Question

A ship’s boiler steam comes out at 435 K and pushes through the system, exiting into the condenser, which is kept at 176 K by circulating seawater. What is the ideal efficiency of the ship’s boiler rounded to the nearest thousandth ?

A) 0.404
B) 0.4046
C) 0.595
D) 0.5954

Answer 1

Using the Carnot efficiency formula, the ideal efficiency of the ship's boiler is 0.5954 or 59.5%, which is option D.

Step-by-step explanation:

The ideal efficiency of the ship’s heat engine (boiler) can be calculated using the Carnot efficiency formula, which is ℓ = 1 - (Tc/Th), where ℓ is the efficiency, Tc is the cold reservoir temperature, and Th is the hot reservoir temperature. All temperatures must be in Kelvin for this calculation.

In this scenario, we have Th = 435 K and Tc = 176 K. Applying these values to the Carnot efficiency formula, we get:

ℓ = 1 - (Tc/Th) = 1 - (176 K / 435 K) = 1 - 0.4046 = 0.5954.

Therefore, the ideal efficiency of the ship’s boiler, rounded to the nearest thousandth, is 0.595 or 59.5%, which corresponds to option D) 0.5954.