11. Certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54°C in the next 5 minutes. The temperature of the surroundings is:

1. 1. 45°C

   
   
   

   2. 20°C

   
   
   

   3. 42°C

   
   
   

   4. 10°C

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the temperature of surroundings be θ₀
   By Newton's law of cooling
   

   θ1 - θ2	= k		θ1 + θ2	- θ0
   t			2

   
   

   ⇒	70 - 60	= k		70 + 60	- θ0
   	5			2

   
   ⇒ 2 = k [65 – θ₀] ...(i)
   

   Similarly,	60 - 54	= k		60 + 54	- θ0
   	5			2

   
   

   ⇒	6	= k[57 - θ0] .............(ii)
   	5

   
   By dividing (i) by (ii) we have
   

   	10	=	65 - θ0	⇒ θ0 = 45°
   	6		57 - θ0

   Correct Option: A

   Let the temperature of surroundings be θ₀
   By Newton's law of cooling
   

   θ1 - θ2	= k		θ1 + θ2	- θ0
   t			2

   
   

   ⇒	70 - 60	= k		70 + 60	- θ0
   	5			2

   
   ⇒ 2 = k [65 – θ₀] ...(i)
   

   Similarly,	60 - 54	= k		60 + 54	- θ0
   	5			2

   
   

   ⇒	6	= k[57 - θ0] .............(ii)
   	5

   
   By dividing (i) by (ii) we have
   

   	10	=	65 - θ0	⇒ θ0 = 45°
   	6		57 - θ0

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12. If λ_m denotes the wavelength at which the radiative emission from a black body at a temperature T K is maximum, then

1. 1. λ_m ∝ T^-1

   
   
   

   2. λ_m ∝ T⁴

   
   
   

   3. λ_m is independent of T

   
   
   

   4. λ_m ∝ T

   
   
   

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1. View Hint View Answer Discuss in Forum

   From Wein’s displacement law
   λ_mT = constant
   ⇒ λ_m ∝ T^–1

   Correct Option: A

   From Wein’s displacement law
   λ_mT = constant
   ⇒ λ_m ∝ T^–1

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13. Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K, respectively. The equivalent thermal conductivity of the slab is

1. 1. 4	K
      3

   
   
   

   2. 2	K
      3

   
   
   

   3. √3 K

   
   
   

   4. 3K

   
   
   

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1. View Hint View Answer Discuss in Forum

   In series, equivalent thermal conductivity
   

   Keq =	2K1K2
   	K1 + K2

   
   

   or, Keq =	2 × K × 2K	=	4	K
   	K + 2K		3

   Correct Option: A

   In series, equivalent thermal conductivity
   

   Keq =	2K1K2
   	K1 + K2

   
   

   or, Keq =	2 × K × 2K	=	4	K
   	K + 2K		3

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14. Wien's law is concerned with
    

1. 1. relation between emissivity and absorptivity of a radiating surface

   
   
   

   2. total radiation, emitted by a hot surface

   
   
   

   3. an expression for spectral distribution of energy of a radiation from any source

   
   
   

   4. a relation between the temperature of a black body and the wavelength at which there is maximum radiant energy per unit wavelength

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Wein's displacement law, product of wavelength belonging to maximum intensity and temperature is constant i.e.,  λ_mT = constant.

   Correct Option: D

   According to Wein's displacement law, product of wavelength belonging to maximum intensity and temperature is constant i.e.,  λ_mT = constant.

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15. Two rods of thermal conductivities K₁ and K₂, cross-sections A₁ and A₂ and specific heats S₁ and S₂ are of equal lengths. The temperatures of two ends of each rod are T₁ and T₂. The rate of flow of heat at the steady state will be equal if

1. 1. K1	=	K2
      A1S1		A2S2

   
   
   

   2. K₁A₁ = K₂A₂

   
   
   

   3. K₁S₁ = K₂S₂

   
   
   

   4. A₁S₁ = A₂S₂

   
   
   

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1. View Hint View Answer Discuss in Forum

   Rate of heat flow for one rod =	K1A1(T1 - T2)	(d → Length)
   	d

   
   Rate of heat flow for other rod
   

   =	K2A2(T1 - T2)
   	d

   
   

   In steady state,	K1A1(T1 - T2)
   	d

   
   

   =	K2A2(T1 - T2)	⇒ K1A1 = K2A2
   	d

   Correct Option: B

   Rate of heat flow for one rod =	K1A1(T1 - T2)	(d → Length)
   	d

   
   Rate of heat flow for other rod
   

   =	K2A2(T1 - T2)
   	d

   
   

   In steady state,	K1A1(T1 - T2)
   	d

   
   

   =	K2A2(T1 - T2)	⇒ K1A1 = K2A2
   	d

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