$1.$ Consider a simple ideal Rankine Cycle operating between the pressure limits of $10$ kPa and $3$ MPa, with a turbine inlet temperature of $600\backslash$deg C$.$ Determine the thermal efficiency for the following cases:

a$)$ Considering all energies involved, except those related to flow rate and position.

b$)$ Neglecting the work of the pump.

c$)$ The isentropic efficiency of the turbine is $37\%$ and the pump is $75\%.$

d$)$ Superheating the steam to $700\backslash$deg C$.$

e$)$ Increasing the condenser pressure.