Figure 4 shows the results of a test on an internal combustion engine which uses purified biogas - AQA - A-Level Physics - Question 3 - 2021 - Paper 6

The thermal efficiency is calculated using the overall efficiency and the mechanical efficiency. Given the calorific value of the biogas, we can derive this as follows:

ext{Thermal Efficiency} = rac{ ext{Overall Efficiency}}{ ext{Fuel Consumption in J/s}}

Using fuel consumption data from Figure 4, we find that fuel consumption at maximum brake power is approximately 0.004 m^3/s. The energy obtained from this quantity of biogas is:

$0.004 ext{ m}^3/s imes 32.3 imes 10^6 ext{ J/m}^3 = 129200 ext{ J/s}$

Thus, the thermal efficiency is:

ext{Thermal Efficiency} = rac{40 ext{ kW}}{129200 ext{ J/s}} = 0.31

This means the thermal efficiency is 31%.

To find the mechanical efficiency, we use the relationship between indicated power and brake power, applying:

ext{Mechanical Efficiency} = rac{ ext{Brake Power}}{ ext{Indicated Power}}

At 4000 rev min^-1, with indicated power at 48 kW and brake power at 40 kW, the mechanical efficiency calculates as:

ext{Mechanical Efficiency} = rac{40}{48} = 0.8333

Hence, the mechanical efficiency is about 83.33%.

Understanding these efficiencies allows engineers to:

1. Optimize engine performance by identifying losses within the engine system.
2. Improve fuel efficiency, leading to cost savings and better environmental outcomes.
3. Design engines that balance power output with thermal and mechanical losses for improved reliability and durability.

Running the engine above 7000 rev min^-1, as indicated in Figure 4, leads to a decrease in brake power and an increase in fuel consumption. This results in reduced efficiency and can potentially cause damage to the engine due to overheating or increased wear, compromising its performance and longevity.