Question

A power plant operates on a regenerative vapor power cycle with one open feedwater heater. Steam enters the first turbine stage at 12 MPa, 560°C and expands to 1 MPa, where some of the steam is extracted and diverted to the open feedwater heater operating at 1 MPa. The remaining steam expands through the second turbine stage to the condenser pressure of 6 kPa. Saturated liquid exits the open feedwater heater at 1 MPa. The net power output for the cycle is 100 MW.

For isentropic processes in the turbines and pumps, determine:
(a) the percent cycle thermal efficiency.
(b) the mass flow rate into the first turbine stage, in kg/s. (c) the rate of entropy production in the open feedwater heater, in kW/K.

Answer 1

The maximum theoretical efficiency of a heat engine operating between temperatures of 300°C (573.15 K) and 27°C (300.15 K) is calculated using the Carnot efficiency formula, yielding approximately 47.63%. Option C is the correct answer.

Step-by-step explanation:

Calculating Maximum Theoretical Efficiency

To identify the maximum theoretical efficiency of a heat engine operating between two temperatures, we utilize the Carnot efficiency formula which is:

Efficiency (EffC) = 1 - (Tc/Th)

where Tc is the absolute temperature of the cold reservoir and Th is the absolute temperature of the hot reservoir. Both temperatures need to be in Kelvin.

Given that the hot reservoir temperature (steam generator output) is 300°C, to convert this to Kelvin we add 273.15, resulting in Th = 573.15 K. Similarly, the cold reservoir temperature (condenser output) is 27°C, which converts to Tc = 300.15 K.

Substituting these values into the efficiency equation, we get:

EffC = 1 - (300.15/573.15)
= 1 - 0.5237
= 0.4763, or 47.63%

The maximum theoretical efficiency of a heat engine operating between temperatures of 300°C and 27°C is therefore approximately 47.63%.