16. N molecules each of mass m of a gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of B type is v² and the mean square rectangular component of the velocity of A type is denoted by ω². Then ω²/v²

1. 1. 2

   
   
   

   2. 1

   
   
   

   3. 1/3

   
   
   

   4. 2/3

   
   
   

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   Mean kinetic energy of the two types of molecules should be equal. The mean square velocity of A type molecules = ω² + ω² + ω² = 3ω²
   

   Therefore,	1	m(3ω²) =	1	(2m)v²
   	2		2

   
   This gives ω²/v² = 2/3

   Correct Option: D

   Mean kinetic energy of the two types of molecules should be equal. The mean square velocity of A type molecules = ω² + ω² + ω² = 3ω²
   

   Therefore,	1	m(3ω²) =	1	(2m)v²
   	2		2

   
   This gives ω²/v² = 2/3

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17. The ratio of the specific heats C_p/C_v = γ in terms of degrees of freedom (n) is given by

1. 1. 	1 +	n
      		3

   
   
   

   2. 	1 +	2
      		3

   
   
   

   3. 	1 +	n
      		2

   
   
   

   4. 	1 +	1
      		n

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let ‘n’ be the degree of freedom
   

   γ =

   =

   n

   + 1

   R

   =

   1 +

   2

   Cp

   2

   n

   Cv

   n

   R

   2

   Correct Option: B

   Let ‘n’ be the degree of freedom
   

   γ =

   =

   n

   + 1

   R

   =

   1 +

   2

   Cp

   2

   n

   Cv

   n

   R

   2

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18. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0JK–1. If the speed of sound in this gas at NTP is 952 ms^–1, then the heat capacity at constant pressure is (Take gas constant R = 8.3 JK^–1 mol^–1)

1. 1. 7.5 JK^–1 mol^–1

   
   
   

   2. 7.0 JK^–1 mol^–1

   
   
   

   3. 8.5 JK^–1 mol^–1

   
   
   

   4. 8.0 JK^–1 mol^–1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Molar mass of the gas = 4g/mol
   Speed of sound
   

   V = √	γRT	⇒ 952 = √	γ × 3.3 × 273
   	m		4 × 10-3

   
   

   ⇒ γ = 1.6 =	16	=	8
   	10		5

   
   

   Also, γ =	CP	=	8
   	CV		5

   
   

   So, CP =	8 × 5	= 8JK–1mol–1 [CV = 5.0 JK–1 given]
   	CV

   Correct Option: D

   Molar mass of the gas = 4g/mol
   Speed of sound
   

   V = √	γRT	⇒ 952 = √	γ × 3.3 × 273
   	m		4 × 10-3

   
   

   ⇒ γ = 1.6 =	16	=	8
   	10		5

   
   

   Also, γ =	CP	=	8
   	CV		5

   
   

   So, CP =	8 × 5	= 8JK–1mol–1 [CV = 5.0 JK–1 given]
   	CV

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19. The mean free path of molecules of a gas, (radius ‘r’) is inversely proportional to :

1. 1. r³

   
   
   

   2. r²

   
   
   

   3. r

   
   
   

   4. √r

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mean free path λm =	1
   	√2πd²n

   
   where d = diameter of molecule and d = 2r
   

   ∴ λm ∝	1	e+jωT1
   	r²

   Correct Option: B

   Mean free path λm =	1
   	√2πd²n

   
   where d = diameter of molecule and d = 2r
   

   ∴ λm ∝	1	e+jωT1
   	r²

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20. The amount of heat energy required to raise the temperature of 1g of Helium at NTP, from T₁K to T₂K is

1. 1. 3	NakB(T2 – T1)
      2

   
   
   

   2. 3	NakB(T2 – T1)
      4

   
   
   

   3. 3	NakB	T2
      4		T1

   
   
   

   4. 3	NakB(T2 – T1)
      8

   
   
   

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1. View Hint View Answer Discuss in Forum

   From first law of thermodynamics
   

   ∆Q = ∆U + ∆W =	3	.	1	R(T2 - T1 + 0
   	2		4

   
   

   =	3	NaKB(T2 - T1)[∵ K =	R	]
   	8		N

   Correct Option: D

   From first law of thermodynamics
   

   ∆Q = ∆U + ∆W =	3	.	1	R(T2 - T1 + 0
   	2		4

   
   

   =	3	NaKB(T2 - T1)[∵ K =	R	]
   	8		N

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