Question

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

Short answer

a. The turbine work output will decrease. b. The amount of heat rejected will increase. c. The cycle efficiency will decrease. d. The moisture content at the turbine exit will increase. e. The amount of heat input will decrease. Answer: Statements b and d are true.

Step-by-step solution

Understand the Rankine cycle process

The Rankine cycle is a heat engine cycle using steam, which undergoes phase changes during its cycle of processes. The cycle consists of four main processes: 1. Isentropic expansion in a turbine 2. Isothermal heat rejection in a condenser 3. Isentropic compression in a pump 4. Isothermal heat addition in a boiler

Analyze the effect of superheating on turbine work output

When steam is superheated to a higher temperature, the enthalpy difference between the steam inlet and outlet of the turbine increases. The work output of the turbine depends on this enthalpy difference. Therefore, as we increase the superheating, the turbine work output will increase. So, statement \((a)\) is false.

Analyze the effect of superheating on heat rejection

The amount of heat rejected is directly related to the amount of heat added in the boiler. When steam is superheated, more heat needs to be added to the boiler as the steam temperature increases. The system will then expel this extra heat during the heat rejection process in the condenser. Therefore, statement \((b)\) is true.

Analyze the effect of superheating on cycle efficiency

The thermal efficiency of the Rankine cycle is given by the following equation: Efficiency = (Turbine Work Output - Pump Work Input) / Heat Input Based on the analysis in Step 2, we know that the turbine work output will increase with superheating. While the heat input will also increase since superheating requires extra heat addition, the ratio of (Turbine Work Output - Pump Work Input) to Heat Input will improve. As a result, statement \((c)\) is false - the cycle efficiency will, in fact, increase due to the superheating.

Analyze the effect of superheating on moisture content at the turbine exit

Superheating increases the temperature of the steam entering the turbine. This means, after expansion in the turbine, the steam will have a higher temperature at the turbine exit than before superheating. The higher the temperature of the steam, the less moisture content it will have at the turbine exit. Therefore, statement \((d)\) is true.

Analyze the effect of superheating on the amount of heat input

As mentioned in Step 4, superheating requires extra heat to increase the temperature of the steam. Thus, the amount of heat input will increase due to superheating, which renders statement \((e)\) as false.

Conclusion

After analyzing each point, we can conclude that: \((a)\) is false - the turbine work output will increase. \((b)\) is true - the amount of heat rejected will decrease. \((c)\) is false - the cycle efficiency will increase. \((d)\) is true - the moisture content at the turbine exit will decrease. \((e)\) is false - the amount of heat input will increase.