Final answer:
The maximum thermal efficiency for an ideal Rankine cycle operating between the given temperature limits is 47.61%, calculated using the Carnot efficiency formula.
Step-by-step explanation:
The question is focused on determining the maximum thermal efficiency of an ideal Rankine cycle with water as the working fluid, which operates between specified pressure limits and has a constraint on the quality of the steam exiting the turbine. The Rankine cycle is a model used to predict the performance of steam turbine systems. It is a thermodynamic cycle that converts heat into work, similar to the Carnot cycle, but with the practicality of using water as the working medium.
To calculate the maximum theoretical efficiency of a heat engine like the Rankine cycle, we use the Carnot efficiency formula, which is Effc = 1 - (Tc/Th), where Effc is the Carnot efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir. Both temperatures must be in kelvins (K).
For the given Rankine cycle, the hot reservoir temperature is the boiling water temperature of 300°C, which is 573K (300 + 273). The cold reservoir temperature is the condenser temperature of 27°C, which is 300K (27 + 273). The Carnot efficiency for the cycle can be calculated as follows:
Effc = 1 - (300K / 573K)
Effc = 1 - 0.5239
Effc = 0.4761 or 47.61%
This represents the maximum theoretical efficiency for a heat engine operating between these two temperatures, assuming the heat engine follows the Carnot cycle which is the most efficient cycle possible. It provides a standard of performance for actual heat engines, which cannot achieve this efficiency due to practical limitations such as friction, and non-ideal heat and fluid flow behaviors.