Question

A steam turbine operates with 1.6 MPa and 350°C steam at its inlet and saturated vapor at 30°C at its exit. The mass flow rate of the steam is 21.4 kg/s, and the turbine produces 12,350 kW of power. Determine the rate at which heat is lost through the casing of this turbine. The enthalpies are h1 = 3146 kJ/kg and h2 = 2555.6 kJ/kg.

Answer 1

The maximum theoretical efficiency of a heat engine operating between 300°C and 27°C temperatures is approximately 47.63%, calculated using the Carnot efficiency formula which factors in the temperatures in kelvins of both the hot and cold reservoirs.

Step-by-step explanation:

To calculate the maximum theoretical efficiency for a heat engine operating between two temperatures, we can use the Carnot efficiency equation, which is:

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

where Tc is the absolute temperature (in kelvins) of the cold reservoir and Th is the absolute temperature (in kelvins) of the hot reservoir.

Given that the hot reservoir's temperature is 300°C and the cold reservoir (condensed water) is at 27°C, we must first convert these temperatures to kelvins:

• Th = 300°C + 273.15 = 573.15 K
• Tc = 27°C + 273.15 = 300.15 K

Now we can plug these values into the Carnot efficiency equation:

Effc = 1 - (300.15/573.15) = 1 - 0.5237 ≈ 0.4763 or 47.63%

Therefore, the maximum theoretical efficiency of the heat engine is approximately 47.63%.