$1.\backslash (\backslash$left$(20\backslash$right$.\backslash )$ points$)$ A cake of mass $0\mathrm{.}3$ kg is initially at a uniform $($room$)$ temperature of $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and is baked in an oven at $\backslash (200^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The specific heat of the cookie is approximately $\backslash (2\mathrm{.}3\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}^\{*\}\backslash$mathrm$\{$~K$\}\backslash ).$ Determine:

$($a$)(5$ points$)$ The amount of heat transfer to the cake by the time its temperature rises to $\backslash (180^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($b$)(5$ points$)$ The entropy change of the cake in $($a$).$

$($c$)(5$ points$)$ The amount of entropy generated for the cake during this process $($here$,$ consider a boundary temperature associated with the air in the oven$).$

$($d$)(5$ points$)$ Determine the entropy generated when the cake is removed from the oven and left to cool to room temperature.