Final answer:
To calculate the parameters for an ideal Rankine cycle, specific formulas involving mass flow rate, enthalpy, and pressure changes are used. Exact values require consulting steam tables for water properties at the given state points as the numerical calculations are based on these properties.
Step-by-step explanation:
Calculating Parameters for an Ideal Rankine Cycle
An ideal Rankine cycle is a theoretical model used to predict the performance of steam turbine systems, which are commonly found in power generation. Since the student's question involves calculations of work, heat input, power output, and thermal efficiency using given temperatures and pressures, these follow established thermodynamic principles. However, as we lack specific enthalpy values for the working fluid (water) at the given state points, exact numerical answers cannot be provided without referring to steam tables or appropriate thermodynamic software. Nevertheless, we can describe the general approach to solving each part of the question.
a. Power required to operate the pump: This can be estimated from the pump work equation, which is the product of the mass flow rate, the specific volume of the fluid at the pump inlet (saturated liquid), and the change in pressure.
b. Heat input to the boiler: This is calculated by multiplying the mass flow rate by the difference in enthalpy between the inlet and outlet of the boiler.
c. Power developed by the turbine: Similar to the boiler, this is the product of mass flow rate and the enthalpy difference across the turbine.
d. Thermal efficiency of the cycle: This can be found from the definition of efficiency, which is the net work output of the cycle divided by the heat input to the boiler. Note that the net work output is the work developed by the turbine minus the work required to operate the pump.
To perform these calculations with accuracy, one would ideally turn to the steam tables to obtain the necessary thermodynamic properties (e.g., specific volume, enthalpy) of water at the provided state points and then apply the formulas for work and efficiency in a Rankine cycle.