The heat engine operates from a heater, the absolute temperature of which is n times higher than the absolute

The heat engine operates from a heater, the absolute temperature of which is n times higher than the absolute temperature of the refrigerator. What proportion of the heat received from the heater goes to useful work?

To determine what fraction of the heat received from the heater Qн is spent on the useful work A of the heat engine, we will use the definition of the efficiency of the heat engine: η = A / Qн, then A = η ∙ Qн. On the other hand, to calculate the efficiency of a heat engine, there is a formula: η = (Тн – Тх) / Тн. It is known that a heat engine operates from a heater, the absolute temperature of which Тн is n times higher than the absolute temperature of the refrigerator Тх, that is, Тн = n ∙ Тх. Then η = (n ∙ Тх – Тх) / n ∙ Тх = (n – 1) / n = 1 – 1 / n. We get A = (1 – 1 / n) ∙ Qн.
Answer: А = (1 – 1 / n) ∙ Qн.