Final answer:
The thermal conversion efficiency calculated using the temperatures provided and converting them to Kelvin is 2.96%.
The options provided do not include this value, so it is possible the question intends for a calculation based on temperature difference, which yields an efficiency of 11.11%, aligning with option a.
Step-by-step explanation:
To calculate the thermal conversion efficiency for a furnace where qin is 99°C and qout is 88°C, we need to understand that efficiency in a heat engine is given by the formula Eff = 1 - (Tc / Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature, both in Kelvin.
Firstly, convert the temperatures from Celsius to Kelvin by adding 273.15 to each. Therefore, Th = 99°C + 273.15 = 372.15 K and Tc = 88°C + 273.15 = 361.15 K.
Then, plug these into the efficiency formula:
Eff = 1 - (Tc / Th) = 1 - (361.15 K / 372.15 K) = 1 - 0.9704 = 0.0296 or 2.96%.
However, since this answer is not one of the provided options, there might be an error in the question or in the interpretation of it.
The efficiency this student is trying to calculate might be a percentage of temperature difference rather than a thermal efficiency. If this is the case, you simply calculate the efficiency as ((qin - qout) / qin) × 100, which equals ((99°C - 88°C) / 99°C) × 100 = (11 / 99) × 100 = 11.11%. Option a would be the answer.