The energy input to an engine is 4.00 times greater than the work it performs. What fraction of the energy input is expelled to the cold reservoir?

Explanation

Option A: States that the fraction of the energy input expelled to the cold reservoir is 0.25. However, based on the given information that the energy input is 4.00 times greater than the work performed, the correct fraction is 0.75, not 0.25. Therefore, option (A) is incorrect.Option B: To determine the fraction of the energy input that is expelled to the cold reservoir, we can use the concept of efficiency in thermodynamics. The efficiency (η) of an engine is defined as the ratio of the work output to the energy input. Mathematically, it can be expressed as:η = Work output / Energy inputGiven that the energy input is 4.00 times greater than the work performed, we can write:Energy input = 4 * Work performedSubstituting this into the efficiency equation:η = Work output / (4 * Work performed)We can simplify this equation by canceling out the common factor of work performed:η = 1 / 4So, the efficiency of the engine is 1/4, which means that 1/4 of the energy input is converted into useful work. The remaining fraction (3/4) is expelled to the cold reservoir. Therefore, the correct answer is:B) 0.75Approximately 75% of the energy input is expelled to the cold reservoir.Option C: Option C suggests that the entire energy input is expelled to the cold reservoir, implying an efficiency of 0. This contradicts the given information that the energy input is 4.00 times greater than the work performed. Since there is work being performed, it is not possible for the entire energy input to be expelled. Hence, option C is incorrect.Option D: Option D claims that it is impossible to determine the fraction of the energy input expelled to the cold reservoir. However, based on the given information and the calculation of efficiency, it is possible to determine that the fraction is 0.75. Therefore, option (D) is incorrect.To determine the fraction of the energy input that is expelled to the cold reservoir, we need to consider the efficiency of the engine.