36. A refrigerator works between 4°C and 30°C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is :​(Take 1 cal = 4.2 joules)​​
    

1. 1. 2.365 W ​

   
   
   

   2. 23.65 W

   
   
   

   3. 236.5 W

   
   
   

   4. 2365 W

   
   
   

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1. View Hint View Answer Discuss in Forum

   Coefficient of performance of a refrigerator, β =	Q2	=	T2
   	W		T1 - T2

   
   (Where Q₂ is heat removed) ​
   Given : T₂ = 4°C = 4 + 273 = 277 k ​
   T₁ = 30°C = 30 + 273 = 303 k
   

   β =	600 × 4.2	=	277
   	W		303 - 277

   
   ⇒ W = 236.5 joule
   

   Power , P =	W	=	236.5 joule	= 236.5 watt
   	t		1 sec

   Correct Option: C

   Coefficient of performance of a refrigerator, β =	Q2	=	T2
   	W		T1 - T2

   
   (Where Q₂ is heat removed) ​
   Given : T₂ = 4°C = 4 + 273 = 277 k ​
   T₁ = 30°C = 30 + 273 = 303 k
   

   β =	600 × 4.2	=	277
   	W		303 - 277

   
   ⇒ W = 236.5 joule
   

   Power , P =	W	=	236.5 joule	= 236.5 watt
   	t		1 sec

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37. A carnot engine having an efficiency of	1	as heat engine, is used as a refrigerator.
    	10

    
    If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is :-​​​​
    

1. 1. 90 J

   
   
   

   2. 99 J

   
   
   

   3. 100 J

   
   
   

   4. 1 J

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given, efficiency of engine, η =	1
   	10

   
   work done on system  W = 10 J ​
   Coefficient of performance of refrigerator
   

   β =	Q2	=	1 - η	=	1 -	1	=		9		= 9
   						10			10
   	W		η			1			1
   						10			10

   
   Energy absorbed from reservoir ​Q₂ = βw ​
   Q₂ = 9 × 10 = 90 J​

   Correct Option: A

   Given, efficiency of engine, η =	1
   	10

   
   work done on system  W = 10 J ​
   Coefficient of performance of refrigerator
   

   β =	Q2	=	1 - η	=	1 -	1	=		9		= 9
   						10			10
   	W		η			1			1
   						10			10

   
   Energy absorbed from reservoir ​Q₂ = βw ​
   Q₂ = 9 × 10 = 90 J​

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38. At 27° C a gas is compressed suddenly such that its pressure becomes (1/8) of original pressure. Final temperature will be (γ = 5/3)​
    

1. 1. 420 K

   
   
   

   2. 300 K

   
   
   

   3. – 142°C

   
   
   

   4. 327°C

   
   
   

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1. View Hint View Answer Discuss in Forum

   T₁ ^γ P₁^{1 - γ} = T₂ ^γ P₂^{1 - γ}
   

   ⇒		T2		γ	=		P1		1 - γ
   		T1					P2

   
   

   ⇒ T2 = T1		P1		(1 - γ) / γ	= 300 × (8)–2 / 5 = 142°C
   		P2

   Correct Option: C

   T₁ ^γ P₁^{1 - γ} = T₂ ^γ P₂^{1 - γ}
   

   ⇒		T2		γ	=		P1		1 - γ
   		T1					P2

   
   

   ⇒ T2 = T1		P1		(1 - γ) / γ	= 300 × (8)–2 / 5 = 142°C
   		P2

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39. A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are
    
    P_A = 3 × 10⁴ Pa ​
    V_A = 2 × 10^-3 m³ ​
    P_B = 8 × 10⁴ Pa ​
    V_D = 5 × 10^-3 m³. ​
    In process AB, 600 J of heat is added to the system and in process BC, 200 J of heat is added to the system. The change in internal energy of the system in process AC would be​

1. 1. 560 J

   
   
   

   2. 800 J

   
   
   

   3. 600 J ​

   
   
   

   4. 640 J

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since AB is an isochoric process, so, no work is done. BC is isobaric process, ​
   ∴ W = P_B × (V_D – V_A) = 240 J
   ​∆Q = 600 + 200 = 800 J ​
   Using ∆Q = ∆U + ∆W ​
   ⇒ ∆U = ∆Q – ∆W = 800 – 240 = 560 J

   Correct Option: A

   Since AB is an isochoric process, so, no work is done. BC is isobaric process, ​
   ∴ W = P_B × (V_D – V_A) = 240 J
   ​∆Q = 600 + 200 = 800 J ​
   Using ∆Q = ∆U + ∆W ​
   ⇒ ∆U = ∆Q – ∆W = 800 – 240 = 560 J

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40. A thermodynamic system is taken from state A to B along ACB and is brought back to A along BDA  as shown in the PV diagram. The net work done during the complete cycle is given by the area​​​​
    

1. 1. P₁ACBP₂P₁

   
   
   

   2. ACBB'A'A

   
   
   

   3. ACBDA

   
   
   

   4. ADBB'A'A

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work done = Area under curve ACBDA

   Correct Option: C

   Work done = Area under curve ACBDA

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