Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?

The correct option is: Increasing the turbine inlet temperature

Let us analyze how increasing the turbine inlet temperature affects the simple ideal Rankine cycle step-by-step:

1. Effect on Thermal Efficiency:
According to the principles of thermodynamics, the thermal efficiency (${\eta }_{\mathrm{th}}$) of a Rankine cycle is generally given by:
${\eta }_{\mathrm{th}}=1-\frac{T_{\text{out}}}{T_{\text{in,avg}}}$
where $T_{\text{in,avg}}$ is the average temperature at which heat is added to the steam in the boiler, and $T_{\text{out}}$ is the temperature at which heat is rejected in the condenser. By increasing the turbine inlet temperature (superheating the steam to a higher temperature at a constant boiler pressure), the average temperature at which heat is added to the cycle ($T_{\text{in,avg}}$) increases while the heat rejection temperature remains constant. As a result, the thermal efficiency of the cycle increases.

2. Effect on Moisture Content at the Turbine Outlet:
When the steam is heated to a higher inlet temperature before entering the turbine, the expansion process (ideally isentropic) on a temperature-entropy (T-s) diagram shifts to the right. Consequently, the state of the steam at the turbine outlet (condenser inlet) moves closer to the saturated vapor line or even into the superheated region. This shift significantly increases the quality (dryness fraction) of the steam at the turbine exit, which directly means a reduction in the moisture content of the steam at the turbine outlet.

Comparison with other options:

• Decreasing the condenser pressure increases the thermal efficiency but shifts the turbine exit state further into the wet region, thereby increasing the moisture content.
• Increasing the boiler pressure increases the thermal efficiency but also shifts the turbine exit state further to the left, which increases the moisture content of the steam.
• Decreasing the boiler pressure reduces the thermal efficiency of the cycle.

Therefore, superheating the steam to a higher turbine inlet temperature is the only modification among the choices that simultaneously increases the thermal efficiency and reduces the moisture content at the turbine outlet.