Two ideal Carnot thermodynamic engines have the same efficiency.One operates between 5.0 × 10² K and 3.0 × 10² K,and the other between 4.0 × 10² K and some lower temperature.What is the lower temperature?

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by 1 - (T_cold/T_hot). For the first engine, the efficiency is 1 - (300/500) = 0.4. For the second engine, let the lower temperature be T. The efficiency is 1 - (T/400) = 0.4. Solving for T gives T = 240 K.

Two Ideal Carnot Thermodynamic Engines Have the Same Efficiency