Question

The engine of a large ship does 2.00×10⁸ J of work with an efficiency of 5.00%. (a) How much heat transfer occurs to the environment? (b) How many barrels of fuel are consumed, if each barrel produces 6.00×10⁹ J of heat transfer when burned?

a) 1.90×10⁸ J, 0.03 barrels
b) 2.10×10⁸ J, 0.05 barrels
c) 2.30×10⁸ J, 0.07 barrels
d) 2.50×10⁸ J, 0.09 barrels

Answer 1

The total heat transfer to the environment is 3.80×109 J, and the ship's engine consumes 0.667 barrels of fuel.

Step-by-step explanation:

The engine of a large ship does 2.00×108 J of work with an efficiency of 5.00%. First, we will calculate the total energy input based on this efficiency and then determine the heat transfer to the environment. Efficiency (η) is the ratio of work output (W) to the energy input (Qin), so we can write it as η = W/Qin. Rearranging the formula and solving for Qin gives us Qin = W/η. Substituting the given values, we have Qin = (2.00×108 J) / 0.05 = 4.00×109 J. The heat transfer to the environment is the energy input minus work output, which is Qin - W = 4.00×109 J - 2.00×108 J = 3.80×109 J.

Next, we need to calculate how many barrels of fuel are consumed. Each barrel produces 6.00×109 J, so to find the number of barrels (n), we use n = Qin/Ebarrel, where Ebarrel is the energy per barrel. The calculation results in n = 4.00×109 J / 6.00×109 J/barrel = 0.667 barrels.