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Efficiency of a Carnot engine

  • A.depends on the nature of the working substance
  • B.does not depend on the nature of the working substance
  • C.depends only on the temperature of the source \(T^{1}\)
  • D.depends only on the temperature of the sink \(T^{2}\)
  • E.does not depend on both temperature of the source\(T^{1}\) and temperature of the sink \(T^{2}\)

Answer: B

The efficiency does not depend on the nature of the working substance.

Carnot efficiency is \(\eta = 1 - \frac{T_{2}}{T_{1}}\), where \(T_{1}\) is the source and \(T_{2}\) the sink temperature. Only these two temperatures appear, which is Carnot's theorem: every reversible engine working between the same two reservoirs has the same efficiency, whatever it uses.

Because both temperatures enter the formula, it depends on the source and on the sink together, not on one alone, and it certainly depends on them, which rules out the last option.

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