An engine operating between the boiling and freezing points of water will have 1. efficiency more than $27 \%$ 2. efficiency less than the efficiency a Carnot engine operating between the same two temperatures. 3. efficiency equal to $27 \%$ 4. efficiency less than $27 \%$

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Heat & Thermodynamics

An engine operating between the boiling and freezing points of water will have

efficiency more than $27%$
efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
efficiency equal to $27%$
efficiency less than $27%$

(A)2, 3 and 4 only
(B)2 and 3 only
(C)2 and 4 only✓ Correct
(D)1 and 2 only

Answer: (C)

Solution

The maximum efficiency for any engine operating between two temperatures is given by the Carnot efficiency:

η_{Carnot} = 1 - \frac{T _{cold}}{T _{hot}} = 1 - \frac{273}{373} = 0.268 = 26.8%

This is less than 27%. Any real engine operating between these temperatures will have efficiency less than or equal to the Carnot efficiency (statement 2 is correct). Since the Carnot efficiency itself is less than 27%, any real engine will also have efficiency less than 27% (statement 4 is correct).

Therefore, statements 2 and 4 only are correct.

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Heat & Thermodynamics

Solution

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