Problem $2)$ Consider a regenerative vapor power cycle with two feedwater heaters, a closed one and an open one, and reheat. Steam enters the first turbine stage at $\backslash (12\backslash$mathrm$\{$MPa$\},480^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and expands to $2$ MPa $.$ The steam then is reheated at $2$ MPa to $\backslash (440^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ where some steam is extracted at $2$ MPa and fed to the closed feedwater heater. The remainder expands through the second$-$stage turbine to $0\mathrm{.}3$ MPa $,$ where an additional amount is extracted and fed into the open feedwater heater operating at $0\mathrm{.}3$ MPa $.$ The steam expanding through the third$-$stage turbine exits at the condenser pressure of $6$ kPa $.$ The condensate of the closed feedwater heater is $\backslash (2^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ cooler than the other outlet of the closed feedwater heater $($Terminal Temperature Difference $($TTD$)\backslash (=-2^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ))$ and exits at $2$ MPa as saturated liquid to be trapped into the open feedwater heater. Saturated liquid at $0\mathrm{.}3$ MPa leaves the open feedwater heater. Assume all pumps and turbine stages operate isentropically$.$ Determine for the cycle.

a$)$ the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the first$-$stage turbine.

b$)$ the thermal efficiency.

c$)$ the heat transfer from the working fluid passing through the condenser to the cooling water, in $\backslash ($ k J $\backslash )$ per kg of steam entering the first$-$stage turbine.