Question

A well-insulated turbine operating at steady state develops 25 MW of power for a steam flow rate of 50 kg/s. The steam enters at 15 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in °C.

Answer 1

The maximum theoretical efficiency of a heat engine operating between temperatures of 300°C and 27°C is calculated using the Carnot efficiency formula and is found to be 47.64%.

Step-by-step explanation:

The student asks for the calculation of the maximum theoretical efficiency for a heat engine operating between temperatures of 300°C and 27°C. To find this efficiency, we use the Carnot efficiency formula, which states that the efficiency (ηc) depends on the temperatures of the hot reservoir (Th) and the cold reservoir (Tc) expressed in kelvin (K). The formula is ηc = 1 - Tc/Th.

First, convert the temperatures from °C to K:

• For the hot reservoir, Th = 300°C + 273.15 = 573.15 K
• For the cold reservoir, Tc = 27°C + 273.15 = 300.15 K

Now, calculate the Carnot efficiency:

ηc = 1 - (Tc/Th)
ηc = 1 - (300.15/573.15)
ηc = 1 - 0.5236
ηc = 0.4764 or 47.64%

Therefore, the maximum theoretical efficiency of a heat engine operating between 300°C and 27°C is 47.64%.