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A scientist says that the efficiency of his heat engine which works at source temperature $127^\circ C$ and sink temperature $27^\circ C$ is 26%, then
A
It is impossible
B
It is possible but less probable
C
It is quite probable
D
Data are incomplete
Detailed Solution
A Carnot engine is an ideal engine, so its efficiency is the maximum possible for any engine working between the same two temperatures (Carnot's theorem).
$T_1 = 127 + 273 = 400$ K, $T_2 = 27 + 273 = 300$ K
$\eta_{max} = \dfrac{T_1 - T_2}{T_1} \times 100 = \dfrac{400 - 300}{400} \times 100 = 25$ percent
The claimed efficiency of 26 percent is more than the maximum possible 25 percent.
Therefore a 26 percent efficient engine is impossible.
$T_1 = 127 + 273 = 400$ K, $T_2 = 27 + 273 = 300$ K
$\eta_{max} = \dfrac{T_1 - T_2}{T_1} \times 100 = \dfrac{400 - 300}{400} \times 100 = 25$ percent
The claimed efficiency of 26 percent is more than the maximum possible 25 percent.
Therefore a 26 percent efficient engine is impossible.