Example $4$:

Carbon Dioxide $\backslash (\backslash$left$(\backslash$mathrm$\{$CO$\}\_\{2\}\backslash$right$)\backslash )$ as an ideal gas executes a Carnot cycle while operating between thermal reservoirs at $\backslash (232^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (38^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The pressures at the initial and final states of the isothermal expansion are $2\mathrm{.}8$ MPa and $1\mathrm{.}4$ MPa $,$ respectively. The specific heat ratio is $1\mathrm{.}24.$ Determine the work and heat transfer for each of the four processes in a Carnot cycle, the thermal efficiency and the pressures at the initial and final states of the isothermal compression?

$($Answer: $38\mathrm{.}4\backslash \%,0\mathrm{.}114$ MPa, $0\mathrm{.}228$ MPa$)$