text: # Choose the option that most accurately represents the following statement:A heat engine absorbs 1800 kJ of heat from a hot body and rejects 600 kJ of heat to a cold sink. What is the heat engine's efficiency?
  
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  UPSSSC JE Mechanical Official Paper (Held on 19 Dec 2021)
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  1. 33.37
  2. 66.67
  3. 100
  4. 50
  
  Option 2 : 66.67
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  CT 1: Ancient Indian History
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  ## Detailed Solution
  
  Concept:
  
  • Carnot engine is a theoretical engine that operates on an ideal theoretical cycle called the Carnot cycle
  • The efficiency of a heat engine is defined as the ratio of work output divided by heat input and is given by
  
  $$η = 1 - \frac{T_{2}}{T_{1}}$$ or $$η = 1 - \frac{Q_{2}}{Q_{1}}$$
  
  Where T2 =Temperature of the sink, T1= Temperature of the source, Q1 = Heat absorbed from the source, Q2= Heat rejected to the sink
  
  Calculation:
  
  Given:
  
  Q1 = 1800 kJ and Q2 = 600 kJ
  
  • The efficiency of the heat engine is given by
  
  $$\Rightarrow η = 1 - \frac{Q_{2}}{Q_{1}}$$
  
  Substituting the given values in the above equation
  
  $$\Rightarrow η = 1 - \frac{6000}{1800}=1-\frac{1}{3}=\frac23=0.67$$
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