An outboard motor for a boat is cooled by lake water at 16.0°C and has a compression ratio of 13.3. Assume that the air is a diatomic gas.

a) Calculate the efficiency of the engine's Otto cycle.

b) Using your answer to part (a) and the fact that the efficiency of the Carnot cycle is greater than that of the Otto cycle, calculate the maximum temperature (in °C) of the engine.

To answer the given questions, we need to understand the concepts of thermodynamics and the Otto cycle. Let's break down the steps to find the answers:

a) Calculate the efficiency of the engine's Otto cycle:

1. The efficiency of the Otto cycle can be found using the formula:

Efficiency = 1 - (1 / compression ratio)^(gamma - 1)

where the compression ratio = 13.3 and gamma is the ratio of specific heats for a diatomic gas, which can be approximated as 1.4.

2. Calculate the efficiency using the given values:

Efficiency = 1 - (1 / 13.3)^(1.4 - 1)

b) Calculate the maximum temperature of the engine:

1. The maximum temperature of the engine can be determined by using the Carnot efficiency equation:

Carnot efficiency = 1 - (Tc / Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

2. Rearrange the equation to solve for Th:

Th = Tc / (1 - Carnot efficiency)

3. The Carnot efficiency is greater than the Otto cycle efficiency, so we can substitute the Otto cycle efficiency from part (a) into the Carnot efficiency equation.

Th = Tc / (1 - Otto cycle efficiency)

4. Convert the temperature from Kelvin to Celsius if necessary.

Now, let's calculate the answers:

a) Calculate the efficiency of the engine's Otto cycle:

Efficiency = 1 - (1 / 13.3)^(1.4 - 1)

b) Calculate the maximum temperature of the engine:

Th = Tc / (1 - Otto cycle efficiency)

where the temperature Tc is equal to 16.0°C.

Th = 16.0 / (1 - Otto cycle efficiency)