Q67 / 90 · JEE Main 2012 (19 May Online) · Physics

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: An inventor claims to have constructed an engine that has an efficiency of $30 \%$ when operated between the boiling and freezing points of water. This is not possible. Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

  • A
    Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
  • B
    Statement 1 is true, Statement 2 is false.
  • C
    Statement 1 is false, Statement 2 is true.
  • Correct answer
    D
    Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution

According to Carnot's theorem - no heat engine working between two given temperatures of source and sink can be more efficient than a perfectly reversible engine i.e. Carnot engine working between the same two temperatures. Efficiency of Carnot's engine, $n=1-\frac{T_2}{T_1}$ where, $T_1=$ temperature of source $T_2=$ temperature of sink

Hence, the correct answer is option: 'D'.

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