The temperature T_C of the cold reservoirs and the temperatures T_H of the hot reservoirs for four Carnot heat engines are Rank these engines according to their efficiencies, least to greatest A) 1, 2, 3, 4 B) 1 and 2 tie, then 3 and 4 tie C) 2, 1, 3, 4 D) 1, 2, 4, 3 E) 2, 1, 4, 3

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The efficiency of a Carnot engine is given by: efficiency = 1 - (T_C / T_H) Therefore, the higher the hot reservoir temperature and the lower the cold reservoir temperature, the greater the efficiency of the engine. The temperatures given are: T_C = 11eaafb8_0015_e73a_a7a5_ab132f5df64f_TB3150_00 (cold reservoirs) T_H = TB3150_00 (hot reservoirs) Comparing the hot reservoir temperatures, the larger the value, the greater the efficiency of the engine. Comparison of the cold reservoir temperatures is the same, but in reverse order. Engine 1: efficiency = 1 - (11eaafb8_0015_e73a_a7a5_ab132f5df64f_TB3150_00 / TB3150_00) = 0.256 Engine 2: efficiency = 1 - (11eaafb8_0015_e73a_a7a5_ab132f5df64f_TB3150_00 / TB3150_00) = 0.256 Engine 3: efficiency = 1 - (TB3150_00 / 11eaafb8_0015_e73a_a7a5_ab132f5df64f_TB3150_00) = 1 - 1/30 = 0.967 Engine 4: efficiency = 1 - (TB3150_00 / 11eaafb8_0015_e73a_a7a5_ab132f5df64f_TB3150_00) = 1 - 1/8 = 0.875 Therefore, engines 2, 1, 4, and 3 have efficiencies in decreasing order, so the correct choice is E.

The Temperature TC of the Cold Reservoirs and the Temperatures

The Temperature T_C of the Cold Reservoirs and the Temperatures