Question

A steam power plant operates on a Rankine cycle with a high pressure of 2.0 MPa and a boiler exit temperature of 600°C. The heat transfer per mass to the boiler is 3437 kJ/kg. The condenser operates at 60°C and the outlet of the condenser is saturated liquid. All components are ideal except the turbine, which has an isentropic efficiency of 95

Answer 1

The maximum theoretical efficiency of a heat engine operating between 300°C and 27°C temperatures is calculated using the Carnot efficiency formula, which yields an efficiency of 48%.

Step-by-step explanation:

The question is asking about the maximum theoretical efficiency for a heat engine operating between two specific temperatures. To find this, we use the Carnot efficiency formula: Efficiency (Effc) = 1 - (Tc / Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature, both in kelvins. First, we need to convert the given temperatures of 300°C (which is 573K) and 27°C (which is 300K) into kelvins by adding 273.15 to each. Then we apply the formula to calculate the Carnot efficiency.

To find the efficiency of the heat engine, we use the formula:
Efficiency (Effc) = 1 - (Tc / Th) = 1 - (300K / 573K) = 1 - 0.52 = 0.48 or 48%.

This is the maximum theoretical efficiency that the engine can achieve under ideal circumstances, according to the Carnot principle. It is important to note that actual efficiencies will always be lower due to real-world factors like friction, heat losses, and material limitations.