Question

A special engineer may serve as an apprentice in what size maximum vapor boiler plant?

a) 100 hp high or low pressure plant
b) in any plant under direct supervision of the properly licensed engineer
c) 50 horsepower high or low pressure plant

Answer 1

The maximum efficiency of a heat engine is determined using Carnot's efficiency formula, 1 - (Tc/Th). The first engine operating between 450°C and 270°C has a maximum efficiency of 24.9%, and the second engine operating from 270°C to 150°C has 22.1% maximum efficiency. Calculating overall efficiency of the combined engines involves complex thermodynamics.

Step-by-step explanation:

To determine the maximum efficiency of a heat engine, we invoke the Carnot efficiency equation, which is defined as 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir, both in Kelvin. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature.

Efficiency of the First Engine

For the first engine operating between 450°C (723.15K) and 270°C (543.15K), the maximum efficiency can be calculated as follows:

1 - (Tc/Th) = 1 - (543.15/723.15) = 1 - 0.751 = 0.249 or 24.9%.

Efficiency of the Second Engine

For the second engine, which operates between 270°C (543.15K) and 150°C (423.15K), the efficiency is:

1 - (Tc/Th) = 1 - (423.15/543.15) = 1 - 0.779 = 0.221 or 22.1%.

Overall Efficiency

The overall efficiency of both engines cannot be simply summed up, as the calculation involves considering the heat discarded by the first engine and absorbed by the second engine. This requires detailed thermodynamic analysis that invokes concepts like enthalpy and entropy, which are beyond the scope of this response.