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A system consists of $2$ kg of carbon dioxide gas initially at state $1,$ where $p_1=\frac{1}{b}ar,T_1=300K.$ The system undergoes a power cycle consisting of the following processes:

Process $1-2$: Constant volume to $p_2=8$ bar.

Process $2-3$: Expansion with $p{v}^{1\mathrm{.}2}=$ constant.

Process $3-1$: Constant$-$pressure compression.

Assuming the ideal gas model and neglecting kinetic and potential energy effects, calculate thermal efficiency.

$=\%$

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