), (2) & (3), it is obvious that
   t₁ < t₂ < t₃

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