Final answer:
The hot reservoir temperature of a Carnot engine can be determined using the formula T₁ = Tc + (Efficiency/100) * (Th - Tc). For a Carnot engine with an efficiency of 30.0% and a cold reservoir temperature of 200°C, the hot reservoir temperature is 868.28 K.
Step-by-step explanation:
The hot reservoir temperature of a Carnot engine can be determined using the formula:
T₁ = Tc + (Efficiency/100) * (Th - Tc)
Where T₁ is the hot reservoir temperature, Tc is the cold reservoir temperature, and Th is the hot reservoir temperature.
For example, in question 28 where the efficiency is 30.0% and the cold reservoir temperature is 200°C:
Convert the temperatures to Kelvin: Tc = 200 + 273.15 = 473.15 K
Use the formula: T₁ = 473.15 + (30.0/100) * (Th - 473.15)
Rearrange the equation and solve for Th: Th = T₁ * (100/(30.0/100)) + 473.15 = 868.28 K
Therefore, the hot reservoir temperature for a Carnot engine with an efficiency of 30.0% and a cold reservoir temperature of 200°C is 868.28 K.