ThermodynamicsHard
Question
An ideal gas ($\gamma$ = 1.40) is used in a Carnot cycle as a working substance. The efficiency of the cycle, if as a result of an adiabatic expansion the gas volume increases 2.75 times, is [(1.5)2.5 = 2.75]
Options
A.$\frac{100}{3}$%
B.$\frac{200}{3}$%
C.50%
D.25%
Solution
$T_{H}.V_{2}^{\gamma - 1} = T_{C}.V_{3}^{\gamma - 1} \Rightarrow \frac{T_{C}}{T_{M}} = \left( \frac{V_{2}}{V_{3}} \right)^{\gamma - 1} = \left( \frac{1}{2.75} \right)^{1.4 - 1} = \frac{1}{1.5}$
$\therefore\eta = 1 - \frac{T_{C}}{T_{H}} = \frac{1}{3}$
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