Correct Answer - Option 2 : 26.8%
CONCEPT:
The efficiency of the Carnot cycle (η):
- It is defined as the ratio of net mechanical work done per cycle the gas (W) to the amount of heat energy absorbed per cycle from the source (Q1) i.e.,
\(η = \frac{W}{{{Q_1}}}\;\)
As work is done by the engine per cycle is
W = Q1 – Q2
Where, Q1 = amount of heat energy absorbed per cycle from the source and Q2 = energy absorbed per cycle from the sink.
\( ⇒ η = \frac{{{Q_1} - {Q_2}}}{{{Q_1}}} = 1 - \frac{{{Q_2}}}{{{Q_1}}}\)
As, \(\frac{{{Q_2}}}{{{Q_1}}} = \frac{{{T_2}}}{{{T_1}}}\)
\( ⇒ η = 1 - \frac{{{T_2}}}{{{T_1}}}\)
Where T1 = temperature of the sink and T2 = temperature of the source.
CALCULATION:
Given -
T1 = 100 + 273 = 373 K
T2 = 0 + 273 = 273 K;
Now the efficiency will be
\(η = 1- \frac {273}{373} = 0.26809\)
∴ Efficiency is 26.81 %
