Final answer:
The high temperature required for a Carnot engine to achieve a 26% efficiency with an exhaust temperature of 300 °C is approximately 773.65 K (500.65 °C).
Step-by-step explanation:
To determine the high temperature required for a Carnot engine to achieve a 26% efficiency with an exhaust temperature of 300 °C, we must first convert the given temperatures from Celsius to Kelvin. The efficiency (η) of a Carnot engine is given by η = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir, both in Kelvin. By rearranging the formula to solve for Th, we get Th = Tc / (1 - η).
To convert the exhaust temperature (300 °C) to Kelvin, we add 273 to the Celsius temperature giving us 573 K. Inserting the values into the formula, we get:
Th = 573 K / (1 - 0.26) = 773.65 K
Therefore, the high temperature needed for the Carnot engine to have a 26% efficiency is approximately 773.65 K (500.65 °C).