The efficiency of a thermodynamic cycle $1-2-3- 1 ($see picture$)$ is $20\%$ and for another thermodynamic cycle $1 - 3-4 - 1$ efficiency is equal to $10\%$. Determine the efficiency $\eta ($ in $\%)$ of the thermodynamic cycle $1-2-3-4- 1.$The gas is assumed to be ideal
Diffcult
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$\frac{1}{5}=1-\frac{Q_{L}}{Q_{g}}$
$\Rightarrow Q_{L}=\frac{4}{5} Q_{g}$$\frac{1}{10}=1-{Q_{L}^{\prime}}$
${Q_{L}}$
$Q_{L}^{\prime}=\frac{9}{10} Q_{L}=\frac{36}{50} Q_{g}$
$\eta=1-\frac{Q_{L}^{\prime}}{Q_{g}}=1-\frac{36}{50}=\frac{14}{15}$
$\Rightarrow 28 \%$
$\Rightarrow Q_{L}=\frac{4}{5} Q_{g}$$\frac{1}{10}=1-{Q_{L}^{\prime}}$
${Q_{L}}$
$Q_{L}^{\prime}=\frac{9}{10} Q_{L}=\frac{36}{50} Q_{g}$
$\eta=1-\frac{Q_{L}^{\prime}}{Q_{g}}=1-\frac{36}{50}=\frac{14}{15}$
$\Rightarrow 28 \%$
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