Question

A gas-turbine power plant operates on the simple brayton cycle between the pressure limits of 100 and 1600 kpa. the working fluid is air, which enters the compressor at 40°c at a rate of 700 m3/min and leaves the turbine at 650°c. assume a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent. use constant specific heats with cv = 0.821 kj/ kg⋅k, cp = 1.108 kj/kg⋅k, and k = 1.35.

Answer 1

The maximum theoretical efficiency of a heat engine operating between 300°C and 27°C is calculated using the Carnot efficiency formula and is found to be 47.62%.

Step-by-step explanation:

To calculate the maximum theoretical efficiency for a heat engine operating between two temperatures, we use the Carnot efficiency formula, which is given by Efficiency (Effc) = 1 - (Tc / Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir, both expressed in kelvins (K).

First, convert the given temperatures from degrees Celsius to kelvins by adding 273.15. Therefore, the hot reservoir temperature Th is 300 °C + 273.15 = 573.15 K, and the cold reservoir temperature Tc is 27 °C + 273.15 = 300.15 K.

Now apply the Carnot efficiency formula:
Effc = 1 - (300.15 / 573.15) = 1 - 0.5238 = 0.4762 or 47.62%.

The maximum theoretical efficiency of the heat engine operating between these temperatures is 47.62%.