Final answer:
The maximum efficiency of an ideal heat engine with an intake temperature of 357.0°C and an exhaust temperature of 27.0°C is calculated to be approximately 52.4%, using the formula for Carnot efficiency which considers the absolute temperatures of the hot and cold reservoirs.
Step-by-step explanation:
The question posed by the student involves calculating the maximum efficiency of an ideal heat engine that operates between two temperatures, specifically an intake temperature of 357.0°C and an exhaust temperature of 27.0°C. To calculate the maximum possible efficiency (Emax) for an ideal, Carnot heat engine, we use the formula:
Emax = 1 - (Tc/Th)
Where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir. Since efficiency is unitless, we need to convert the given temperatures from Celsius to Kelvin by adding 273.15 to each value.
Thus, Th = 357.0 + 273.15 = 630.15 K and Tc = 27.0 + 273.15 = 300.15 K.
Using these values, we calculate the maximum efficiency as follows:
Emax = 1 - (300.15/630.15) ≈ 0.524, or 52.4%
Thus, the maximum efficiency for an ideal heat engine with the given intake and exhaust temperatures is approximately 52.4%.