Question

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with reheating, \((a)\) the turbine work output will decrease. \((b)\) the amount of heat rejected will decrease. \((c)\) the pump work input will decrease. \((d)\) the moisture content at turbine exit will decrease. \((e)\) the amount of heat input will decrease.

Short answer

Answer: The moisture content at turbine exit will decrease.

Step-by-step solution

Understanding the Reheat Rankine Cycle

Reheating is a process in which the steam exhausted from the high-pressure turbine is heated again in the boiler before entering the low-pressure turbine. Reheating helps to increase the quality of the steam at the turbine exit and to increase the efficiency of the Rankine cycle. It is important to understand how the reheating process affects the various cycle parameters before analyzing the given options.

Analyzing Option (a) - Turbine Work Output

The turbine work output is the difference between the enthalpy of the steam entering the turbine and the enthalpy of the steam leaving the turbine. With the addition of reheating, the enthalpy of steam entering the low-pressure turbine increases, which results in an increase in the difference between the enthalpies. Therefore, the turbine work output will increase, so \((a)\) is incorrect.

Analyzing Option (b) - Heat Rejected

The amount of heat rejected is the difference between the enthalpy of the steam entering and leaving the condenser. With reheating, the quality of steam at the exit of the low-pressure turbine improves, resulting in higher enthalpy. So, the heat rejected will increase, which means \((b)\) is incorrect.

Analyzing Option (c) - Pump Work Input

The pump work input is determined by the difference in enthalpy between the liquid entering the pump and the compressed liquid leaving the pump. Since the boiler and condenser pressures are fixed, and there is no mention of a change in pump efficiency, the pump work input remains the same. So, \((c)\) is incorrect.

Analyzing Option (d) - Moisture Content at Turbine Exit

The moisture content at the turbine exit is generally higher in an ideal Rankine cycle than in a reheat Rankine cycle. Reheating helps to improve the quality of steam at the low-pressure turbine exit, reducing the moisture content. Therefore, \((d)\) is correct.

Analyzing Option (e) - Heat Input

The heat input is the heat added to the steam during the boiler and reheat processes. With reheating, more heat is added to the steam because of the extra reheating process, increasing the enthalpy of the steam entering the low-pressure turbine. So, the heat input will increase, which means \((e)\) is incorrect. In conclusion, the correct answer is: \((d)\) the moisture content at turbine exit will decrease.