26. The temperature of source and sink of a heat engine are 127°C and 27°C respectively. An inventor claims its efficiency to be 26%, then :
    

1. 1. it is impossible ​

   
   
   

   2. ​it is possible with high probability

   
   
   

   3. it is possible with low probability ​

   
   
   

   4. data are insufficient.

   
   
   

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1. View Hint View Answer Discuss in Forum

   η = 1 -	300	=	100	=	1
   	400		400		4

   
   

   η =	1	× 100 = 25%
   	4

   
   Hence, it is not possible to have efficiency more than 25%.

   Correct Option: A

   η = 1 -	300	=	100	=	1
   	400		400		4

   
   

   η =	1	× 100 = 25%
   	4

   
   Hence, it is not possible to have efficiency more than 25%.

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27. An ideal gas heat engine operates in a Carnot cycle between 227°C and 127°C. It absorbs 6 kcal at the higher temperature. The amount of heat (in kcal) converted into work is equal to​​
    

1. 1. ​1.2

   
   
   

   2. 4.8 ​

   
   
   

   3. 3.5

   
   
   

   4. 1.6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Efficiency =	T1 - T2
   	T1

   
   T₁ = 227 + 273 = 500 K ​
   T₂ = 127 + 273 = 400 K
   

   η =	500 - 400	=	1
   	500		5

   
   

   Hence, output work = η × Heat input =	1	× 6 = 1.2 kcal
   	5

   Correct Option: A

   Efficiency =	T1 - T2
   	T1

   
   T₁ = 227 + 273 = 500 K ​
   T₂ = 127 + 273 = 400 K
   

   η =	500 - 400	=	1
   	500		5

   
   

   Hence, output work = η × Heat input =	1	× 6 = 1.2 kcal
   	5

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28. A Carnot engine whose efficiency is 50% has an exhaust temperature of 500 K. If the efficiency is to be 60% with the same intake temperature, the exhaust temperature must be (in K)​​
    

1. 1. ​800

   
   
   

   2. 200

   
   
   

   3. 400

   
   
   

   4. 600

   
   
   

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1. View Hint View Answer Discuss in Forum

   η = 1 -	T2	or	50	= 1 -	500
   	T1		100		T1

   
   ⇒ T₁ = 1000 K
   

   Also ,	60	= 1 -	T2	⇒ T2 = 400 K
   	100		1000

   
   

   Correct Option: C

   η = 1 -	T2	or	50	= 1 -	500
   	T1		100		T1

   
   ⇒ T₁ = 1000 K
   

   Also ,	60	= 1 -	T2	⇒ T2 = 400 K
   	100		1000

   
   

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29. An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 × 10⁴ cals of heat at higher temperature. Amount of heat converted to work is​​
    

1. 1. 4.8 × 10⁴ cals

   
   
   

   2. 6 × 10⁴ cals

   
   
   

   3. 2.4 × 10⁴ cals

   
   
   

   4. 1.2 × 10⁴ cals

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that efficiency of carnot engine
   

   = 1 -	T2	= 1 -	400	=	1
   	T1		500		5

   
   [∵ T₁ = (273 + 227)K = 500 K ​and T₂ = (273 + 127)K = 400 K] ​
   

   Efficiency of Heat engine =	Work output
   	Heat input

   
   

   or ,	1	=	Work output
   	5		6 × 104

   
   ⇒ work output = 1.2 × 10⁴ cal
   

   Correct Option: D

   We know that efficiency of carnot engine
   

   = 1 -	T2	= 1 -	400	=	1
   	T1		500		5

   
   [∵ T₁ = (273 + 227)K = 500 K ​and T₂ = (273 + 127)K = 400 K] ​
   

   Efficiency of Heat engine =	Work output
   	Heat input

   
   

   or ,	1	=	Work output
   	5		6 × 104

   
   ⇒ work output = 1.2 × 10⁴ cal
   

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30. ​Which of the following processes is reversible?​​​
    

1. 1. Transfer of heat by conduction ​

   
   
   

   2. Transfer of heat by radiation

   
   
   

   3. Isothermal compression

   
   
   

   4. ​Electrical heating of a nichrome wire

   
   
   

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1. View Hint View Answer Discuss in Forum

   For a process to be reversible, it must be quasi-static. For quasi static process, all changes take place infinitely slowly. Isothermal process occur very slowly so it is quasi-static and hence it is reversible.

   Correct Option: C

   For a process to be reversible, it must be quasi-static. For quasi static process, all changes take place infinitely slowly. Isothermal process occur very slowly so it is quasi-static and hence it is reversible.

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