41. When a system executes an irreversible cycle
    

1. 1. ∮	δQ	< 0
      	T

      
      

   
   
   

   2. ∮ dS > 0
      

   
   
   

   3. ∮	dQ	= 0
      	T

      
      

   
   
   

   4. ∮	δQ	> 0
      	T

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∮	δQ	< 0 clausius inequality
   	T

   
   

   Correct Option: A

   ∮	δQ	< 0 clausius inequality
   	T

   
   

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42. Any thermodynamic cycle operating between two temperature limits is reversible if the product of the efficiency when operating as a heat engine and the COP when operating as a refrigerator is equal to l.

1. 1. True

   
   
   

   2. True/False

   
   
   

   3. False

   
   
   

   4. Both

   
   
   

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1. View Hint View Answer Discuss in Forum

   False
   η_HE × COP_HP = 1
   Where , HP = Heat pump
   

   Correct Option: C

   False
   η_HE × COP_HP = 1
   Where , HP = Heat pump
   

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43. Figure below shows a reversible heat engine ER having heat interactions with three constant temperature systems. Calculate the thermal efficiency of the heat engine
    
    

1. 1. 60%

   
   
   

   2. 30%

   
   
   

   3. 20%

   
   
   

   4. 5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Q₁ + Q₂ - Q₃ = W .... (i)
   

   	Q1	+	Q2	-	Q3	= 0 ...... (ii)
   	1000		500		300

   
   From equation (ii) , we have
   

   	Q1	+	Q2	-	Q3	= 0
   	1000		500		300

   
   ⇒ Q₃ = 60 kJ
   W ⇒ 100 + 50 - 60 = 90 kJ
   

   η =	W	=	90	= 60%
   	Q1 + Q2		150

   
   

   Correct Option: A

   Q₁ + Q₂ - Q₃ = W .... (i)
   

   	Q1	+	Q2	-	Q3	= 0 ...... (ii)
   	1000		500		300

   
   From equation (ii) , we have
   

   	Q1	+	Q2	-	Q3	= 0
   	1000		500		300

   
   ⇒ Q₃ = 60 kJ
   W ⇒ 100 + 50 - 60 = 90 kJ
   

   η =	W	=	90	= 60%
   	Q1 + Q2		150

   
   

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44. A solar energy based heat engine which receives 80 kJ of heat at 100°C and rejects 70 kJ of heat to the ambient at 30°C is to be designed. The thermal efficiency of the heat engine is
    

1. 1. 70%
      

   
   
   

   2. 18.8%
      

   
   
   

   3. 12.5%
      

   
   
   

   4. Indetermine

   
   
   

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1. View Hint View Answer Discuss in Forum

   ηth =	( 80 - 70 )	× 100 =	1	× 100 = 12.5%
   	80		8

   Correct Option: C

   ηth =	( 80 - 70 )	× 100 =	1	× 100 = 12.5%
   	80		8

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45. For two cycles coupled in series, the topping cycle has an efficiency of 30% and the bottoming cycle has an efficiency of 20%. The overall combined cycle efficiency is
    

1. 1. 50%
      

   
   
   

   2. 44%
      

   
   
   

   3. 38%
      

   
   
   

   4. 55%

   
   
   

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1. View Hint View Answer Discuss in Forum

   η₀ = η₁ + η₂ - η₁η₂
   η₀ = 0.3 + 0.2 – (0.3) (0.2) = 0.44 = 44%

   Correct Option: B

   η₀ = η₁ + η₂ - η₁η₂
   η₀ = 0.3 + 0.2 – (0.3) (0.2) = 0.44 = 44%

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